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Improving Robust Generalization by Direct PAC-Bayesian Bound MinimizationZifan WangNan DingTomer LevinboimXi ChenRadu SoricutIEEE Conference on Computer Vision and Pattern Recognition
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11 (L) 12 (o) 11 (s) 4 (s) 4 ( ) ] TJ ET Q q 0.1075488 0 0 0.1075488 523.5448 241.1821
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (!) Tj ET Q q 0.1075488 0 0 0.1075488 522.3303 239.999
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (") Tj ET Q 0.8509804 0.8509804
0.8509804 sc 484.5112 499.3463 m 494.2735 485.9954 l 484.5112 472.6445 l 484.5112
479.3199 l 474.7489 479.3199 l 474.7489 492.6708 l 484.5112 492.6708 l h f*
0 0 0 sc q 0.1075488 0 0 0.1075488 330.2712 280.2223 cm BT -0.0016 Tc 58.33333 0 0 58.33333 0 2250
Tm /TT1 1 Tf [ (cl) 2 (e) 1 (a) -3 (n) ] TJ ET Q 0.772549 0.8784314 0.7058824
sc 500.9996 518.0297 m 500.9996 522.9503 504.9886 526.9393 509.9092 526.9393
c 538.484 526.9393 l 543.4046 526.9393 547.3935 522.9503 547.3935 518.0297
c 547.3935 518.0297 l 547.3935 513.1091 543.4046 509.1202 538.484 509.1202
c 509.9092 509.1202 l 504.9886 509.1202 500.9996 513.1091 500.9996 518.0297
c h f* q 0.00003528504 0 0 -0.00003528504 500.9996 526.9393 cm 0 252501.5
m 0 113048.8 113048.6 0 252501 0 c 1062330 0 l 1201782 0 1314831 113048.8
1314831 252501.5 c 1314831 252501.5 l 1314831 391954.2 1201782 505003 1062330
505003 c 252501 505003 l 113048.6 505003 0 391954.2 0 252501.5 c h S Q 0 0
0 sc q 0.1075488 0 0 0.1075488 508.1508 278.7166 cm BT -0.002 Tc 41.66666 0 0 41.66666 0 2250
Tm /TT5 1 Tf (Tr) Tj ET Q q 0.1075488 0 0 0.1075488 512.9121 278.7166 cm BT
-0.0025 Tc 41.66666 0 0 41.66666 0 2250 Tm /TT2 1 Tf [ (ac) -5 (e) -7 ( )
3 (o) 2 (f) -1 ( ) ] TJ ET Q q 0.1075488 0 0 0.1075488 525.1794 278.7166 cm
BT 41.66666 0 0 41.66666 0 2250 Tm /TT5 1 Tf (H) Tj ET Q q 0.1075488 0 0 0.1075488 528.7644 278.7166
cm BT 0.0045 Tc 41.66666 0 0 41.66666 0 2250 Tm /TT2 1 Tf [ (es) 2 (s) 2 (i)
11 (a) 7 (n) 7 ( ) ] TJ ET Q q 0.1075488 0 0 0.1075488 511.7515 271.5108 cm
BT 0.0032 Tc 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (#$) Tj ET Q q 0.1075488 0 0 0.1075488 518.6122 271.5108
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (%) Tj ET Q q 0.1075488 0 0 0.1075488 521.1889 271.5108
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (&) Tj ET Q 1 0 0 sc q 0.1075488 0 0 0.1075488 524.9419 270.0051
cm BT 41.66666 0 0 41.66666 0 2250 Tm /TT7 1 Tf (!) Tj ET Q q 0.1075488 0 0 0.1075488 527.6127 269.0372
cm BT 33.33333 0 0 33.33333 0 2250 Tm /TT9 1 Tf (!) Tj ET Q 0 0 0 sc q 0.1075488 0 0 0.1075488 524.9419 274.1995
cm BT 41.66666 0 0 41.66666 0 2250 Tm /TT7 1 Tf (") Tj ET Q q 0.1075488 0 0 0.1075488 531.07 272.8014
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (!) Tj ET Q q 0.1075488 0 0 0.1075488 529.8555 271.5108
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (") Tj ET Q q 0.1075488 0 0 0.1075488 534.0163 271.5108
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (') Tj ET Q 22225 w 0.2666667
0.4470588 0.7686275 SC q 0 0.00003528504 0.00003528504 0 370.8417 533.8955
cm 0 0 m 68596.13 0 124204.3 9267.884 124204.3 20700.4 c 124204.3 774211.6
l 124204.3 785644.1 179812.4 794912 248408.6 794912 c 179812.4 794912 124204.3
804179.9 124204.3 815612.4 c 124204.3 1569124 l 124204.3 1580556 68596.13
1589824 0 1589824 c S Q q 0.1075488 0 0 0.1075488 386.3195 303.1302 cm BT
58.33333 0 0 58.33333 0 2250 Tm /TT1 1 Tf (w) Tj ET Q q 0.1075488 0 0 0.1075488 390.9486 303.1302
cm BT -0.0026 Tc 58.33333 0 0 58.33333 0 2250 Tm /TT1 1 Tf [ (ei) 2 (g) -4
(h) -4 (t) -4 (s) -2 (:) ] TJ ET Q q 0.1075488 0 0 0.1075488 409.5456 303.1302
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (\() Tj ET Q q 0.1075488 0 0 0.1075488 412.855 301.8396
cm BT 41.66666 0 0 41.66666 0 2250 Tm /TT7 1 Tf (#) Tj ET Q q 0.1075488 0 0 0.1075488 448.9159 303.1302
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT1 1 Tf (w) Tj ET Q q 0.1075488 0 0 0.1075488 453.545 303.1302
cm BT -0.0026 Tc 58.33333 0 0 58.33333 0 2250 Tm /TT1 1 Tf [ (ei) 2 (g) -4
(h) -4 (t) -4 (s) -2 (:) ] TJ ET Q 1 0 0 sc q 0.1075488 0 0 0.1075488 472.142 303.1302
cm BT 58.33333 0 0 58.33333 0 2250 Tm /TT4 1 Tf (\() Tj ET Q q 0.1075488 0 0 0.1075488 475.4514 301.8396
cm BT 41.66666 0 0 41.66666 0 2250 Tm /TT7 1 Tf ($) Tj ET Q q 0 0.00003528504 0.00003528504 0 451.4727 533.8955
cm 0 0 m 68588.14 0 124189.8 9266.415 124189.8 20697.12 c 124189.8 267536.9
l 124189.8 278967.6 179791.5 288234 248379.6 288234 c 179791.5 288234 124189.8
297500.4 124189.8 308931.1 c 124189.8 555770.9 l 124189.8 567201.6 68588.14
576468 0 576468 c S Q 0 0 0 sc q 0.1075488 0 0 0.1075488 521.3753 259.4654
cm BT 75 0 0 75 0 2250 Tm /TT11 1 Tf (!) Tj ET Q 0.8509804 0.8509804 0.8509804
sc 386.0274 481.1546 3.115509 13.82773 re f 0.772549 0.8784314 0.7058824 sc
500.9996 456.6691 m 500.9996 461.5897 504.9886 465.5786 509.9092 465.5786
c 538.484 465.5786 l 543.4046 465.5786 547.3935 461.5897 547.3935 456.6691
c 547.3935 456.6691 l 547.3935 451.7485 543.4046 447.7596 538.484 447.7596
c 509.9092 447.7596 l 504.9886 447.7596 500.9996 451.7485 500.9996 456.6691
c h f* 12700 w 0.1843137 0.3215686 0.5607843 SC q 0.00003528504 0 0 -0.00003528504 500.9996 465.5786
cm 0 252501.5 m 0 113048.8 113048.6 0 252501 0 c 1062330 0 l 1201782 0 1314831
113048.8 1314831 252501.5 c 1314831 252501.5 l 1314831 391954.2 1201782 505003
1062330 505003 c 252501 505003 l 113048.6 505003 0 391954.2 0 252501.5 c h
S Q 0 0 0 sc q 0.1075488 0 0 0.1075488 506.5429 212.7892 cm BT 45.83333 0 0 45.83333 0 2250
Tm /TT13 1 Tf (!) Tj ET Q 515.3223 458.3836 m 515.693 458.3836 l 515.693 453.9044
l 515.3223 453.9044 l h 508.7058 458.3836 m 509.0765 458.3836 l 509.0765 453.9044
l 508.7058 453.9044 l h f* q 0.1075488 0 0 0.1075488 509.6708 212.7892 cm
BT 45.83333 0 0 45.83333 0 2250 Tm /TT13 1 Tf (") Tj ET Q q 0.1075488 0 0 0.1075488 512.2989 211.7137
cm BT 33.33333 0 0 33.33333 0 2250 Tm /TT9 1 Tf (") Tj ET Q q 0.1075488 0 0 0.1075488 516.2872 212.7892
cm BT 45.83333 0 0 45.83333 0 2250 Tm /TT13 1 Tf (!) Tj ET Q q 0.1075488 0 0 0.1075488 517.8557 211.6061
cm BT 33.33333 0 0 33.33333 0 2250 Tm /TT9 1 Tf (#) Tj ET Q q 0.1075488 0 0 0.1075488 517.8557 214.6175
cm BT 33.33333 0 0 33.33333 0 2250 Tm /TT9 1 Tf (#) Tj ET Q q 0.1075488 0 0 0.1075488 522.0119 212.7892
cm BT 45.83333 0 0 45.83333 0 2250 Tm /TT13 1 Tf (#) Tj ET Q q 0.1075488 0 0 0.1075488 526.8046 212.7892
cm BT 45.83333 0 0 45.83333 0 2250 Tm /TT13 1 Tf (!) Tj ET Q 535.0239 458.3836
m 535.3945 458.3836 l 535.3945 453.9044 l 535.0239 453.9044 l h 528.9675 458.3836
m 529.3382 458.3836 l 529.3382 453.9044 l 528.9675 453.9044 l h f* q 0.1075488 0 0 0.1075488 529.9325 212.7892
cm BT 45.83333 0 0 45.83333 0 2250 Tm /TT13 1 Tf (") Tj ET Q q 0.1075488 0 0 0.1075488 532.5607 211.7137
cm BT 33.33333 0 0 33.33333 0 2250 Tm /TT9 1 Tf ($) Tj ET Q q 0.1075488 0 0 0.1075488 535.9888 212.7892
cm BT 45.83333 0 0 45.83333 0 2250 Tm /TT13 1 Tf (!) Tj ET Q q 0.1075488 0 0 0.1075488 537.5573 211.6061
cm BT 33.33333 0 0 33.33333 0 2250 Tm /TT9 1 Tf (#) Tj ET Q q 0.1075488 0 0 0.1075488 537.5573 214.6175
cm BT 33.33333 0 0 33.33333 0 2250 Tm /TT9 1 Tf (#) Tj ET Q q 0.1075488 0 0 0.1075488 521.1612 227.2007
cm BT 75 0 0 75 0 2250 Tm /TT11 1 Tf (!) Tj ET Q Q q 0 0 612 792 re W n BT
8.9664 0 0 8.9664 308.862 416.349 Tm /Ty2 1 Tf [ (Figure) -337 (1.) -573 (W)
80 (e) -337 (propose) -338 (T) 35 (race) -337 (of) -337 (Hessian) -338 (\(T)
35 (rH\)) -337 (re) 15 (gularization) -337 (for) ] TJ ET BT 8.9664 0 0 8.9664 308.862 405.391
Tm /Ty2 1 Tf [ (training) -369 (adv) 15 (ersarially) -368 (rob) 20 (ust) -369
(models.) -666 (In) -369 (addition) -369 (to) -369 (an) -368 (ordinary) ]
TJ ET BT 8.9664 0 0 8.9664 308.862 394.432 Tm /Ty2 1 Tf [ (rob) 20 (ust) -230
(loss) -229 (\(e.g.,) -234 (TRADES) -230 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 8.9664 0 0 8.9664 409.3574 394.432
Tm /Ty2 1 Tf (54) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 418.3238 394.432
Tm /Ty2 1 Tf [ (]\),) -233 (we) -230 (re) 15 (gularize) -230 (the) -229 (T)
35 (rH) -230 (of) -230 (the) -229 (loss) ] TJ ET BT 8.9664 0 0 8.9664 308.862 383.473
Tm /Ty2 1 Tf [ (with) -287 (respect) -287 (to) -287 (the) -288 (weight) 1
(s) -288 (of) -287 (the) -287 (top) -287 (layer) -287 (to) -287 (encourage)
-287 (atness.) ] TJ ET BT 8.9664 0 0 8.9664 308.862 372.514 Tm /Ty2 1 Tf
[ (The) -280 (training) -281 (objecti) 25 (v) 15 (e) -280 (is) -281 (the)
-280 (result) -280 (of) -281 (direct) -280 (P) 92 (A) 40 (C-Bayesian) -280
(bound) ] TJ ET BT 8.9664 0 0 8.9664 308.862 361.555 Tm /Ty2 1 Tf [ (minimization)
-250 (in) -250 (Theorem) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 402.7581 361.555
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 407.2413 361.555
Tm /Ty2 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 308.862 324.241 Tm /Ty2 1 Tf [
(adv) 15 (ersarial) -429 (attacks) -430 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 391.96 324.241
Tm /Ty2 1 Tf (8) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 396.9413 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 401.9226 324.241
Tm /Ty2 1 Tf (20) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 411.8852 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 416.8566 324.241
Tm /Ty2 1 Tf (31) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 426.8192 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 431.8005 324.241
Tm /Ty2 1 Tf (32) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 441.7631 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 446.7444 324.241
Tm /Ty2 1 Tf (36) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 456.707 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 461.6783 324.241
Tm /Ty2 1 Tf (41) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 471.6409 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 476.6222 324.241
Tm /Ty2 1 Tf (46) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 486.5848 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 491.5661 324.241
Tm /Ty2 1 Tf (48) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 501.5287 324.241
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 506.5001 324.241
Tm /Ty2 1 Tf (54) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 516.4627 324.241
Tm /Ty2 1 Tf [ (].) -849 (Im-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 312.286
Tm /Ty2 1 Tf [ (portantly) 65 (,) -323 (Rice) -309 (et) -308 (al.) -309 ([)
] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 397.579 312.286 Tm /Ty2 1 Tf
(38) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 407.5416 312.286 Tm /Ty2 1 Tf
[ (]) -308 (observ) 15 (e) -309 (a) -309 (rob) 20 (ust) -308 (o) 15 (v) 15
(ertting) -309 (phe-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 300.331 Tm /Ty2
1 Tf [ (nomenon,) -393 (referred) -364 (to) -365 (as) -364 (the) ] TJ ET BT
9.9626 0 0 9.9626 426.618 300.331 Tm /Ty6 1 Tf [ (r) 45 (ob) 20 (ust) -364
(g) 10 (ener) 15 (alization) -365 (gap) ] TJ ET BT 9.9626 0 0 9.9626 530.955 300.331
Tm /Ty2 1 Tf [ (,) -393 (in) ] TJ ET BT 9.9626 0 0 9.9626 308.862 288.376
Tm /Ty2 1 Tf [ (which) -347 (a) -347 (rob) 20 (ustly-trained) -347 (classier)
-347 (sho) 25 (ws) -347 (much) -348 (higher) -347 (ac-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 276.421
Tm /Ty2 1 Tf [ (curac) 15 (y) -279 (on) -278 (adv) 15 (ersarial) -279 (e)
15 (xamples) -279 (from) -278 (the) -279 (training) -279 (set,) -286 (com-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 264.465 Tm /Ty2 1 Tf [ (pared) -210 (to)
-209 (lo) 25 (wer) -210 (accurac) 15 (y) -209 (on) -210 (the) -209 (test)
-210 (set.) -296 (Indeed,) -218 (se) 25 (v) 15 (eral) -210 (tech-) ] TJ ET
BT 9.9626 0 0 9.9626 308.862 252.51 Tm /Ty2 1 Tf [ (nical) -339 (approaches)
-340 (ha) 20 (v) 15 (e) -339 (been) -340 (de) 25 (v) 15 (eloped) -339 (that)
-339 (could) -340 (alle) 25 (viate) ] TJ ET BT 9.9626 0 0 9.9626 308.862 240.555
Tm /Ty2 1 Tf [ (this) -365 (o) 15 (v) 15 (ertting) -366 (phenomenon,) -394
(including) ] TJ ET BT 9.9626 0 0 9.9626 470.912 240.555 Tm /Ty8 1 Tf (!)
Tj ET BT 6.9738 0 0 6.9738 475.063 239.061 Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 483.172 240.555
Tm /Ty2 1 Tf [ (weight) -365 (re) 15 (gular) 20 (-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 228.6
Tm /Ty2 1 Tf [ (ization,) -258 (early) -256 (stopping) -257 ([) ] TJ ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 403.706 228.6 Tm /Ty2 1 Tf (38) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 413.6686 228.6 Tm /Ty2 1 Tf [ (],) -258 (label)
-256 (smoothing,) -258 (data) -257 (augmen-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 216.645
Tm /Ty2 1 Tf [ (tation) -250 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 337.365 216.645
Tm /Ty2 1 Tf (51) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 347.3276 216.645
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 351.1134 216.645
Tm /Ty2 1 Tf (53) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 361.076 216.645
Tm /Ty2 1 Tf [ (],) -250 (using) -250 (synthetic) -250 (data) -250 ([) ] TJ
ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 454.3259 216.645 Tm /Ty2 1 Tf (21)
Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 464.2885 216.645 Tm /Ty2 1 Tf [ (])
-250 (and) -250 (etc.) ] TJ ET BT 9.9626 0 0 9.9626 320.817 202.621 Tm /Ty2
1 Tf [ (According) -193 (to) -193 (learning) -193 (theory) 65 (,) -205 (the)
-193 (phenomenon) -193 (of) -193 (o) 15 (v) 15 (ert-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 190.665
Tm /Ty2 1 Tf [ (ting) -197 (can) -197 (be) -196 (characterized) -197 (by)
-197 (a) -197 (P) 92 (A) 40 (C-Bayesian) -196 (bound) -197 ([) ] TJ ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 516.8911 190.665 Tm /Ty2 1 Tf (4) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 521.8724 190.665 Tm /Ty2 1 Tf (,) Tj ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 524.7715 190.665 Tm /Ty2 1 Tf (9) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 529.7528 190.665 Tm /Ty2 1 Tf (,) Tj ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 532.6618 190.665 Tm /Ty2 1 Tf (18) Tj ET
/Cs2 cs 0 sc BT 9.9626 0 0 9.9626 542.6244 190.665 Tm /Ty2 1 Tf (,) Tj ET
/Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 308.862 178.71 Tm /Ty2 1 Tf (34) Tj
ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 318.8246 178.71 Tm /Ty2 1 Tf (,) Tj ET
/Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 322.8196 178.71 Tm /Ty2 1 Tf (42) Tj
ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 332.7822 178.71 Tm /Ty2 1 Tf [ (]) -280
(which) -281 (upper) 20 (-bounds) -281 (the) -281 (e) 15 (xpected) -281 (performance)
-281 (of) -281 (a) ] TJ ET BT 9.9626 0 0 9.9626 308.862 166.755 Tm /Ty2 1
Tf [ (random) -200 (classier) -200 (o) 15 (v) 15 (er) -200 (the) -199 (underlying)
-200 (data) -200 (distrib) 20 (ution) -200 (by) -200 (its) ] TJ ET BT 9.9626 0 0 9.9626 308.862 154.8
Tm /Ty2 1 Tf [ (performance) -261 (on) -260 (a) -261 (nite) -260 (set) -261
(of) -260 (training) -261 (points) -261 (plus) -260 (some) -261 (ad-) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 142.845 Tm /Ty2 1 Tf [ (ditional) -238 (terms.)
-305 (Although) -238 (se) 25 (v) 15 (eral) -238 (prior) -237 (w) 10 (orks)
-238 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 491.2075 142.845 Tm
/Ty2 1 Tf (21) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 501.1701 142.845 Tm
/Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 504.7466 142.845
Tm /Ty2 1 Tf (24) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 514.7092 142.845
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 518.2858 142.845
Tm /Ty2 1 Tf (26) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 528.2484 142.845
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 531.835 142.845
Tm /Ty2 1 Tf (49) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 541.7976 142.845
Tm /Ty2 1 Tf (]) Tj ET BT 9.9626 0 0 9.9626 308.862 130.89 Tm /Ty2 1 Tf [
(ha) 20 (v) 15 (e) -458 (b) 20 (uilt) -458 (upon) -458 (insights) -458 (from)
-458 (the) -459 (P) 92 (A) 40 (C-Bayesian) -458 (bound,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 118.934
Tm /Ty2 1 Tf [ (none) -211 (attempted) -211 (to) -212 (directly) -211 (minimize)
-211 (the) -211 (upper) -212 (bound,) -219 (lik) 10 (ely) ] TJ ET BT 9.9626 0 0 9.9626 308.862 106.979
Tm /Ty2 1 Tf [ (due) -334 (to) -333 (the) -334 (f) 10 (act) -334 (that) -334
(the) -333 (minimization) -334 (of) -334 (their) -333 (forms) -334 (of) -334
(the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 95.024 Tm /Ty2 1 Tf [ (P) 92 (A)
40 (C-Bayesian) -250 (bound) -250 (do) -250 (not) -250 (ha) 20 (v) 15 (e)
-250 (an) -250 (analytical) -250 (solution.) ] TJ ET BT 9.9626 0 0 9.9626 320.817 81
Tm /Ty2 1 Tf [ (In) -368 (this) -368 (paper) 40 (,) -397 (we) -368 (rely)
-368 (on) -368 (a) -368 (dif) 25 (ferent) -368 (form) -368 (of) -368 (the)
-368 (P) 92 (A) 40 (C-) ] TJ ET Q
Q
Q
q
1 0 0 1 0 0 cm
/bRCXeVn-jengqVyQ56D2Yw Do
Q
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(D) Tj ET BT 4.9813 0 0 4.9813 196.609 163.854 Tm /Ty20 1 Tf (m) Tj ET BT
9.9626 0 0 9.9626 204.885 174.231 Tm /Ty7 1 Tf (l) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 208.054 174.231
Tm /Ty12 1 Tf (\(\() Tj 0 Tc ET BT 0.0005 Tc 9.9626 0 0 9.9626 215.802 174.231
Tm /Ty7 1 Tf [ (x,) -167 (y) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 231.166 174.231
Tm /Ty12 1 Tf (\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 235.04 174.231 Tm
/Ty7 1 Tf (,g) Tj 0 Tc ET BT 6.9738 0 0 6.9738 244.22 172.737 Tm /Ty11 1 Tf
(!) Tj ET BT 9.9626 0 0 9.9626 248.727 174.231 Tm /Ty12 1 Tf (\)) Tj ET BT
9.9626 0 0 9.9626 252.602 174.231 Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 50.112 140.776
Tm /Ty2 1 Tf [ (respecti) 25 (v) 15 (ely) -396 (and) ] TJ ET BT 9.9626 0 0 9.9626 120.135 140.776
Tm /Ty7 1 Tf (l) Tj ET BT 9.9626 0 0 9.9626 127.252 140.776 Tm /Ty2 1 Tf [
(denotes) -396 (the) -397 (loss) -396 (function.) -749 (Ideally) 65 (,) -433
(the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 128.821 Tm /Ty2 1 Tf [ (classication)
-390 (error) -390 (of) ] TJ ET BT 9.9626 0 0 9.9626 141.453 128.821 Tm /Ty7
1 Tf (g) Tj ET BT 6.9738 0 0 6.9738 146.205 127.326 Tm /Ty11 1 Tf (!) Tj ET
BT 9.9626 0 0 9.9626 154.599 128.821 Tm /Ty2 1 Tf [ (should) -390 (be) -390
(represented) -390 (by) -391 (the) -390 (0-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 116.866
Tm /Ty2 1 Tf [ (1) -362 (loss) ] TJ ET BT 9.9626 0 0 9.9626 77.804 116.866
Tm /Ty7 1 Tf (l) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 80.973 116.866 Tm /Ty12
1 Tf (\(\() Tj 0 Tc ET BT 0.0005 Tc 9.9626 0 0 9.9626 88.722 116.866 Tm /Ty7
1 Tf [ (x,) -167 (y) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 104.085 116.866 Tm
/Ty12 1 Tf (\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 107.96 116.866 Tm /Ty7
1 Tf (,g) Tj 0 Tc ET BT 6.9738 0 0 6.9738 117.139 115.371 Tm /Ty11 1 Tf (!)
Tj ET BT 0.4859 Tc 9.9626 0 0 9.9626 121.647 116.866 Tm /Ty12 1 Tf (\)=) Tj
0 Tc ET BT 9.9626 0 0 9.9626 142.931 116.866 Tm /Ty17 1 Tf (I) Tj ET BT 9.9626 0 0 9.9626 146.805 116.866
Tm /Ty12 1 Tf ([) Tj ET BT 9.9626 0 0 9.9626 149.573 116.866 Tm /Ty7 1 Tf
(F) Tj ET BT 6.9738 0 0 6.9738 155.979 115.371 Tm /Ty11 1 Tf (!) Tj ET BT
9.9626 0 0 9.9626 160.486 116.866 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 164.361 116.866
Tm /Ty7 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 170.055 116.866 Tm /Ty12 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 178.76 116.866 Tm /Ty14 1 Tf (") Tj ET BT
9.9626 0 0 9.9626 178.76 116.866 Tm /Ty12 1 Tf (=) Tj ET BT 9.9626 0 0 9.9626 191.339 116.866
Tm /Ty7 1 Tf (y) Tj ET BT 9.9626 0 0 9.9626 196.581 116.866 Tm /Ty12 1 Tf
(]) Tj ET BT 9.9626 0 0 9.9626 199.348 116.866 Tm /Ty2 1 Tf [ (.) -645 (Ho)
25 (we) 25 (v) 15 (er) 40 (,) -390 (since) -362 (the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 104.91
Tm /Ty2 1 Tf [ (0-1) -314 (loss) -315 (is) -314 (infeasible) -314 (to) -315
(mi) 1 (nimize) -315 (and) -314 (inferior) -314 (for) -315 (general-) ] TJ
ET BT 9.9626 0 0 9.9626 50.112 92.955 Tm /Ty2 1 Tf [ (ization,) -423 (it)
-388 (is) -388 (common) -388 (to) -388 (use) -388 (surrog) 5 (ate) -388 (losses)
-388 (such) -388 (as) -388 (the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 81 Tm
/Ty2 1 Tf [ (Cross-Entrop) 10 (y) -240 (loss) ] TJ ET BT 0.0002 Tc 9.9626 0 0 9.9626 128.401 81
Tm /Ty12 1 Tf [ (CE\() -1 (\() ] TJ 0 Tc ET BT 0.0005 Tc 9.9626 0 0 9.9626 150.125 81
Tm /Ty7 1 Tf [ (x,) -167 (y) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 165.489 81
Tm /Ty12 1 Tf (\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 169.363 81 Tm /Ty7
1 Tf (,g) Tj 0 Tc ET BT 6.9738 0 0 6.9738 178.543 79.506 Tm /Ty11 1 Tf (!)
Tj ET BT 0.2789 Tc 9.9626 0 0 9.9626 183.05 81 Tm /Ty12 1 Tf (\)=) Tj 0 Tc
ET BT 9.9626 0 0 9.9626 200.208 81 Tm /Ty14 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 209.617 81
Tm /Ty12 1 Tf [ (l) -0.8 (og) ] TJ ET BT 9.9626 0 0 9.9626 222.486 81 Tm /Ty13
1 Tf ({) Tj ET BT 9.9626 0 0 9.9626 227.467 81 Tm /Ty7 1 Tf (s) Tj ET BT 9.9626 0 0 9.9626 232.137 81
Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 236.011 81 Tm /Ty7 1 Tf (g)
Tj ET BT 6.9738 0 0 6.9738 240.763 79.506 Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 245.271 81
Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 249.145 81 Tm /Ty7 1 Tf (x)
Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 254.839 81 Tm /Ty12 1 Tf (\)\)) Tj 0
Tc ET BT 9.9626 0 0 9.9626 262.588 81 Tm /Ty13 1 Tf (}) Tj ET BT 6.9738 0 0 6.9738 267.569 79.506
Tm /Ty10 1 Tf (y) Tj ET BT 9.9626 0 0 9.9626 274.746 81 Tm /Ty2 1 Tf (for)
Tj ET BT 9.9626 0 0 9.9626 308.862 710.037 Tm /Ty2 1 Tf [ (training) -405
(instead,) -444 (where) ] TJ ET BT 9.9626 0 0 9.9626 407.399 710.037 Tm /Ty13
1 Tf ({) Tj ET BT 9.9626 0 0 9.9626 412.38 710.037 Tm /Ty7 1 Tf (v) Tj ET
BT 9.9626 0 0 9.9626 417.567 710.037 Tm /Ty13 1 Tf (}) Tj ET BT 6.9738 0 0 6.9738 422.548 708.543
Tm /Ty10 1 Tf (j) Tj ET BT 9.9626 0 0 9.9626 430.781 710.037 Tm /Ty2 1 Tf
[ (denotes) -405 (the) ] TJ ET BT 9.9626 0 0 9.9626 481.461 710.037 Tm /Ty7
1 Tf (j) Tj ET BT 9.9626 0 0 9.9626 486.134 710.037 Tm /Ty2 1 Tf [ (-th) -405
(element) -405 (of) ] TJ ET BT 9.9626 0 0 9.9626 308.862 698.082 Tm /Ty2 1
Tf [ (the) -429 (v) 15 (ector) ] TJ ET BT 9.9626 0 0 9.9626 354.326 698.082
Tm /Ty7 1 Tf (v) Tj ET BT 9.9626 0 0 9.9626 359.513 698.082 Tm /Ty2 1 Tf [
(.) -846 (Finally) 65 (,) -474 (we) -428 (denote) -429 (the) -429 (KL-di)
25 (v) 15 (er) 18 (gence) -429 (be-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 686.127
Tm /Ty2 1 Tf [ (tween) -254 (tw) 10 (o) -254 (distrib) 20 (utions) ] TJ ET
BT 9.9626 0 0 9.9626 404.712 686.127 Tm /Ty13 1 Tf (P) Tj ET BT 9.9626 0 0 9.9626 412.461 686.127
Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 416.889 686.127 Tm /Ty13 1 Tf
(Q) Tj ET BT 9.9626 0 0 9.9626 427.556 686.127 Tm /Ty2 1 Tf (as) Tj ET BT
9.9626 0 0 9.9626 438.385 686.127 Tm /Ty12 1 Tf [ (K) -0.8 (L\() ] TJ ET BT
0.0826 Tc 9.9626 0 0 9.9626 456.235 686.127 Tm /Ty13 1 Tf [ (P|) 82 (|) 82
(Q) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 477.655 686.127 Tm /Ty12 1 Tf (\)) Tj
ET BT 9.9626 0 0 9.9626 481.529 686.127 Tm /Ty2 1 Tf [ (.) -322 (F) 15 (or)
-254 (an) 15 (y) -254 (twice-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 674.172
Tm /Ty2 1 Tf [ (dif) 25 (ferentiable) -308 (function) ] TJ ET BT 9.9626 0 0 9.9626 401.627 674.172
Tm /Ty7 1 Tf (L) Tj ET BT 9.9626 0 0 9.9626 408.407 674.172 Tm /Ty2 1 Tf [
(,) -323 (we) -308 (denote) -308 (its) -308 (Jacobian) -309 (and) -308 (Hes-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 662.217 Tm /Ty2 1 Tf [ (sian) -250 (matrix)
-250 (as) ] TJ ET BT 9.9626 0 0 9.9626 366.694 662.217 Tm /Ty22 1 Tf (!) Tj
ET BT 9.9626 0 0 9.9626 373.89 662.217 Tm /Ty7 1 Tf (L) Tj ET BT 9.9626 0 0 9.9626 383.16 662.217
Tm /Ty2 1 Tf (and) Tj ET BT 9.9626 0 0 9.9626 400.037 662.217 Tm /Ty22 1 Tf
(!) Tj ET BT 6.9738 0 0 6.9738 407.232 665.832 Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 411.702 662.217
Tm /Ty7 1 Tf (L) Tj ET BT 9.9626 0 0 9.9626 420.972 662.217 Tm /Ty2 1 Tf [
(respecti) 25 (v) 15 (ely) 65 (.) ] TJ ET BT 10.9589 0 0 10.9589 308.862 641.754
Tm /Ty1 1 Tf [ (2.1.) -250 (Adv) 10 (ersarial) -250 (Rob) 20 (ustness) ] TJ
ET BT 9.9626 0 0 9.9626 320.817 623.642 Tm /Ty2 1 Tf [ (The) -243 (goal) -242
(of) ] TJ ET BT 9.9626 0 0 9.9626 369.011 623.642 Tm /Ty6 1 Tf [ (adver) 10
(sarial) -242 (r) 45 (ob) 20 (ustness) ] TJ ET BT 9.9626 0 0 9.9626 461.652 623.642
Tm /Ty2 1 Tf [ (is) -242 (to) -243 (train) -242 (a) -243 (deep) -242 (net-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 611.687 Tm /Ty2 1 Tf [ (w) 10 (ork) -258
(that) -258 (is) -258 (rob) 20 (ust) -258 (ag) 5 (ainst) ] TJ ET BT 9.9626 0 0 9.9626 416.561 611.687
Tm /Ty8 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 420.712 610.193 Tm /Ty10 1 Tf
(p) Tj ET BT 9.9626 0 0 9.9626 427.888 611.687 Tm /Ty2 1 Tf [ (norm-bounded)
-258 (noises.) -334 (In) -258 (this) ] TJ ET BT 9.9626 0 0 9.9626 308.862 599.732
Tm /Ty2 1 Tf [ (case,) -445 (the) -405 (test) -406 (and) -406 (training) -406
(loss) -405 (functions) -406 (are) -406 (replaced) -406 (by) ] TJ ET BT 9.9626 0 0 9.9626 308.862 587.777
Tm /Ty2 1 Tf [ (their) -381 (respecti) 25 (v) 15 (e) -381 (rob) 20 (ust) -381
(counterparts) -380 ] TJ ET BT 9.9626 0 0 9.9626 465.02 587.777 Tm /Ty7
1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 472.661 587.777 Tm /Ty12 1 Tf (\() Tj
ET BT 0.0284 Tc 9.9626 0 0 9.9626 476.536 587.777 Tm /Ty8 1 Tf (") Tj /Ty7
1 Tf (,) Tj 0 Tc ET BT 9.9626 0 0 9.9626 485.917 587.777 Tm /Ty13 1 Tf (D)
Tj ET BT 9.9626 0 0 9.9626 493.879 587.777 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 501.548 587.777
Tm /Ty2 1 Tf [ (on) -381 (the) -381 (test) ] TJ ET BT 9.9626 0 0 9.9626 308.862 575.822
Tm /Ty2 1 Tf [ (set) -250 (and) ] TJ ET BT 9.9626 0 0 9.9626 341.458 578.34
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 339.298 575.822 Tm /Ty7 1 Tf
(R) Tj ET BT 9.9626 0 0 9.9626 346.939 575.822 Tm /Ty12 1 Tf (\() Tj ET BT
0.0284 Tc 9.9626 0 0 9.9626 350.813 575.822 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf
[ (,) -139 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 368.72 579.437 Tm /Ty10 1
Tf (m) Tj ET BT 9.9626 0 0 9.9626 376.288 575.822 Tm /Ty12 1 Tf (\)) Tj ET
BT 9.9626 0 0 9.9626 382.653 575.822 Tm /Ty2 1 Tf [ (on) -250 (the) -250 (training)
-250 (set,) -250 (such) -250 (that) ] TJ ET BT 9.9626 0 0 9.9626 335.348 551.973
Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 342.989 551.973 Tm /Ty12 1 Tf
(\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 346.864 551.973 Tm /Ty8 1 Tf (")
Tj /Ty7 1 Tf (,) Tj 0 Tc ET BT 9.9626 0 0 9.9626 356.245 551.973 Tm /Ty13
1 Tf (D) Tj ET BT 9.9626 0 0 9.9626 364.207 551.973 Tm /Ty12 1 Tf (\)) Tj
ET BT 4.9813 0 0 4.9813 371.543 557.62 Tm /Ty2 1 Tf (def) Tj ET BT 9.9626 0 0 9.9626 370.849 551.973
Tm /Ty12 1 Tf (=) Tj ET BT 9.9626 0 0 9.9626 381.365 551.973 Tm /Ty17 1 Tf
(E) Tj ET BT 6.9738 0 0 6.9738 388.007 550.174 Tm /Ty9 1 Tf (\() Tj ET BT
0.0008 Tc 6.9738 0 0 6.9738 391.12 550.174 Tm /Ty10 1 Tf [ (x,) 1 (y) ] TJ
0 Tc ET BT 6.9738 0 0 6.9738 402.295 550.174 Tm /Ty9 1 Tf (\)) Tj ET BT 0.0009
Tc 6.9738 0 0 6.9738 405.408 550.174 Tm /Ty16 1 Tf (") Tj /Ty15 1 Tf (D) Tj
0 Tc ET BT 9.9626 0 0 9.9626 424.474 551.973 Tm /Ty12 1 Tf [ (m) -0.3 (ax)
] TJ ET BT 0.0003 Tc 6.9738 0 0 6.9738 420.211 545.082 Tm /Ty15 1 Tf (||)
Tj 0 Tc ET BT 6.9738 0 0 6.9738 424.943 545.082 Tm /Ty11 1 Tf (") Tj ET BT
0.0003 Tc 6.9738 0 0 6.9738 428.263 545.082 Tm /Ty15 1 Tf (||) Tj 0 Tc ET
BT 4.9813 0 0 4.9813 432.996 544.086 Tm /Ty20 1 Tf (p) Tj ET BT 6.9738 0 0 6.9738 437.178 545.082
Tm /Ty16 1 Tf ($) Tj ET BT 6.9738 0 0 6.9738 443.405 545.082 Tm /Ty11 1 Tf
(#) Tj ET BT 9.9626 0 0 9.9626 448.94 551.973 Tm /Ty7 1 Tf (l) Tj ET BT 0.0009
Tc 9.9626 0 0 9.9626 452.108 551.973 Tm /Ty12 1 Tf (\(\() Tj 0 Tc ET BT 9.9626 0 0 9.9626 459.857 551.973
Tm /Ty7 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 467.765 551.973 Tm /Ty12 1 Tf
(+) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 477.727 551.973 Tm /Ty8 1 Tf (#)
Tj /Ty7 1 Tf [ (,) -167 (y) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 491.441 551.973
Tm /Ty12 1 Tf (\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 495.315 551.973 Tm
/Ty7 1 Tf (,g) Tj 0 Tc ET BT 6.9738 0 0 6.9738 504.495 550.478 Tm /Ty11 1
Tf (!) Tj ET BT 9.9626 0 0 9.9626 509.002 551.973 Tm /Ty12 1 Tf (\)) Tj ET
BT 9.9626 0 0 9.9626 512.877 551.973 Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 318.471 521.684
Tm /Ty2 1 Tf (and) Tj ET BT 9.9626 0 0 9.9626 337.508 524.202 Tm /Ty12 1 Tf
Tj ET BT 9.9626 0 0 9.9626 335.348 521.684 Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 342.989 521.684
Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 346.864 521.684 Tm
/Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 364.77 525.797
Tm /Ty10 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 372.338 521.684 Tm /Ty12 1 Tf
(\)) Tj ET BT 4.9813 0 0 4.9813 379.674 527.331 Tm /Ty2 1 Tf (def) Tj ET BT
9.9626 0 0 9.9626 378.98 521.684 Tm /Ty12 1 Tf (=) Tj ET BT 9.9626 0 0 9.9626 392.574 528.423
Tm /Ty12 1 Tf (1) Tj ET q 1 0 0 1 390.691 524.174 cm 0 0 m 8.747 0 l S Q BT
9.9626 0 0 9.9626 390.691 514.85 Tm /Ty7 1 Tf (m) Tj ET BT 6.9738 0 0 6.9738 416.817 534.137
Tm /Ty10 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 413.156 531.148 Tm /Ty19 1 Tf
(!) Tj ET BT 6.9738 0 0 6.9738 402.295 509.313 Tm /Ty9 1 Tf (\() Tj ET BT
0.0008 Tc 6.9738 0 0 6.9738 405.408 509.313 Tm /Ty10 1 Tf [ (x,) 1 (y) ] TJ
0 Tc ET BT 6.9738 0 0 6.9738 416.582 509.313 Tm /Ty9 1 Tf (\)) Tj ET BT 6.9738 0 0 6.9738 419.696 509.313
Tm /Ty16 1 Tf (#) Tj ET BT 6.9738 0 0 6.9738 425.065 509.313 Tm /Ty10 1 Tf
(D) Tj ET BT 4.9813 0 0 4.9813 431.793 511.306 Tm /Ty20 1 Tf (m) Tj ET BT
9.9626 0 0 9.9626 444.332 521.684 Tm /Ty12 1 Tf [ (m) -0.3 (ax) ] TJ ET BT
0.0003 Tc 6.9738 0 0 6.9738 440.069 514.793 Tm /Ty15 1 Tf (||) Tj 0 Tc ET
BT 6.9738 0 0 6.9738 444.801 514.793 Tm /Ty11 1 Tf (") Tj ET BT 0.0003 Tc
6.9738 0 0 6.9738 448.122 514.793 Tm /Ty15 1 Tf (||) Tj 0 Tc ET BT 4.9813 0 0 4.9813 452.854 513.797
Tm /Ty20 1 Tf (p) Tj ET BT 6.9738 0 0 6.9738 457.037 514.793 Tm /Ty16 1 Tf
($) Tj ET BT 6.9738 0 0 6.9738 463.263 514.793 Tm /Ty11 1 Tf (#) Tj ET BT
9.9626 0 0 9.9626 468.798 521.684 Tm /Ty7 1 Tf (l) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 471.967 521.684
Tm /Ty12 1 Tf (\(\() Tj 0 Tc ET BT 9.9626 0 0 9.9626 479.715 521.684 Tm /Ty7
1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 487.623 521.684 Tm /Ty12 1 Tf (+) Tj ET
BT 0.0009 Tc 9.9626 0 0 9.9626 497.586 521.684 Tm /Ty8 1 Tf (#) Tj /Ty7 1
Tf [ (,) -167 (y) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 511.299 521.684 Tm /Ty12
1 Tf (\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 515.174 521.684 Tm /Ty7 1 Tf
(,g) Tj 0 Tc ET BT 6.9738 0 0 6.9738 524.353 520.189 Tm /Ty11 1 Tf (!) Tj
ET BT 9.9626 0 0 9.9626 528.861 521.684 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 532.735 521.684
Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 308.862 488.338 Tm /Ty2 1 Tf (where)
Tj ET BT 9.9626 0 0 9.9626 336.963 488.338 Tm /Ty8 1 Tf ($) Tj ET BT 9.9626 0 0 9.9626 345.53 488.338
Tm /Ty2 1 Tf [ (is) -378 (the) -377 (maximum) -378 (noise) -378 (b) 20 (udget.)
-693 (V) 111 (ari) 1 (ou) -1 (s) -377 (methods) ] TJ ET BT 9.9626 0 0 9.9626 308.862 476.383
Tm /Ty2 1 Tf [ (ha) 20 (v) 15 (e) -334 (been) -335 (proposed) -334 (to) -334
(impro) 15 (v) 15 (e) -335 (adv) 15 (ersarial) -334 (rob) 20 (ustness.) -563
(In) ] TJ ET BT 9.9626 0 0 9.9626 308.862 464.428 Tm /Ty2 1 Tf [ (this) -320
(paper) 40 (,) -338 (we) -321 (focus) -320 (on) -320 (the) -321 (follo) 25
(wing) -320 (tw) 10 (o) -320 (well-kno) 25 (wn) -321 (de-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 452.472
Tm /Ty2 1 Tf (fenses:) Tj ET BT 9.9626 0 0 9.9626 339.717 452.472 Tm /Ty6
1 Tf [ (adver) 10 (sarial) -255 (tr) 15 (aining) ] TJ ET BT 9.9626 0 0 9.9626 422.597 452.472
Tm /Ty2 1 Tf ([) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 425.9145 452.472
Tm /Ty2 1 Tf (32) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 435.8771 452.472
Tm /Ty2 1 Tf [ (],) -256 (denote) -255 (A) 111 (T) -255 (\(Denition) ] TJ
ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 534.3176 452.472 Tm /Ty2 1 Tf (1)
Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 539.2989 452.472 Tm /Ty2 1 Tf (\),)
Tj ET BT 9.9626 0 0 9.9626 308.862 440.517 Tm /Ty2 1 Tf [ (and) -269 (TRADES)
-270 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 370.6799 440.517 Tm
/Ty2 1 Tf (54) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 380.6425 440.517 Tm
/Ty2 1 Tf [ (]) -269 (\(Denition) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 433.0458 440.517
Tm /Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 438.0271 440.517
Tm /Ty2 1 Tf [ (\).) -368 (A) 111 (T) -269 (is) -269 (a) -269 (classical)
-270 (method) ] TJ ET BT 9.9626 0 0 9.9626 308.862 428.562 Tm /Ty2 1 Tf [
(in) -293 (enforcing) -292 (rob) 20 (ustness;) -315 (while) -292 (TRADES)
-293 (achie) 25 (v) 15 (es) -293 (state-of-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 416.607
Tm /Ty2 1 Tf [ (the-art) -250 (rob) 20 (ust) -250 (accurac) 15 (y) -250 (on)
-250 (CIF) 74 (AR-10) -250 (and) -250 (ImageNet) -250 ([) ] TJ ET /Cs1 cs
0 1 0 sc BT 9.9626 0 0 9.9626 521.0853 416.607 Tm /Ty2 1 Tf (21) Tj ET /Cs2
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Tm /Ty1 1 Tf [ (Denition) -250 (1) -250 (\(Adv) 10 (ersarial) -250 (T) 74
(raining) -250 (\(A) 95 (T\)) -250 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 481.7031 393.794
Tm /Ty1 1 Tf (32) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 491.6657 393.794
Tm /Ty1 1 Tf (]\)) Tj ET BT 9.9626 0 0 9.9626 503.281 393.794 Tm /Ty6 1 Tf
[ (Given) -1311 (a) ] TJ ET BT 9.9626 0 0 9.9626 308.862 381.838 Tm /Ty6 1
Tf [ (network) -378 (with) -378 (par) 15 (ameter) ] TJ ET BT 9.9626 0 0 9.9626 410.773 381.838
Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 415.727 381.838 Tm /Ty6 1 Tf [
(,) -410 (a) -378 (tr) 15 (aining) -377 (set) ] TJ ET BT 9.9626 0 0 9.9626 481.601 381.838
Tm /Ty7 1 Tf (D) Tj ET BT 6.9738 0 0 6.9738 490.126 385.454 Tm /Ty10 1 Tf
(m) Tj ET BT 9.9626 0 0 9.9626 497.694 381.838 Tm /Ty6 1 Tf [ (,) -410 (the)
-378 (bound) ] TJ ET BT 9.9626 0 0 9.9626 308.862 369.883 Tm /Ty6 1 Tf [ (of)
-418 (noise) ] TJ ET BT 9.9626 0 0 9.9626 345.977 369.883 Tm /Ty8 1 Tf ($)
Tj ET BT 9.9626 0 0 9.9626 354.948 369.883 Tm /Ty6 1 Tf [ (and) -418 (norm)
] TJ ET BT 0.0008 Tc 9.9626 0 0 9.9626 399.256 369.883 Tm /Ty13 1 Tf [ (||)
-347 -347 (||) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 420.003 368.389 Tm /Ty10
1 Tf (p) Tj ET BT 9.9626 0 0 9.9626 424.608 369.883 Tm /Ty6 1 Tf [ (,) -460
(A) 37 (T) -418 (minimizes) -418 (the) -419 (following) ] TJ ET BT 9.9626 0 0 9.9626 308.862 357.928
Tm /Ty6 1 Tf [ (objective) -250 (w) 74 (.r) 111 (.t) ] TJ ET BT 9.9626 0 0 9.9626 366.236 357.928
Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 371.19 357.928 Tm /Ty6 1 Tf (,)
Tj ET BT 9.9626 0 0 9.9626 319.272 333.912 Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 317.111 331.394
Tm /Ty7 1 Tf (R) Tj ET BT 6.9738 0 0 6.9738 324.676 329.899 Tm /Ty23 1 Tf
(AT) Tj ET BT 9.9626 0 0 9.9626 333.543 331.394 Tm /Ty12 1 Tf (\() Tj ET BT
0.0284 Tc 9.9626 0 0 9.9626 337.417 331.394 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf
[ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 355.324 335.507 Tm /Ty10
1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 362.891 331.394 Tm /Ty12 1 Tf (\)) Tj
ET BT 4.9813 0 0 4.9813 370.364 337.184 Tm /Ty6 1 Tf (def) Tj ET BT 9.9626 0 0 9.9626 369.533 331.394
Tm /Ty12 1 Tf (=) Tj ET BT 9.9626 0 0 9.9626 383.128 338.133 Tm /Ty12 1 Tf
(1) Tj ET q 1 0 0 1 381.245 333.884 cm 0 0 m 8.747 0 l S Q BT 9.9626 0 0 9.9626 381.245 324.56
Tm /Ty7 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 403.709 340.858 Tm /Ty19 1 Tf
(!) Tj ET BT 6.9738 0 0 6.9738 392.848 319.023 Tm /Ty9 1 Tf (\() Tj ET BT
0.0008 Tc 6.9738 0 0 6.9738 395.961 319.023 Tm /Ty10 1 Tf [ (x,) 1 (y) ] TJ
0 Tc ET BT 6.9738 0 0 6.9738 407.136 319.023 Tm /Ty9 1 Tf (\)) Tj ET BT 6.9738 0 0 6.9738 410.249 319.023
Tm /Ty16 1 Tf (#) Tj ET BT 6.9738 0 0 6.9738 415.618 319.023 Tm /Ty10 1 Tf
(D) Tj ET BT 4.9813 0 0 4.9813 422.346 321.016 Tm /Ty20 1 Tf (m) Tj ET BT
9.9626 0 0 9.9626 434.886 331.394 Tm /Ty12 1 Tf [ (m) -0.3 (ax) ] TJ ET BT
0.0003 Tc 6.9738 0 0 6.9738 430.622 324.503 Tm /Ty15 1 Tf (||) Tj 0 Tc ET
BT 6.9738 0 0 6.9738 435.354 324.503 Tm /Ty11 1 Tf (") Tj ET BT 0.0003 Tc
6.9738 0 0 6.9738 438.675 324.503 Tm /Ty15 1 Tf (||) Tj 0 Tc ET BT 4.9813 0 0 4.9813 443.407 323.507
Tm /Ty20 1 Tf (p) Tj ET BT 6.9738 0 0 6.9738 447.59 324.503 Tm /Ty16 1 Tf
($) Tj ET BT 6.9738 0 0 6.9738 453.817 324.503 Tm /Ty11 1 Tf (#) Tj ET BT
0.0002 Tc 9.9626 0 0 9.9626 459.351 331.394 Tm /Ty12 1 Tf [ (CE\() -1 (\()
] TJ 0 Tc ET BT 9.9626 0 0 9.9626 481.075 331.394 Tm /Ty7 1 Tf (x) Tj ET BT
9.9626 0 0 9.9626 488.983 331.394 Tm /Ty12 1 Tf (+) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 498.946 331.394
Tm /Ty8 1 Tf (#) Tj /Ty7 1 Tf [ (,) -167 (y) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 512.659 331.394
Tm /Ty12 1 Tf (\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 516.534 331.394 Tm
/Ty7 1 Tf (,g) Tj 0 Tc ET BT 6.9738 0 0 6.9738 525.713 329.899 Tm /Ty11 1
Tf (!) Tj ET BT 9.9626 0 0 9.9626 530.221 331.394 Tm /Ty12 1 Tf (\)) Tj ET
BT 9.9626 0 0 9.9626 534.095 331.394 Tm /Ty7 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 308.862 297.869
Tm /Ty2 1 Tf [ (which) -390 (considers) -390 (the) -390 (adv) 15 (ersarial)
-391 (sample) ] TJ ET BT 9.9626 0 0 9.9626 474.228 297.869 Tm /Ty7 1 Tf (x)
Tj ET BT 9.9626 0 0 9.9626 483.17 297.869 Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 494.167 297.869
Tm /Ty8 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 502.098 297.869 Tm /Ty2 1 Tf [
(in) -390 (a) ] TJ ET BT 9.9626 0 0 9.9626 522.046 297.869 Tm /Ty8 1 Tf ($)
Tj ET BT 9.9626 0 0 9.9626 526.851 297.869 Tm /Ty2 1 Tf (-ball) Tj ET BT 9.9626 0 0 9.9626 308.862 285.914
Tm /Ty2 1 Tf [ (around) -250 (each) -250 (input,) -250 (instead) -250 (of)
-250 (the) -250 (input) -250 (itself.) ] TJ ET BT 9.9626 0 0 9.9626 308.862 263.1
Tm /Ty1 1 Tf [ (Denition) -250 (2) -250 (\(TRADES) -250 ([) ] TJ ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 410.4307 263.1 Tm /Ty1 1 Tf (54) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 420.3933 263.1 Tm /Ty1 1 Tf (]\)) Tj ET BT 9.9626 0 0 9.9626 432.009 263.1
Tm /Ty6 1 Tf [ (Given) -248 (the) -247 (same) -248 (assumptions) ] TJ ET BT
9.9626 0 0 9.9626 308.862 251.145 Tm /Ty6 1 Tf [ (as) -273 (in) -272 (Denition)
] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 373.4695 251.145 Tm /Ty6 1 Tf
(1) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 378.4508 251.145 Tm /Ty6 1 Tf
[ (,) -278 (TRADES) -272 (minimizes) -273 (the) -272 (following) -273 (objec-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 239.19 Tm /Ty6 1 Tf [ (tive) -250 (w)
74 (.r) 111 (.t) ] TJ ET BT 9.9626 0 0 9.9626 344.657 239.19 Tm /Ty8 1 Tf
(") Tj ET BT 9.9626 0 0 9.9626 349.611 239.19 Tm /Ty6 1 Tf (:) Tj ET BT 9.9626 0 0 9.9626 329.355 217.052
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 327.195 214.534 Tm /Ty7 1 Tf
(R) Tj ET BT 6.9738 0 0 6.9738 334.759 213.039 Tm /Ty23 1 Tf (T) Tj ET BT
9.9626 0 0 9.9626 339.442 214.534 Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 343.316 214.534
Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 361.223 218.647
Tm /Ty10 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 368.79 214.534 Tm /Ty12 1 Tf
(\)) Tj ET BT 4.9813 0 0 4.9813 376.263 220.324 Tm /Ty6 1 Tf (def) Tj ET BT
9.9626 0 0 9.9626 375.432 214.534 Tm /Ty12 1 Tf (=) Tj ET BT 9.9626 0 0 9.9626 389.027 221.273
Tm /Ty12 1 Tf (1) Tj ET q 1 0 0 1 387.144 217.024 cm 0 0 m 8.747 0 l S Q BT
9.9626 0 0 9.9626 387.144 207.7 Tm /Ty7 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 409.609 223.998
Tm /Ty19 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 398.747 202.163 Tm /Ty9 1 Tf
(\() Tj ET BT 0.0008 Tc 6.9738 0 0 6.9738 401.86 202.163 Tm /Ty10 1 Tf [ (x,)
1 (y) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 413.035 202.163 Tm /Ty9 1 Tf (\))
Tj ET BT 6.9738 0 0 6.9738 416.148 202.163 Tm /Ty16 1 Tf (#) Tj ET BT 6.9738 0 0 6.9738 421.517 202.163
Tm /Ty10 1 Tf (D) Tj ET BT 4.9813 0 0 4.9813 428.245 204.156 Tm /Ty20 1 Tf
(m) Tj ET BT 9.9626 0 0 9.9626 436.521 225.592 Tm /Ty19 1 Tf (") Tj ET BT
0.0002 Tc 9.9626 0 0 9.9626 441.226 214.533 Tm /Ty12 1 Tf [ (CE\() -1 (\()
] TJ 0 Tc ET BT 0.0005 Tc 9.9626 0 0 9.9626 462.95 214.533 Tm /Ty7 1 Tf [
(x,) -167 (y) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 478.314 214.533 Tm /Ty12 1
Tf (\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 482.188 214.533 Tm /Ty7 1 Tf
(,g) Tj 0 Tc ET BT 6.9738 0 0 6.9738 491.368 213.039 Tm /Ty11 1 Tf (!) Tj
ET BT 9.9626 0 0 9.9626 495.875 214.533 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 380.413 183.981
Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 390.376 183.981 Tm /Ty8 1 Tf
(%) Tj ET BT 6.9738 0 0 6.9738 396.187 182.487 Tm /Ty10 1 Tf (t) Tj ET BT
9.9626 0 0 9.9626 401.909 183.981 Tm /Ty13 1 Tf Tj ET BT 9.9626 0 0 9.9626 411.154 183.981
Tm /Ty12 1 Tf [ (m) -0.3 (ax) ] TJ ET BT 0.0003 Tc 6.9738 0 0 6.9738 406.89 177.09
Tm /Ty15 1 Tf (||) Tj 0 Tc ET BT 6.9738 0 0 6.9738 411.623 177.09 Tm /Ty11
1 Tf (") Tj ET BT 0.0003 Tc 6.9738 0 0 6.9738 414.943 177.09 Tm /Ty15 1 Tf
(||) Tj 0 Tc ET BT 4.9813 0 0 4.9813 419.675 176.094 Tm /Ty20 1 Tf (p) Tj
ET BT 6.9738 0 0 6.9738 423.858 177.09 Tm /Ty16 1 Tf ($) Tj ET BT 6.9738 0 0 6.9738 430.085 177.09
Tm /Ty11 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 435.619 183.981 Tm /Ty12 1 Tf
[ (K) -0.8 (Ll) -0.8 (os) -0.4 (s) -0.4 (\() -0.9 (\() ] TJ ET BT 0.0005 Tc
9.9626 0 0 9.9626 472.952 183.981 Tm /Ty7 1 Tf [ (x,) -167 (x) ] TJ 0 Tc ET
BT 9.9626 0 0 9.9626 490.981 183.981 Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 500.944 183.981
Tm /Ty8 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 504.988 183.981 Tm /Ty12 1 Tf
(\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 508.862 183.981 Tm /Ty7 1 Tf (,g)
Tj 0 Tc ET BT 6.9738 0 0 6.9738 518.042 182.487 Tm /Ty11 1 Tf (!) Tj ET BT
9.9626 0 0 9.9626 522.549 183.981 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 526.423 195.04
Tm /Ty19 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 308.862 161.776 Tm /Ty6 1 Tf
[ (wher) 37 (e) ] TJ ET BT 9.9626 0 0 9.9626 335.332 161.776 Tm /Ty12 1 Tf
[ (K) -0.8 (Ll) -0.8 (os) -0.4 (s) -0.4 (\() -0.9 (\() ] TJ ET BT 0.0005 Tc
9.9626 0 0 9.9626 372.665 161.776 Tm /Ty7 1 Tf [ (x,) -167 (x) ] TJ 0 Tc ET
BT 9.9626 0 0 9.9626 390.694 161.776 Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 400.657 161.776
Tm /Ty8 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 404.701 161.776 Tm /Ty12 1 Tf
(\)) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 408.575 161.776 Tm /Ty7 1 Tf (,g)
Tj 0 Tc ET BT 6.9738 0 0 6.9738 417.755 160.281 Tm /Ty11 1 Tf (!) Tj ET BT
9.9626 0 0 9.9626 422.262 161.776 Tm /Ty12 1 Tf [ (\)) -278.9 (=) -278.8 (K)
-0.8 (L\() ] TJ ET BT 9.9626 0 0 9.9626 457.27 161.776 Tm /Ty7 1 Tf (s) Tj
ET BT 9.9626 0 0 9.9626 461.94 161.776 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 465.814 161.776
Tm /Ty7 1 Tf (g) Tj ET BT 6.9738 0 0 6.9738 470.566 160.281 Tm /Ty11 1 Tf
(!) Tj ET BT 9.9626 0 0 9.9626 475.073 161.776 Tm /Ty12 1 Tf (\() Tj ET BT
9.9626 0 0 9.9626 478.948 161.776 Tm /Ty7 1 Tf (x) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 484.642 161.776
Tm /Ty12 1 Tf (\)\)) Tj 0 Tc ET BT 0.0008 Tc 9.9626 0 0 9.9626 492.39 161.776
Tm /Ty13 1 Tf (||) Tj 0 Tc ET BT 9.9626 0 0 9.9626 497.925 161.776 Tm /Ty7
1 Tf (s) Tj ET BT 9.9626 0 0 9.9626 502.595 161.776 Tm /Ty12 1 Tf (\() Tj
ET BT 9.9626 0 0 9.9626 506.469 161.776 Tm /Ty7 1 Tf (g) Tj ET BT 6.9738 0 0 6.9738 511.221 160.281
Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 515.729 161.776 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 519.603 161.776 Tm /Ty7 1 Tf (x) Tj ET BT
9.9626 0 0 9.9626 527.511 161.776 Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 537.473 161.776
Tm /Ty8 1 Tf (#) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 541.517 161.776 Tm /Ty12
1 Tf (\)\)) Tj 0 Tc ET BT 9.9626 0 0 9.9626 549.266 161.776 Tm /Ty7 1 Tf (,)
Tj ET BT 9.9626 0 0 9.9626 308.862 139.5 Tm /Ty8 1 Tf (%) Tj ET BT 6.9738 0 0 6.9738 314.674 138.005
Tm /Ty10 1 Tf (t) Tj ET BT 9.9626 0 0 9.9626 321.24 139.5 Tm /Ty6 1 Tf [ (is)
-307 (a) -307 (penalty) -307 (hyper) 20 (-par) 15 (ameter) 111 (,) -321 (whic)
15 (h) -307 (balances) -307 (the) -307 (clean) ] TJ ET BT 9.9626 0 0 9.9626 308.862 127.545
Tm /Ty6 1 Tf [ (accur) 15 (acy) -250 (and) -250 (the) -250 (r) 45 (ob) 20
(ustness.) ] TJ ET BT 9.9626 0 0 9.9626 308.862 104.91 Tm /Ty2 1 Tf [ (Intuiti)
25 (v) 15 (ely) 65 (,) -639 (TRADES) -561 (minimizes) -562 (the) -561 (cross-entrop)
10 (y) -562 (loss,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 92.955 Tm /Ty2 1
Tf [ (while) -330 (also) -330 (re) 15 (gularizing) -329 (for) -330 (prediction)
-330 (smoothness) -330 (in) -330 (an) ] TJ ET BT 9.9626 0 0 9.9626 536.99 92.955
Tm /Ty8 1 Tf ($) Tj ET BT 9.9626 0 0 9.9626 541.794 92.955 Tm /Ty2 1 Tf (-)
Tj ET BT 9.9626 0 0 9.9626 308.862 81 Tm /Ty2 1 Tf [ (ball) -250 (around)
-250 (each) -250 (input.) ] TJ ET Q
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Tm /Ty2 1 Tf [ (Rice) -262 (et) -261 (al.) -262 ([) ] TJ ET /Cs1 cs 0 1 0
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(meth-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 679.755 Tm /Ty2 1 Tf [ (ods) -281
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(v) 15 (ertting.) -403 (Namely) 65 (,) -289 (the) -281 (model) ] TJ ET BT
9.9626 0 0 9.9626 50.112 667.8 Tm /Ty2 1 Tf [ (e) 15 (xhibits) -261 (higher)
-260 (rob) 20 (ustness) -261 (on) -260 (the) -261 (training) -261 (data) -260
(compared) -261 (to) ] TJ ET BT 9.9626 0 0 9.9626 50.112 655.844 Tm /Ty2 1
Tf [ (the) -309 (test) -310 (data.) -488 (A) -309 (number) -309 (of) -310
(traditional) -309 (strate) 15 (gies) -309 (ha) 20 (v) 15 (e) -310 (been)
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(to) -314 (alle) 25 (viate) -314 (the) -314 (o) 15 (v) 15 (ertting) -314
(problem) -315 (in) -314 (rob) 20 (ust) -314 (train-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 631.934
Tm /Ty2 1 Tf [ (ing,) -297 (such) -288 (as) ] TJ ET BT 9.9626 0 0 9.9626 100.587 631.934
Tm /Ty8 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 104.738 630.44 Tm /Ty9 1 Tf (2)
Tj ET BT 9.9626 0 0 9.9626 112.074 631.934 Tm /Ty2 1 Tf [ (weight) -288 (re)
15 (gularization,) -297 (early) -287 (stop) -288 ([) ] TJ ET /Cs1 cs 0 1 0
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(data) -302 (augmentation) -302 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 177.9919 619.979
Tm /Ty2 1 Tf (51) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 187.9545 619.979
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 192.089 619.979
Tm /Ty2 1 Tf (53) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 202.0516 619.979
Tm /Ty2 1 Tf [ (]) -303 (and) -302 (using) -303 (synthetic) ] TJ ET BT 9.9626 0 0 9.9626 50.112 608.024
Tm /Ty2 1 Tf [ (data) -316 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 73.17542 608.024
Tm /Ty2 1 Tf (21) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 83.13802 608.024
Tm /Ty2 1 Tf [ (].) -507 (Belo) 25 (w) -315 (we) -316 (describe) -316 (popular)
-315 (and) -316 (recent) -316 (methods) ] TJ ET BT 9.9626 0 0 9.9626 50.112 596.068
Tm /Ty2 1 Tf [ (that) -250 (were) -250 (designed) -250 (specically) -250
(for) -250 (adv) 15 (ersarial) -250 (training.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 567.372
Tm /Ty1 1 Tf [ (Stochastic) -916 (W) 65 (eight) -916 (A) 100 (v) 10 (eraging)
-917 (\(SW) 120 (A\).) ] TJ ET BT 9.9626 0 0 9.9626 234.774 567.372 Tm /Ty2
1 Tf [ (Izmailo) 15 (v) -916 (et) ] TJ ET BT 9.9626 0 0 9.9626 50.112 555.417
Tm /Ty2 1 Tf [ (al.) -696 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 70.04716 555.417
Tm /Ty2 1 Tf (24) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 80.00976 555.417
Tm /Ty2 1 Tf [ (]) -695 (introduces) -696 (SW) 120 (A) -695 (for) -696 (impro)
15 (v) 15 (ed) -696 (generalization) ] TJ ET BT 9.9626 0 0 9.9626 50.112 543.462
Tm /Ty2 1 Tf [ (performance) -580 (in) -580 (standard) -580 (training.) -1299
(SW) 120 (A) -580 (maintains) -580 (an) ] TJ ET BT 9.9626 0 0 9.9626 50.112 531.507
Tm /Ty2 1 Tf [ (e) 15 (xponential) -308 (running) -308 (a) 20 (v) 15 (erage)
] TJ ET BT 9.9626 0 0 9.9626 167.273 531.507 Tm /Ty8 1 Tf (") Tj ET BT 6.9738 0 0 6.9738 171.95 530.012
Tm /Ty4 1 Tf (avg) Tj ET BT 9.9626 0 0 9.9626 188.07 531.507 Tm /Ty2 1 Tf
[ (of) -308 (the) -308 (model) -308 (parameters) ] TJ ET BT 9.9626 0 0 9.9626 50.112 519.551
Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 59.101 519.551 Tm /Ty2 1 Tf [
(at) -405 (each) -405 (training) -405 (iteration) -405 (and) -405 (uses) -405
(the) -405 (running) -405 (a) 20 (v) 15 (erage) ] TJ ET BT 9.9626 0 0 9.9626 50.112 507.596
Tm /Ty8 1 Tf (") Tj ET BT 6.9738 0 0 6.9738 54.789 506.102 Tm /Ty4 1 Tf (avg)
Tj ET BT 9.9626 0 0 9.9626 70.331 507.596 Tm /Ty2 1 Tf [ (for) -250 (inference.)
-310 (Namely) 65 (,) ] TJ ET BT 9.9626 0 0 9.9626 57.905 484.889 Tm /Ty8 1
Tf (") Tj ET BT 6.9738 0 0 6.9738 62.859 489.002 Tm /Ty9 1 Tf (\() Tj ET BT
6.9738 0 0 6.9738 65.972 489.002 Tm /Ty10 1 Tf (t) Tj ET BT 6.9738 0 0 6.9738 68.981 489.002
Tm /Ty9 1 Tf [ (+1) -0.5 (\)) ] TJ ET BT 9.9626 0 0 9.9626 85.448 484.889
Tm /Ty14 1 Tf ($) Tj ET BT 9.9626 0 0 9.9626 98.178 484.889 Tm /Ty4 1 Tf (SGD)
Tj ET BT 9.9626 0 0 9.9626 116.11 484.889 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 119.985 484.889
Tm /Ty8 1 Tf (") Tj ET BT 6.9738 0 0 6.9738 124.938 489.002 Tm /Ty9 1 Tf (\()
Tj ET BT 6.9738 0 0 6.9738 128.052 489.002 Tm /Ty10 1 Tf (t) Tj ET BT 6.9738 0 0 6.9738 131.061 489.002
Tm /Ty9 1 Tf (\)) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 134.673 484.889 Tm
/Ty12 1 Tf (\);) Tj 0 Tc ET BT 9.9626 0 0 9.9626 152.937 484.889 Tm /Ty8 1
Tf (") Tj ET BT 6.9738 0 0 6.9738 157.614 483.395 Tm /Ty4 1 Tf (avg) Tj ET
BT 9.9626 0 0 9.9626 173.433 484.889 Tm /Ty14 1 Tf ($) Tj ET BT 0.0047 Tc
9.9626 0 0 9.9626 186.163 484.889 Tm /Ty8 1 Tf (&") Tj 0 Tc ET BT 6.9738 0 0 6.9738 197.25 483.395
Tm /Ty4 1 Tf (avg) Tj ET BT 0.2228 Tc 9.9626 0 0 9.9626 212.515 484.889 Tm
/Ty12 1 Tf [ (+\() 222 (1) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 233.547 484.889
Tm /Ty14 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 243.509 484.889 Tm /Ty8 1 Tf
(&) Tj ET BT 9.9626 0 0 9.9626 249.919 484.889 Tm /Ty12 1 Tf (\)) Tj ET BT
9.9626 0 0 9.9626 253.794 484.889 Tm /Ty8 1 Tf (") Tj ET BT 6.9738 0 0 6.9738 258.747 489.002
Tm /Ty9 1 Tf (\() Tj ET BT 6.9738 0 0 6.9738 261.861 489.002 Tm /Ty10 1 Tf
(t) Tj ET BT 6.9738 0 0 6.9738 264.87 489.002 Tm /Ty9 1 Tf [ (+1) -0.5 (\))
] TJ ET BT 9.9626 0 0 9.9626 50.112 462.182 Tm /Ty2 1 Tf (where) Tj ET BT
9.9626 0 0 9.9626 77.721 462.182 Tm /Ty8 1 Tf (&) Tj ET BT 9.9626 0 0 9.9626 87.402 462.182
Tm /Ty2 1 Tf [ (is) -328 (commonly) -329 (set) -328 (to) ] TJ ET BT 9.9626 0 0 9.9626 168.569 462.182
Tm /Ty12 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 173.55 462.182 Tm /Ty7 1 Tf (.)
Tj ET BT 9.9626 0 0 9.9626 176.317 462.182 Tm /Ty12 1 Tf (995) Tj ET BT 9.9626 0 0 9.9626 191.261 462.182
Tm /Ty2 1 Tf [ (.) -545 (Recent) -328 (w) 10 (ork) -329 (has) -328 (also)
] TJ ET BT 9.9626 0 0 9.9626 50.112 450.227 Tm /Ty2 1 Tf [ (sho) 25 (wn) -388
(that) -388 (SW) 120 (A) -388 (helps) -388 (generalization) -388 (in) -388
(the) -388 (rob) 20 (ust) -388 (train-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 438.271
Tm /Ty2 1 Tf [ (ing) -307 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 69.22027 438.271
Tm /Ty2 1 Tf (21) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 79.18287 438.271
Tm /Ty2 1 Tf [ (]) -308 (scenario.) -482 (Note) -307 (that) -308 (maintaining)
-307 (the) -307 (running) -308 (a) 20 (v) 15 (er) 20 (-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 426.316
Tm /Ty2 1 Tf [ (age) -250 (requires) -250 (additional) -250 (memory) -250
(resources.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 397.62 Tm /Ty1 1 Tf [ (Adv)
10 (ersarial) -561 (W) 65 (eight) -562 (P) 20 (erturbation) -561 (\(A) 130
(WP\).) ] TJ ET BT 9.9626 0 0 9.9626 243.678 397.62 Tm /Ty2 1 Tf [ (Similar)
-561 (to) ] TJ ET BT 9.9626 0 0 9.9626 50.112 385.665 Tm /Ty2 1 Tf [ (Sharpness-A)
92 (w) 10 (are) -230 (Minimization) -230 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 181.5087 385.665
Tm /Ty2 1 Tf (15) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 191.4713 385.665
Tm /Ty2 1 Tf [ (],) -234 (W) 50 (u) -230 (et) -230 (al.) -230 ([) ] TJ ET
/Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 240.567 385.665 Tm /Ty2 1 Tf (49) Tj
ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 250.5296 385.665 Tm /Ty2 1 Tf [ (]) -230
(encour) 20 (-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 373.709 Tm /Ty2 1 Tf [
(ages) -363 (model) -364 (rob) 20 (ustness) -363 (by) -364 (penalizing) -363
(ag) 5 (ainst) -364 (the) -363 (most) -364 (of-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 361.754
Tm /Ty2 1 Tf [ (fending) -193 (local) -193 (weight) -192 (perturbation) -193
(to) -193 (the) -193 (model.) -291 (Specically) 65 (,) ] TJ ET BT 9.9626 0 0 9.9626 50.112 349.799
Tm /Ty2 1 Tf [ (gi) 25 (v) 15 (en) -224 (a) -224 (rob) 20 (ust) -224 (loss)
] TJ ET BT 9.9626 0 0 9.9626 127.572 352.317 Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 125.412 349.799
Tm /Ty7 1 Tf (R) Tj ET BT 6.9738 0 0 6.9738 132.976 347.084 Tm /Ty4 1 Tf (*)
Tj ET BT 9.9626 0 0 9.9626 137.659 349.799 Tm /Ty12 1 Tf (\() Tj ET BT 0.0284
Tc 9.9626 0 0 9.9626 141.533 349.799 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138
(D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 159.44 353.414 Tm /Ty10 1 Tf (m) Tj
ET BT 9.9626 0 0 9.9626 167.007 349.799 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 170.882 349.799
Tm /Ty2 1 Tf [ (,) -229 (A) 90 (WP) -224 (minimizes) -224 (the) -224 (follo)
25 (w-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 337.844 Tm /Ty2 1 Tf [ (ing) -250
(objecti) 25 (v) 15 (e) -250 (w) 65 (.r) 55 (.t) ] TJ ET BT 9.9626 0 0 9.9626 123.506 337.844
Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 128.46 337.844 Tm /Ty2 1 Tf (:)
Tj ET BT 9.9626 0 0 9.9626 126.904 315.137 Tm /Ty12 1 Tf [ (m) -0.3 (ax) ]
TJ ET BT 6.9738 0 0 6.9738 116.845 308.246 Tm /Ty11 1 Tf ($) Tj ET BT 6.9738 0 0 6.9738 122.367 308.246
Tm /Ty9 1 Tf (\() Tj ET BT 6.9738 0 0 6.9738 125.48 308.246 Tm /Ty11 1 Tf
(%) Tj ET BT 6.9738 0 0 6.9738 129.343 308.246 Tm /Ty9 1 Tf (\)) Tj ET BT
6.9738 0 0 6.9738 132.457 308.246 Tm /Ty16 1 Tf ($) Tj ET BT 6.9738 0 0 6.9738 138.683 308.246
Tm /Ty11 1 Tf (#) Tj ET BT 0.0004 Tc 4.9813 0 0 4.9813 142.305 307.25 Tm /Ty20
1 Tf [ (aw) -27 (p) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 159.326 317.655 Tm /Ty12
1 Tf Tj ET BT 9.9626 0 0 9.9626 157.166 315.137 Tm /Ty7 1 Tf (R) Tj ET
BT 6.9738 0 0 6.9738 164.73 312.422 Tm /Ty4 1 Tf (*) Tj ET BT 9.9626 0 0 9.9626 169.413 315.137
Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 173.287 315.137 Tm /Ty8 1 Tf
(") Tj ET BT 9.9626 0 0 9.9626 180.455 315.137 Tm /Ty12 1 Tf (+) Tj ET BT
0.0465 Tc 9.9626 0 0 9.9626 190.417 315.137 Tm /Ty8 1 Tf (') Tj /Ty7 1 Tf
[ (,) -121 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 208.187 319.25 Tm /Ty10 1
Tf (m) Tj ET BT 9.9626 0 0 9.9626 215.755 315.137 Tm /Ty12 1 Tf (\)) Tj ET
BT 9.9626 0 0 9.9626 274.746 315.137 Tm /Ty2 1 Tf (\(1\)) Tj ET BT 9.9626 0 0 9.9626 50.112 286.618
Tm /Ty2 1 Tf [ (where) -389 (*) -389 (denotes) -389 (either) ] TJ ET BT 9.9626 0 0 9.9626 148.057 286.618
Tm /Ty4 1 Tf (AT) Tj ET BT 9.9626 0 0 9.9626 163.888 286.618 Tm /Ty2 1 Tf
(or) Tj ET BT 9.9626 0 0 9.9626 176.063 286.618 Tm /Ty4 1 Tf (T) Tj ET BT
9.9626 0 0 9.9626 182.041 286.618 Tm /Ty2 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 188.754 286.618
Tm /Ty8 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 199.477 286.618 Tm /Ty2 1 Tf
[ (measures) -389 (the) -389 (amount) ] TJ ET BT 9.9626 0 0 9.9626 50.112 274.663
Tm /Ty2 1 Tf [ (of) -315 (noise) ] TJ ET BT 9.9626 0 0 9.9626 85.714 274.663
Tm /Ty8 1 Tf (') Tj ET BT 9.9626 0 0 9.9626 93.667 274.663 Tm /Ty2 1 Tf (\(e.g.)
Tj ET BT 9.9626 0 0 9.9626 116.395 274.663 Tm /Ty8 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 120.546 273.168
Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 128.152 274.663 Tm /Ty2 1 Tf [
(norm\)) -315 (and) ] TJ ET BT 9.9626 0 0 9.9626 173.158 274.663 Tm /Ty8 1
Tf ($) Tj ET BT 0.0007 Tc 6.9738 0 0 6.9738 177.586 273.168 Tm /Ty10 1 Tf
[ (aw) -27 (p) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 195.6 274.663 Tm /Ty2 1 Tf
[ (denotes) -315 (the) -315 (noise) -314 (total) ] TJ ET BT 9.9626 0 0 9.9626 50.112 262.708
Tm /Ty2 1 Tf [ (b) 20 (udget.) -461 (Note) -300 (that) -301 (solving) -300
(the) -300 (inner) -300 (maximization) -301 (problem) ] TJ ET BT 9.9626 0 0 9.9626 50.112 250.752
Tm /Ty2 1 Tf [ (requires) -345 (at) -345 (least) -346 (one) -345 (additional)
-345 (gradient) -345 (ascent) -345 (step) -346 (i) 1 (n) -346 (the) ] TJ ET
BT 9.9626 0 0 9.9626 50.112 238.797 Tm /Ty2 1 Tf [ (parameter) -250 (space.)
] TJ ET BT 9.9626 0 0 9.9626 50.112 210.101 Tm /Ty1 1 Tf [ (Second-Order)
-202 (Statistic) -202 (\(S2O\).) ] TJ ET BT 9.9626 0 0 9.9626 186.127 210.101
Tm /Ty2 1 Tf [ (Jin) -202 (et) -202 (al.) -201 ([) ] TJ ET /Cs1 cs 0 1 0 sc
BT 9.9626 0 0 9.9626 223.9749 210.101 Tm /Ty2 1 Tf (26) Tj ET /Cs2 cs 0 sc
BT 9.9626 0 0 9.9626 233.9375 210.101 Tm /Ty2 1 Tf [ (]) -202 (impro) 15 (v)
15 (e) -202 (the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 198.146 Tm /Ty2 1 Tf
[ (rob) 20 (ustness) -240 (generalization) -240 (by) -240 (re) 15 (gularizing)
-240 (the) -240 (statistical) -240 (cor) 20 (-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 186.19
Tm /Ty2 1 Tf [ (relations) -246 (between) -246 (the) -246 (weights) -245 (of)
-246 (the) -246 (netw) 10 (ork.) -309 (Furthermore,) ] TJ ET BT 9.9626 0 0 9.9626 50.112 174.235
Tm /Ty2 1 Tf [ (the) 15 (y) -394 (pro) 15 (vide) -393 (a) -394 (second-order)
-393 (and) -394 (data-dependent) -394 (approxi-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 162.28
Tm /Ty2 1 Tf (mation) Tj ET BT 9.9626 0 0 9.9626 80.98 162.28 Tm /Ty7 1 Tf
(A) Tj ET BT 6.9738 0 0 6.9738 88.452 160.786 Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 96.152 162.28
Tm /Ty2 1 Tf [ (of) -320 (the) -321 (weight) -320 (correlation) -321 (matrix.)
-521 (During) -320 (train-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 150.325 Tm
/Ty2 1 Tf [ (ing,) -250 (S2O) -250 (minimizes) -250 (the) -250 (follo) 25
(wing) -250 (objecti) 25 (v) 15 (e) -250 (w) 65 (.r) 55 (.t) ] TJ ET BT 9.9626 0 0 9.9626 245.856 150.325
Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 250.81 150.325 Tm /Ty2 1 Tf (:)
Tj ET BT 9.9626 0 0 9.9626 123.533 130.136 Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 121.373 127.618
Tm /Ty7 1 Tf (R) Tj ET BT 6.9738 0 0 6.9738 128.937 124.903 Tm /Ty4 1 Tf (*)
Tj ET BT 9.9626 0 0 9.9626 133.62 127.618 Tm /Ty12 1 Tf (\() Tj ET BT 0.0284
Tc 9.9626 0 0 9.9626 137.494 127.618 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138
(D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 155.4 131.731 Tm /Ty10 1 Tf (m) Tj ET
BT 0.2229 Tc 9.9626 0 0 9.9626 162.968 127.618 Tm /Ty12 1 Tf (\)+) Tj 0 Tc
ET BT 9.9626 0 0 9.9626 179.019 127.618 Tm /Ty8 1 Tf (&) Tj ET BT 0.0008 Tc
9.9626 0 0 9.9626 185.429 127.618 Tm /Ty13 1 Tf (||) Tj 0 Tc ET BT 9.9626 0 0 9.9626 190.964 127.618
Tm /Ty7 1 Tf (A) Tj ET BT 6.9738 0 0 6.9738 198.436 126.123 Tm /Ty11 1 Tf
(!) Tj ET BT 0.0008 Tc 9.9626 0 0 9.9626 202.943 127.618 Tm /Ty13 1 Tf (||)
Tj 0 Tc ET BT 6.9738 0 0 6.9738 208.478 126.123 Tm /Ty10 1 Tf (F) Tj ET BT
9.9626 0 0 9.9626 274.746 127.618 Tm /Ty2 1 Tf (\(2\)) Tj ET BT 9.9626 0 0 9.9626 50.112 104.91
Tm /Ty2 1 Tf (where) Tj ET BT 0.2937 Tc 9.9626 0 0 9.9626 77.002 104.91 Tm
/Ty8 1 Tf (&) Tj /Ty7 1 Tf (>) Tj 0 Tc ET BT 9.9626 0 0 9.9626 96.921 104.91
Tm /Ty12 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 104.454 104.91 Tm /Ty2 1 Tf [
(is) -256 (a) -256 (h) 5 (yper) 20 (-parameter) 55 (.) -328 (Computing) ]
TJ ET BT 9.9626 0 0 9.9626 238.815 104.91 Tm /Ty7 1 Tf (A) Tj ET BT 6.9738 0 0 6.9738 246.287 103.416
Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 253.346 104.91 Tm /Ty2 1 Tf [
(in) 40 (v) 20 (olv) 15 (es) ] TJ ET BT 9.9626 0 0 9.9626 50.112 92.955 Tm
/Ty2 1 Tf [ (computing) -375 (the) -375 (per) 20 (-instance) -375 (self-Kroneck)
10 (er) -375 (product) -375 (of) -375 (the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 81
Tm /Ty2 1 Tf [ (logit) -250 (outputs) -250 (for) -250 (the) -250 (clean) -250
(and) -250 (adv) 15 (ersarial) -250 (inputs.) ] TJ ET BT 10.9589 0 0 10.9589 308.862 710.037
Tm /Ty1 1 Tf [ (2.3.) -250 (P) 74 (A) 55 (C-Bay) 10 (esian) -250 (Theory)
-250 (f) 25 (or) -250 (Rob) 20 (ust) -250 (T) 74 (raining) ] TJ ET BT 9.9626 0 0 9.9626 320.817 692.085
Tm /Ty2 1 Tf [ (P) 92 (A) 40 (C-Bayesian) -197 (theory) -197 ([) ] TJ ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 411.4169 692.085 Tm /Ty2 1 Tf (4) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 416.3982 692.085 Tm /Ty2 1 Tf (,) Tj ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 419.2973 692.085 Tm /Ty2 1 Tf (9) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 424.2786 692.085 Tm /Ty2 1 Tf (,) Tj ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 427.1877 692.085 Tm /Ty2 1 Tf (18) Tj ET
/Cs2 cs 0 sc BT 9.9626 0 0 9.9626 437.1503 692.085 Tm /Ty2 1 Tf (,) Tj ET
/Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 440.0494 692.085 Tm /Ty2 1 Tf (34) Tj
ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 450.012 692.085 Tm /Ty2 1 Tf (,) Tj ET
/Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 452.9211 692.085 Tm /Ty2 1 Tf (35) Tj
ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 462.8837 692.085 Tm /Ty2 1 Tf (,) Tj
ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 465.7828 692.085 Tm /Ty2 1 Tf (42)
Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 475.7454 692.085 Tm /Ty2 1 Tf [ (])
-197 (pro) 15 (vides) -197 (a) -197 (foun-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 680.13
Tm /Ty2 1 Tf [ (dation) -207 (for) -206 (deri) 25 (ving) -207 (an) -207 (upper)
-206 (bound) -207 (of) -206 (the) -207 (generalization) -207 (g) 5 (ap) ]
TJ ET BT 9.9626 0 0 9.9626 308.862 668.175 Tm /Ty2 1 Tf [ (between) -384 (the)
-383 (training) -384 (and) -383 (test) -384 (error) 55 (.) -710 (Both) -384
(A) 90 (WP) -383 (and) -384 (S2O) ] TJ ET BT 9.9626 0 0 9.9626 308.862 656.22
Tm /Ty2 1 Tf [ (plug) -307 (the) -307 (rob) 20 (ust) -306 (loss) -307 (into)
-307 (the) -307 (classical) -306 (bound) -307 ([) ] TJ ET /Cs1 cs 0 1 0 sc
BT 9.9626 0 0 9.9626 493.0605 656.22 Tm /Ty2 1 Tf (35) Tj ET /Cs2 cs 0 sc
BT 9.9626 0 0 9.9626 503.0231 656.22 Tm /Ty2 1 Tf [ (]) -307 (to) -307 (obtain)
] TJ ET BT 9.9626 0 0 9.9626 308.862 644.265 Tm /Ty2 1 Tf [ (the) -250 (follo)
25 (wing) -250 (form:) ] TJ ET BT 9.9626 0 0 9.9626 308.862 622.251 Tm /Ty1
1 Tf [ (Theor) 18 (em) -250 (1) -250 (\(Squar) 18 (e) -250 (Root-F) 25 (orm)
-250 (P) 74 (A) 55 (C-Bay) 10 (esian) -250 (Bound) -250 ([) ] TJ ET /Cs1 cs
0 1 0 sc BT 9.9626 0 0 9.9626 540.4227 622.251 Tm /Ty1 1 Tf (49) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 550.3853 622.251 Tm /Ty1 1 Tf (]\)) Tj ET BT
9.9626 0 0 9.9626 308.862 610.296 Tm /Ty6 1 Tf [ (Given) -292 (a) -291 (prior)
-292 (distrib) 20 (ution) ] TJ ET BT 9.9626 0 0 9.9626 416.044 610.296 Tm
/Ty13 1 Tf (P) Tj ET BT 9.9626 0 0 9.9626 426.698 610.296 Tm /Ty6 1 Tf [ (on)
-292 (the) -291 (weight) ] TJ ET BT 9.9626 0 0 9.9626 484.12 610.296 Tm /Ty8
1 Tf (") Tj ET BT 9.9626 0 0 9.9626 491.979 610.296 Tm /Ty6 1 Tf [ (of) -292
(a) -291 (network,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 598.341 Tm /Ty6 1
Tf (any) Tj ET BT 9.9626 0 0 9.9626 328.353 598.341 Tm /Ty8 1 Tf (\)) Tj ET
BT 9.9626 0 0 9.9626 341.444 598.341 Tm /Ty14 1 Tf (!) Tj ET BT 0.0009 Tc
9.9626 0 0 9.9626 355.693 598.341 Tm /Ty12 1 Tf (\(0) Tj 0 Tc ET BT 9.9626 0 0 9.9626 364.549 598.341
Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 368.977 598.341 Tm /Ty12 1 Tf
(1]) Tj ET BT 9.9626 0 0 9.9626 376.726 598.341 Tm /Ty6 1 Tf [ (,) -578 (a)
-512 (r) 45 (ob) 20 (ustness) -513 (loss) ] TJ ET BT 9.9626 0 0 9.9626 462.743 598.341
Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 470.385 598.341 Tm /Ty12 1 Tf
(\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 474.259 598.341 Tm /Ty8 1 Tf (")
Tj /Ty7 1 Tf (,) Tj 0 Tc ET BT 9.9626 0 0 9.9626 483.641 598.341 Tm /Ty13
1 Tf (D) Tj ET BT 9.9626 0 0 9.9626 491.603 598.341 Tm /Ty12 1 Tf (\)) Tj
ET BT 9.9626 0 0 9.9626 500.582 598.341 Tm /Ty6 1 Tf [ (for) -512 (a) -513
(data) ] TJ ET BT 9.9626 0 0 9.9626 308.862 586.385 Tm /Ty6 1 Tf [ (distrib)
20 (ution) ] TJ ET BT 9.9626 0 0 9.9626 357.769 586.385 Tm /Ty13 1 Tf (D)
Tj ET BT 9.9626 0 0 9.9626 368.333 586.385 Tm /Ty6 1 Tf [ (and) -261 (its)
-261 (empirical) -261 (ver) 10 (sion) ] TJ ET BT 9.9626 0 0 9.9626 472.674 588.904
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 470.514 586.385 Tm /Ty7 1 Tf
(R) Tj ET BT 9.9626 0 0 9.9626 478.155 586.385 Tm /Ty12 1 Tf (\() Tj ET BT
0.0284 Tc 9.9626 0 0 9.9626 482.03 586.385 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf [
(,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 499.936 590.001 Tm /Ty10 1
Tf (m) Tj ET BT 9.9626 0 0 9.9626 507.504 586.385 Tm /Ty12 1 Tf (\)) Tj ET
BT 9.9626 0 0 9.9626 511.378 586.385 Tm /Ty6 1 Tf [ (,) -264 (for) -261 (any)
] TJ ET BT 9.9626 0 0 9.9626 308.862 574.43 Tm /Ty6 1 Tf [ (posterior) -236
(distrib) 20 (ution) ] TJ ET BT 9.9626 0 0 9.9626 396.398 574.43 Tm /Ty13
1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 406.883 574.43 Tm /Ty6 1 Tf (of) Tj ET
BT 9.9626 0 0 9.9626 416.983 574.43 Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 421.936 574.43
Tm /Ty6 1 Tf [ (,) -239 (the) -235 (following) -236 (inequality) -236 (holds)
] TJ ET BT 9.9626 0 0 9.9626 308.862 562.475 Tm /Ty6 1 Tf [ (with) -250 (a)
-250 (pr) 45 (obability) -250 (at) -250 (least) ] TJ ET BT 9.9626 0 0 9.9626 413.867 562.475
Tm /Ty12 1 Tf (1) Tj ET BT 9.9626 0 0 9.9626 421.062 562.475 Tm /Ty14 1 Tf
(#) Tj ET BT 9.9626 0 0 9.9626 431.025 562.475 Tm /Ty8 1 Tf (\)) Tj ET BT
9.9626 0 0 9.9626 436.508 562.475 Tm /Ty6 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 335.6 540.519
Tm /Ty17 1 Tf (E) Tj ET BT 6.9738 0 0 6.9738 342.242 539.024 Tm /Ty11 1 Tf
(!) Tj ET BT 0.0008 Tc 6.9738 0 0 6.9738 346.251 539.024 Tm /Ty16 1 Tf (#)
Tj /Ty15 1 Tf (Q) Tj 0 Tc ET BT 9.9626 0 0 9.9626 358.645 540.519 Tm /Ty7
1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 366.286 540.519 Tm /Ty12 1 Tf (\() Tj
ET BT 0.0284 Tc 9.9626 0 0 9.9626 370.161 540.519 Tm /Ty8 1 Tf (") Tj /Ty7
1 Tf (,) Tj 0 Tc ET BT 9.9626 0 0 9.9626 379.542 540.519 Tm /Ty13 1 Tf (D)
Tj ET BT 9.9626 0 0 9.9626 387.504 540.519 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 394.146 540.519
Tm /Ty14 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 404.662 540.519 Tm /Ty17 1 Tf
(E) Tj ET BT 6.9738 0 0 6.9738 411.304 539.024 Tm /Ty11 1 Tf (!) Tj ET BT
0.0008 Tc 6.9738 0 0 6.9738 415.313 539.024 Tm /Ty16 1 Tf (#) Tj /Ty15 1 Tf
(Q) Tj 0 Tc ET BT 9.9626 0 0 9.9626 429.867 543.037 Tm /Ty12 1 Tf Tj ET
BT 9.9626 0 0 9.9626 427.707 540.519 Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 435.348 540.519
Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 439.223 540.519 Tm
/Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 457.129 544.632
Tm /Ty10 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 464.697 540.519 Tm /Ty12 1 Tf
(\)) Tj ET BT 0.2228 Tc 9.9626 0 0 9.9626 393.592 516.496 Tm /Ty12 1 Tf (+4)
Tj 0 Tc ET BT 9.9626 0 0 9.9626 408.536 532.15 Tm /Ty19 1 Tf ($) Tj ET 0.398
w q 1 0 0 1 418.499 532.349 cm 0 0 m 97.107 0 l S Q BT 9.9626 0 0 9.9626 421.578 523.235
Tm /Ty12 1 Tf (1) Tj ET q 1 0 0 1 419.695 518.986 cm 0 0 m 8.747 0 l S Q BT
9.9626 0 0 9.9626 419.695 509.662 Tm /Ty7 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 429.637 516.496
Tm /Ty12 1 Tf [ (K) -0.8 (L\() ] TJ ET BT 0.0007 Tc 9.9626 0 0 9.9626 447.487 516.496
Tm /Ty13 1 Tf (Q||P) Tj 0 Tc ET BT 9.9626 0 0 9.9626 468.907 516.496 Tm /Ty12
1 Tf [ (\)) -222.9 (+) -222.8 (l) -0.8 (og) ] TJ ET BT 9.9626 0 0 9.9626 500.682 523.235
Tm /Ty12 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 505.663 523.235 Tm /Ty7 1 Tf
(m) Tj ET q 1 0 0 1 500.682 518.986 cm 0 0 m 13.729 0 l S Q BT 9.9626 0 0 9.9626 504.805 509.662
Tm /Ty8 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 515.606 516.496 Tm /Ty7 1 Tf
(.) Tj ET BT 9.9626 0 0 9.9626 533.496 516.496 Tm /Ty2 1 Tf (\(3\)) Tj ET
BT 9.9626 0 0 9.9626 320.817 490.827 Tm /Ty2 1 Tf [ (Generally) -314 (speaking,)
-330 (the) -314 (goal) -314 (of) -314 (P) 92 (A) 40 (C-Bayesian) -314 (learning)
] TJ ET BT 9.9626 0 0 9.9626 308.862 478.872 Tm /Ty2 1 Tf [ (is) -254 (to)
-254 (optimize) ] TJ ET BT 9.9626 0 0 9.9626 365.724 478.872 Tm /Ty13 1 Tf
(Q) Tj ET BT 9.9626 0 0 9.9626 376.393 478.872 Tm /Ty2 1 Tf [ (on) -254 (the)
-254 (RHS) -255 (of) -254 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 452.4276 478.872
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 459.9394 478.872
Tm /Ty2 1 Tf [ (so) -254 (as) -255 (to) -254 (obtain) -254 (a) -254 (tight)
] TJ ET BT 9.9626 0 0 9.9626 308.862 466.917 Tm /Ty2 1 Tf [ (upper) -264 (bound)
-264 (on) -264 (the) -264 (test) -264 (error) -264 (\(LHS\).) -264 (Ho) 25
(we) 25 (v) 15 (er) 40 (,) -268 (directly) -264 (op-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 454.962
Tm /Ty2 1 Tf [ (timizing) -246 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 360.538 454.962
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 367.9701 454.962
Tm /Ty2 1 Tf [ (o) 15 (v) 15 (er) ] TJ ET BT 9.9626 0 0 9.9626 387.822 454.962
Tm /Ty13 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 398.408 454.962 Tm /Ty2 1 Tf
[ (is) -246 (dif) 25 (cult) -246 (because) -246 (of) -246 (the) -246 (square)
-245 (root) ] TJ ET BT 9.9626 0 0 9.9626 308.862 443.007 Tm /Ty2 1 Tf [ (term.)
-339 (Instead) -260 (of) -260 (optimi) 1 (zing) -260 (the) -260 (RHS,) -260
(A) 90 (WP) -259 (replaces) -260 (it) -260 (with) ] TJ ET BT 9.9626 0 0 9.9626 308.862 431.051
Tm /Ty12 1 Tf [ (m) -0.3 (ax) ] TJ ET BT 6.9738 0 0 6.9738 327.404 429.557
Tm /Ty11 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 335.586 433.57 Tm /Ty12 1 Tf
Tj ET BT 9.9626 0 0 9.9626 333.425 431.051 Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 341.067 431.051
Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 344.941 431.051 Tm /Ty8 1 Tf
(") Tj ET BT 9.9626 0 0 9.9626 353.194 431.051 Tm /Ty12 1 Tf (+) Tj ET BT
0.0465 Tc 9.9626 0 0 9.9626 364.242 431.051 Tm /Ty8 1 Tf (') Tj /Ty7 1 Tf
[ (,) -121 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 382.012 434.667 Tm /Ty10
1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 389.58 431.051 Tm /Ty12 1 Tf (\)) Tj ET
BT 9.9626 0 0 9.9626 397.411 431.051 Tm /Ty2 1 Tf [ (plus) -397 (a) -397 (constant)
-397 (upper) -397 (bound) -397 (on) -398 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 419.096
Tm /Ty2 1 Tf [ (square) -394 (root) -393 (term,) -429 (which) -394 (is) -394
(only) -393 (loosely) -394 (connected) -393 (to) -394 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 407.141
Tm /Ty2 1 Tf [ (bound.) -456 (On) -299 (the) -299 (other) -298 (hand,) -311
(S2O) -299 (assumes) ] TJ ET BT 9.9626 0 0 9.9626 476.377 407.141 Tm /Ty13
1 Tf (P) Tj ET BT 9.9626 0 0 9.9626 487.102 407.141 Tm /Ty2 1 Tf (and) Tj
ET BT 9.9626 0 0 9.9626 504.464 407.141 Tm /Ty13 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 515.576 407.141
Tm /Ty2 1 Tf [ (as) -299 (non-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 395.186
Tm /Ty2 1 Tf [ (spherical) -252 (Gaussian,) -253 (i.e.) ] TJ ET BT 9.9626 0 0 9.9626 404.201 395.186
Tm /Ty13 1 Tf (P) Tj ET BT 9.9626 0 0 9.9626 414.758 395.186 Tm /Ty12 1 Tf
(=) Tj ET BT 9.9626 0 0 9.9626 425.315 395.186 Tm /Ty13 1 Tf (N) Tj ET BT
0.0009 Tc 9.9626 0 0 9.9626 434.957 395.186 Tm /Ty12 1 Tf (\(0) Tj 0 Tc ET
BT 9.9626 0 0 9.9626 443.813 395.186 Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 448.241 395.186
Tm /Ty24 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 455.436 393.691 Tm /Ty10 1 Tf
(p) Tj ET BT 9.9626 0 0 9.9626 460.041 395.186 Tm /Ty12 1 Tf (\)) Tj ET BT
9.9626 0 0 9.9626 463.916 395.186 Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 468.343 395.186
Tm /Ty13 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 479.288 395.186 Tm /Ty12 1 Tf
(=) Tj ET BT 9.9626 0 0 9.9626 489.845 395.186 Tm /Ty13 1 Tf (N) Tj ET BT
9.9626 0 0 9.9626 499.488 395.186 Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 503.362 395.186
Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf (,) Tj 0 Tc ET BT 9.9626 0 0 9.9626 512.744 395.186
Tm /Ty24 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 519.939 393.691 Tm /Ty10 1 Tf
(q) Tj ET BT 9.9626 0 0 9.9626 524.339 395.186 Tm /Ty12 1 Tf (\)) Tj ET BT
9.9626 0 0 9.9626 530.726 395.186 Tm /Ty2 1 Tf (and) Tj ET BT 9.9626 0 0 9.9626 308.862 383.231
Tm /Ty2 1 Tf [ (sho) 25 (w) -274 (that) -274 (the) -274 (square) -273 (root)
-274 (bound) -274 (increases) -274 (as) -274 (the) -274 (Frobenius) ] TJ ET
BT 9.9626 0 0 9.9626 308.862 371.276 Tm /Ty2 1 Tf [ (norm) -322 (and) -323
(singular) -322 (v) 25 (alue) -323 (of) ] TJ ET BT 9.9626 0 0 9.9626 422.069 371.276
Tm /Ty24 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 429.264 369.781 Tm /Ty10 1 Tf
(q) Tj ET BT 9.9626 0 0 9.9626 436.876 371.276 Tm /Ty2 1 Tf [ (increase.)
-527 (T) 80 (o) -323 (o) 15 (v) 15 (ercome) -322 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 359.32
Tm /Ty2 1 Tf [ (comple) 15 (xity) -202 (of) -202 (the) -203 (square) -202
(root) -202 (term,) -212 (the) 15 (y) -202 (approximate) -202 (it) -203 (with)
] TJ ET BT 9.9626 0 0 9.9626 308.862 347.365 Tm /Ty14 1 Tf (&) Tj ET BT 9.9626 0 0 9.9626 313.843 347.365
Tm /Ty7 1 Tf (A) Tj ET BT 6.9738 0 0 6.9738 321.315 345.871 Tm /Ty11 1 Tf
(!) Tj ET BT 9.9626 0 0 9.9626 325.823 347.365 Tm /Ty14 1 Tf (&) Tj ET BT
6.9738 0 0 6.9738 330.804 345.871 Tm /Ty10 1 Tf (F) Tj ET BT 9.9626 0 0 9.9626 339.918 347.365
Tm /Ty2 1 Tf [ (as) -250 (in) -250 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 376.9988 347.365
Tm /Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 381.9801 347.365
Tm /Ty2 1 Tf (.) Tj ET BT 11.9552 0 0 11.9552 308.862 323.397 Tm /Ty1 1 Tf
[ (3.) -250 (Dir) 18 (ect) -250 (P) 74 (A) 55 (C-Bay) 10 (esian) -250 (Bound)
-250 (Minimization) ] TJ ET BT 9.9626 0 0 9.9626 320.817 304.449 Tm /Ty2 1
Tf [ (As) -379 (mentioned) -379 (earlier) 40 (,) -411 (neither) -379 (A) 90
(WP) -380 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 472.916 304.449
Tm /Ty2 1 Tf (49) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 482.8786 304.449
Tm /Ty2 1 Tf [ (]) -379 (nor) -379 (S2O) -379 ([) ] TJ ET /Cs1 cs 0 1 0 sc
BT 9.9626 0 0 9.9626 531.8348 304.449 Tm /Ty2 1 Tf (26) Tj ET /Cs2 cs 0 sc
BT 9.9626 0 0 9.9626 541.7974 304.449 Tm /Ty2 1 Tf (]) Tj ET BT 9.9626 0 0 9.9626 308.862 292.494
Tm /Ty2 1 Tf [ (minimize) -377 (the) -377 (P) 92 (A) 40 (C-Bayesian) -377
(bound) -378 (direct) 1 (ly) 65 (,) -409 (lik) 10 (ely) -378 (due) -377 (to)
] TJ ET BT 9.9626 0 0 9.9626 308.862 280.539 Tm /Ty2 1 Tf [ (the) -305 (complicating)
-306 (square-root) -305 (term) -306 (in) -305 (Eq.) ] TJ ET /Cs1 cs 1 0 0
sc BT 9.9626 0 0 9.9626 473.215 280.539 Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc
BT 9.9626 0 0 9.9626 478.1963 280.539 Tm /Ty2 1 Tf [ (.) -476 (Ho) 25 (we)
25 (v) 15 (er) 40 (,) -320 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 540.1338 280.539
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 308.862 268.583 Tm
/Ty2 1 Tf [ (is) -349 (only) -349 (one) -349 (instance) -349 (out) -349 (of)
-349 (P) 92 (A) 40 (C-Bayesian) -349 (bounds) -349 (dened) ] TJ ET BT 9.9626 0 0 9.9626 308.862 256.628
Tm /Ty2 1 Tf [ (in) -257 (Germain) -258 (et) -257 (al.) -258 ([) ] TJ ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 381.9277 256.628 Tm /Ty2 1 Tf (18) Tj ET
/Cs2 cs 0 sc BT 9.9626 0 0 9.9626 391.8903 256.628 Tm /Ty2 1 Tf [ (].) -332
(According) -258 (to) -257 (their) -257 (frame) 25 (w) 10 (ork,) -260 (there)
] TJ ET BT 9.9626 0 0 9.9626 308.862 244.673 Tm /Ty2 1 Tf [ (is) -248 (also)
-248 (a) ] TJ ET BT 9.9626 0 0 9.9626 343.392 244.673 Tm /Ty6 1 Tf [ (linear)
20 (-form) ] TJ ET BT 9.9626 0 0 9.9626 391.6 244.673 Tm /Ty2 1 Tf [ (of)
-248 (the) -248 (bound) -248 (related) -248 (to) -248 (Bayesian) -248 (infer)
20 (-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 232.718 Tm /Ty2 1 Tf [ (ence)
-266 (which) -267 (can) -266 (be) -266 (analytically) -266 (minimized) -267
(with) -266 (the) -266 (aid) -266 (of) -267 (a) ] TJ ET BT 9.9626 0 0 9.9626 308.862 220.763
Tm /Ty2 1 Tf [ (Gibbs) -234 (distrib) 20 (ution) -234 ([) ] TJ ET /Cs1 cs
0 1 0 sc BT 9.9626 0 0 9.9626 386.391 220.763 Tm /Ty2 1 Tf (12) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 396.3536 220.763 Tm /Ty2 1 Tf (,) Tj ET /Cs1
cs 0 1 0 sc BT 9.9626 0 0 9.9626 399.8803 220.763 Tm /Ty2 1 Tf (17) Tj ET
/Cs2 cs 0 sc BT 9.9626 0 0 9.9626 409.8429 220.763 Tm /Ty2 1 Tf (,) Tj ET
/Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 413.3697 220.763 Tm /Ty2 1 Tf (40) Tj
ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 423.3323 220.763 Tm /Ty2 1 Tf [ (].)
-304 (W) 80 (e) -234 (le) 25 (v) 15 (erage) -235 (this) -234 (linear) 20 (-form)
] TJ ET BT 9.9626 0 0 9.9626 308.862 208.808 Tm /Ty2 1 Tf [ (of) -306 (the)
-305 (P) 92 (A) 40 (C-Bayesian) -306 (bound,) -319 (and) -306 (adapt) -306
(it) -305 (for) -306 (bounding) -306 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 196.852
Tm /Ty2 1 Tf [ (rob) 20 (ustness) -250 (g) 5 (ap:) ] TJ ET BT 9.9626 0 0 9.9626 308.862 174.839
Tm /Ty1 1 Tf [ (Theor) 18 (em) -250 (2) -250 (\(Linear) 37 (-F) 25 (orm) -250
(P) 74 (A) 55 (C-Bay) 10 (esian) -250 (Bound) -250 ([) ] TJ ET /Cs1 cs 0 1
0 sc BT 9.9626 0 0 9.9626 515.6059 174.839 Tm /Ty1 1 Tf (17) Tj ET /Cs2 cs
0 sc BT 9.9626 0 0 9.9626 525.5685 174.839 Tm /Ty1 1 Tf (]\)) Tj ET BT 9.9626 0 0 9.9626 308.862 162.883
Tm /Ty6 1 Tf [ (Under) -481 (the) -482 (same) -481 (assumptions) -482 (as)
-481 (in) -482 (Theor) 37 (em) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 501.459 162.883
Tm /Ty6 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 506.4403 162.883
Tm /Ty6 1 Tf [ (,) -539 (for) -482 (any) ] TJ ET BT 0.3316 Tc 9.9626 0 0 9.9626 308.862 150.928
Tm /Ty8 1 Tf (*) Tj /Ty7 1 Tf (>) Tj 0 Tc ET BT 9.9626 0 0 9.9626 328.306 150.928
Tm /Ty12 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 333.288 150.928 Tm /Ty6 1 Tf
[ (,) -250 (with) -250 (a) -250 (pr) 45 (obability) -250 (at) -250 (least)
] TJ ET BT 9.9626 0 0 9.9626 443.274 150.928 Tm /Ty12 1 Tf (1) Tj ET BT 9.9626 0 0 9.9626 450.469 150.928
Tm /Ty14 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 460.432 150.928 Tm /Ty8 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 465.915 150.928 Tm /Ty6 1 Tf (,) Tj ET BT
9.9626 0 0 9.9626 332.294 128.972 Tm /Ty17 1 Tf (E) Tj ET BT 6.9738 0 0 6.9738 338.936 127.478
Tm /Ty11 1 Tf (!) Tj ET BT 0.0008 Tc 6.9738 0 0 6.9738 342.945 127.478 Tm
/Ty16 1 Tf (#) Tj /Ty15 1 Tf (Q) Tj 0 Tc ET BT 9.9626 0 0 9.9626 355.339 128.972
Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 362.98 128.972 Tm /Ty12 1 Tf (\()
Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 366.855 128.972 Tm /Ty8 1 Tf (") Tj /Ty7
1 Tf (,) Tj 0 Tc ET BT 9.9626 0 0 9.9626 376.236 128.972 Tm /Ty13 1 Tf (D)
Tj ET BT 9.9626 0 0 9.9626 384.198 128.972 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 390.84 128.972
Tm /Ty14 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 401.356 128.972 Tm /Ty17 1 Tf
(E) Tj ET BT 6.9738 0 0 6.9738 407.998 127.478 Tm /Ty11 1 Tf (!) Tj ET BT
0.0008 Tc 6.9738 0 0 6.9738 412.007 127.478 Tm /Ty16 1 Tf (#) Tj /Ty15 1 Tf
(Q) Tj 0 Tc ET BT 9.9626 0 0 9.9626 426.561 131.49 Tm /Ty12 1 Tf Tj ET
BT 9.9626 0 0 9.9626 424.401 128.972 Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 432.042 128.972
Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 435.917 128.972 Tm
/Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 453.823 133.086
Tm /Ty10 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 461.391 128.972 Tm /Ty12 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 400.802 108.24 Tm /Ty12 1 Tf (+) Tj ET BT
9.9626 0 0 9.9626 412.55 114.98 Tm /Ty12 1 Tf (1) Tj ET q 1 0 0 1 411.96 110.731
cm 0 0 m 6.161 0 l S Q BT 9.9626 0 0 9.9626 411.96 101.406 Tm /Ty8 1 Tf (*)
Tj ET BT 9.9626 0 0 9.9626 419.317 108.24 Tm /Ty12 1 Tf [ (K) -0.8 (L\() ]
TJ ET BT 0.0007 Tc 9.9626 0 0 9.9626 437.167 108.24 Tm /Ty13 1 Tf (Q||P) Tj
0 Tc ET BT 0.2229 Tc 9.9626 0 0 9.9626 458.586 108.24 Tm /Ty12 1 Tf (\)+)
Tj 0 Tc ET BT 9.9626 0 0 9.9626 474.637 108.24 Tm /Ty7 1 Tf (C) Tj ET BT 9.9626 0 0 9.9626 482.47 108.24
Tm /Ty12 1 Tf (\() Tj ET BT 0.0582 Tc 9.9626 0 0 9.9626 486.345 108.24 Tm
/Ty8 1 Tf (\)) Tj /Ty7 1 Tf [ (,) -109 ] TJ /Ty8 1 Tf [ (*) 5 ] TJ /Ty7 1
Tf [ (,) -110 (m) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 515.038 108.24 Tm /Ty12
1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 518.912 108.24 Tm /Ty7 1 Tf (,) Tj ET
BT 9.9626 0 0 9.9626 533.496 108.24 Tm /Ty2 1 Tf (\(4\)) Tj ET BT 9.9626 0 0 9.9626 308.862 81
Tm /Ty6 1 Tf [ (wher) 37 (e) ] TJ ET BT 9.9626 0 0 9.9626 335.332 81 Tm /Ty7
1 Tf (C) Tj ET BT 9.9626 0 0 9.9626 343.165 81 Tm /Ty12 1 Tf (\() Tj ET BT
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20 (-parameter) -208 (that) -207 (balances) -207 (the) -207 (three) -208 (terms)
-207 (on) ] TJ ET BT 9.9626 0 0 9.9626 50.112 698.082 Tm /Ty2 1 Tf [ (the)
-300 (RHS.) -301 (A) -300 (common) -300 (choice) -301 (is) ] TJ ET BT 9.9626 0 0 9.9626 176.818 698.082
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1 Tf (13) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 93.78804 686.127 Tm /Ty2
1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 97.73323 686.127 Tm /Ty2
1 Tf (17) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 107.6958 686.127 Tm /Ty2
1 Tf [ (].) -382 (Recently) 65 (,) -274 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 160.6172 686.127
Tm /Ty2 1 Tf (12) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 170.5798 686.127
Tm /Ty2 1 Tf [ (]) -274 (proposed) -274 (to) -273 (set) ] TJ ET BT 9.9626 0 0 9.9626 240.153 686.127
Tm /Ty13 1 Tf (P) Tj ET BT 9.9626 0 0 9.9626 250.631 686.127 Tm /Ty2 1 Tf
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Tm /Ty2 1 Tf [ (uni) 25 (v) 25 (ariate) -360 (Gaussians) -360 (and) -359 (used)
-360 (a) -360 (second-order) -360 (approxima-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 662.217
Tm /Ty2 1 Tf [ (tion) -270 (to) -271 (estimat) 1 (e) -271 (the) -270 (P) 92
(A) 40 (C-Bayesian) -270 (bound.) -371 (Applying) -270 (a) -271 (sim-) ] TJ
ET BT 9.9626 0 0 9.9626 50.112 650.261 Tm /Ty2 1 Tf [ (ilar) -330 (technique,)
-351 (we) -330 (introduce) -331 (Theorem) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 206.485 650.261
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 214.7639 650.261
Tm /Ty2 1 Tf [ (\(see) -330 (Appendix.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 279.1721 650.261
Tm /Ty2 1 Tf (A) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 50.112 638.306 Tm
/Ty2 1 Tf [ (for) -250 (the) -250 (proof\)) -250 (which) -250 (minimizes)
-250 (the) -250 (RHS) -250 (of) -250 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 240.4873 638.306
Tm /Ty2 1 Tf (4) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 245.4686 638.306
Tm /Ty2 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 50.112 616.993 Tm /Ty1 1 Tf [
(Theor) 18 (em) -250 (3) -250 (\(Minimization) -250 (of) -250 (P) 74 (A) 55
(C-Bay) 10 (esian) -250 (Bound\)) ] TJ ET BT 9.9626 0 0 9.9626 50.112 605.037
Tm /Ty6 1 Tf (If) Tj ET BT 9.9626 0 0 9.9626 59.893 605.037 Tm /Ty13 1 Tf
(P) Tj ET BT 9.9626 0 0 9.9626 72.638 605.037 Tm /Ty12 1 Tf (=) Tj ET BT 9.9626 0 0 9.9626 85.383 605.037
Tm /Ty13 1 Tf (N) Tj ET BT 9.9626 0 0 9.9626 95.026 605.037 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 98.9 605.037 Tm /Ty25 1 Tf (0) Tj ET BT 0.1678
Tc 9.9626 0 0 9.9626 104.629 605.037 Tm /Ty7 1 Tf (,) Tj /Ty8 1 Tf (+) Tj
0 Tc ET BT 6.9738 0 0 6.9738 115.107 608.653 Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 114.749 602.565
Tm /Ty9 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 119.576 605.037 Tm /Ty12 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 123.45 605.037 Tm /Ty6 1 Tf [ (,) -401 (and)
] TJ ET BT 9.9626 0 0 9.9626 148.574 605.037 Tm /Ty13 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 160.405 605.037
Tm /Ty6 1 Tf [ (is) -371 (also) -371 (a) -370 (pr) 45 (oduct) -371 (of) -371
(univariate) ] TJ ET BT 9.9626 0 0 9.9626 50.112 593.082 Tm /Ty6 1 Tf [ (Gaussian)
-318 (distrib) 20 (utions,) -335 (then) -318 (the) -318 (mini) 1 (mu) -1 (m)
-317 (of) -318 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 250.4798 593.082
Tm /Ty6 1 Tf (4) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 258.6292 593.082
Tm /Ty6 1 Tf [ (w) 74 (.r) 111 (.t) ] TJ ET BT 9.9626 0 0 9.9626 278.226 593.082
Tm /Ty13 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 50.112 581.127 Tm /Ty6 1 Tf [
(can) -250 (be) -250 (bounded) -250 (by) ] TJ ET BT 0.0003 Tc 9.9626 0 0 9.9626 67.541 559.813
Tm /Ty12 1 Tf [ (mi) -1 (n) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 72.58 553.387
Tm /Ty15 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 85.806 559.813 Tm /Ty17 1 Tf
(E) Tj ET BT 6.9738 0 0 6.9738 92.448 558.319 Tm /Ty11 1 Tf (!) Tj ET BT 0.0008
Tc 6.9738 0 0 6.9738 96.457 558.319 Tm /Ty16 1 Tf (#) Tj /Ty15 1 Tf (Q) Tj
0 Tc ET BT 9.9626 0 0 9.9626 108.851 559.813 Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 116.492 559.813
Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 120.367 559.813 Tm
/Ty8 1 Tf (") Tj /Ty7 1 Tf (,) Tj 0 Tc ET BT 9.9626 0 0 9.9626 129.748 559.813
Tm /Ty13 1 Tf (D) Tj ET BT 9.9626 0 0 9.9626 137.71 559.813 Tm /Ty12 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 58.132 534.568 Tm /Ty14 1 Tf (%) Tj ET BT
0.0003 Tc 9.9626 0 0 9.9626 67.541 534.568 Tm /Ty12 1 Tf [ (mi) -1 (n) ] TJ
0 Tc ET BT 6.9738 0 0 6.9738 72.58 528.142 Tm /Ty15 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 84.146 534.568
Tm /Ty13 1 Tf ({) Tj ET BT 9.9626 0 0 9.9626 89.127 534.568 Tm /Ty17 1 Tf
(E) Tj ET BT 6.9738 0 0 6.9738 95.769 533.074 Tm /Ty11 1 Tf (!) Tj ET BT 0.0008
Tc 6.9738 0 0 6.9738 99.778 533.074 Tm /Ty16 1 Tf (#) Tj /Ty15 1 Tf (Q) Tj
0 Tc ET BT 9.9626 0 0 9.9626 114.332 537.086 Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 112.172 534.568
Tm /Ty7 1 Tf (R) Tj ET BT 9.9626 0 0 9.9626 119.813 534.568 Tm /Ty12 1 Tf
(\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 123.688 534.568 Tm /Ty8 1 Tf (")
Tj /Ty7 1 Tf [ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 141.594 538.681
Tm /Ty10 1 Tf (m) Tj ET BT 0.2229 Tc 9.9626 0 0 9.9626 149.162 534.568 Tm
/Ty12 1 Tf (\)+) Tj 0 Tc ET BT 9.9626 0 0 9.9626 166.998 541.308 Tm /Ty12
1 Tf (1) Tj ET 0.398 w q 1 0 0 1 166.408 537.059 cm 0 0 m 6.161 0 l S Q BT
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Tm /Ty12 1 Tf [ (K) -0.8 (L\() ] TJ ET BT 0.0007 Tc 9.9626 0 0 9.9626 191.615 534.568
Tm /Ty13 1 Tf (Q||P) Tj 0 Tc ET BT 9.9626 0 0 9.9626 213.034 534.568 Tm /Ty12
1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 216.909 534.568 Tm /Ty13 1 Tf (}) Tj
ET BT 9.9626 0 0 9.9626 224.104 534.568 Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 234.067 534.568
Tm /Ty7 1 Tf (C) Tj ET BT 9.9626 0 0 9.9626 241.9 534.568 Tm /Ty12 1 Tf (\()
Tj ET BT 0.0582 Tc 9.9626 0 0 9.9626 245.774 534.568 Tm /Ty8 1 Tf (\)) Tj
/Ty7 1 Tf [ (,) -109 ] TJ /Ty8 1 Tf [ (*) 5 ] TJ /Ty7 1 Tf [ (,) -110 (m)
] TJ 0 Tc ET BT 9.9626 0 0 9.9626 274.467 534.568 Tm /Ty12 1 Tf (\)) Tj ET
BT 0.1678 Tc 9.9626 0 0 9.9626 58.132 506.962 Tm /Ty12 1 Tf [ (=m) 168 (i)
167 (n) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 73.839 500.459 Tm /Ty11 1 Tf (!)
Tj ET BT 9.9626 0 0 9.9626 84.146 506.962 Tm /Ty13 1 Tf ({) Tj ET BT 9.9626 0 0 9.9626 91.287 509.481
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 89.127 506.962 Tm /Ty7 1 Tf (R)
Tj ET BT 9.9626 0 0 9.9626 96.769 506.962 Tm /Ty12 1 Tf (\() Tj ET BT 0.0284
Tc 9.9626 0 0 9.9626 100.643 506.962 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138
(D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 118.549 511.076 Tm /Ty10 1 Tf (m) Tj
ET BT 0.2229 Tc 9.9626 0 0 9.9626 126.117 506.962 Tm /Ty12 1 Tf (\)+) Tj 0
Tc ET BT 0.0008 Tc 9.9626 0 0 9.9626 143.948 513.702 Tm /Ty13 1 Tf (||) Tj
0 Tc ET BT 9.9626 0 0 9.9626 149.483 513.702 Tm /Ty8 1 Tf (") Tj ET BT 0.0008
Tc 9.9626 0 0 9.9626 154.437 513.702 Tm /Ty13 1 Tf (||) Tj 0 Tc ET BT 6.9738 0 0 6.9738 159.971 517.318
Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 159.971 511.229 Tm /Ty9 1 Tf (2)
Tj ET q 1 0 0 1 143.363 509.453 cm 0 0 m 21.662 0 l S Q BT 9.9626 0 0 9.9626 143.363 500.129
Tm /Ty12 1 Tf (2) Tj ET BT 0.0536 Tc 9.9626 0 0 9.9626 148.345 500.129 Tm
/Ty8 1 Tf (*+) Tj 0 Tc ET BT 6.9738 0 0 6.9738 160.556 503.56 Tm /Ty9 1 Tf
(2) Tj ET BT 6.9738 0 0 6.9738 160.199 497.472 Tm /Ty9 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 168.435 506.962
Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 179.593 513.702 Tm /Ty8 1 Tf
(+) Tj ET BT 6.9738 0 0 6.9738 185.643 517.318 Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 185.286 511.229
Tm /Ty9 1 Tf (0) Tj ET q 1 0 0 1 179.593 509.453 cm 0 0 m 10.52 0 l S Q BT
9.9626 0 0 9.9626 182.362 500.129 Tm /Ty12 1 Tf (2) Tj ET BT -0.0828 Tc 9.9626 0 0 9.9626 191.308 506.962
Tm /Ty12 1 Tf [ (Tr) -84 (\() ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 205.449 506.962
Tm /Ty22 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 212.645 511.076 Tm /Ty9 1 Tf
(2) Tj ET BT 6.9738 0 0 6.9738 212.645 504.5 Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 219.312 509.481
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 217.152 506.962 Tm /Ty7 1 Tf
(R) Tj ET BT 9.9626 0 0 9.9626 224.793 506.962 Tm /Ty12 1 Tf (\() Tj ET BT
0.0284 Tc 9.9626 0 0 9.9626 228.668 506.962 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf
[ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 246.574 511.076 Tm /Ty10
1 Tf (m) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 254.142 506.962 Tm /Ty12 1 Tf
(\)\)) Tj 0 Tc ET BT 9.9626 0 0 9.9626 261.891 506.962 Tm /Ty13 1 Tf (}) Tj
ET BT 9.9626 0 0 9.9626 78.057 484.879 Tm /Ty12 1 Tf (+) Tj ET BT 9.9626 0 0 9.9626 88.02 484.879
Tm /Ty7 1 Tf (C) Tj ET BT 9.9626 0 0 9.9626 95.853 484.879 Tm /Ty12 1 Tf (\()
Tj ET BT 0.0582 Tc 9.9626 0 0 9.9626 99.727 484.879 Tm /Ty8 1 Tf (\)) Tj /Ty7
1 Tf [ (,) -109 ] TJ /Ty8 1 Tf [ (*) 5 ] TJ /Ty7 1 Tf [ (,) -110 (m) ] TJ
0 Tc ET BT 0.2229 Tc 9.9626 0 0 9.9626 128.421 484.879 Tm /Ty12 1 Tf (\)+)
Tj 0 Tc ET BT 9.9626 0 0 9.9626 144.472 484.879 Tm /Ty7 1 Tf (O) Tj ET BT
9.9626 0 0 9.9626 152.348 484.879 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 156.222 484.879
Tm /Ty8 1 Tf (+) Tj ET BT 6.9738 0 0 6.9738 162.272 488.993 Tm /Ty9 1 Tf (4)
Tj ET BT 6.9738 0 0 6.9738 161.915 482.416 Tm /Ty9 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 166.742 484.879
Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 170.616 484.879 Tm /Ty7 1 Tf
(.) Tj ET BT 9.9626 0 0 9.9626 274.746 484.879 Tm /Ty2 1 Tf (\(5\)) Tj ET
BT 9.9626 0 0 9.9626 62.067 463.565 Tm /Ty2 1 Tf [ (Assuming) -370 (that)
] TJ ET BT 9.9626 0 0 9.9626 124.797 463.565 Tm /Ty8 1 Tf (+) Tj ET BT 6.9738 0 0 6.9738 130.848 467.181
Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 130.49 461.093 Tm /Ty9 1 Tf (0)
Tj ET BT 0.5018 Tc 9.9626 0 0 9.9626 140.304 463.565 Tm /Ty12 1 Tf (=1) Tj
0 Tc ET BT 9.9626 0 0 9.9626 158.021 463.565 Tm /Ty7 1 Tf (/d) Tj ET BT 9.9626 0 0 9.9626 171.877 463.565
Tm /Ty2 1 Tf [ (is) -370 (the) -371 (v) 25 (ariance) -370 (of) -370 (the)
-371 (init) 1 (ial) ] TJ ET BT 9.9626 0 0 9.9626 50.112 451.61 Tm /Ty2 1 Tf
[ (weight) -197 (matrices) -196 (where) ] TJ ET BT 9.9626 0 0 9.9626 141.198 451.61
Tm /Ty7 1 Tf (d) Tj ET BT 9.9626 0 0 9.9626 148.343 451.61 Tm /Ty2 1 Tf [
(is) -197 (the) -196 (input) -197 (feature) -196 (dimension,) -208 (then)
] TJ ET BT 9.9626 0 0 9.9626 50.112 439.655 Tm /Ty7 1 Tf (O) Tj ET BT 9.9626 0 0 9.9626 57.988 439.655
Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 61.862 439.655 Tm /Ty8 1 Tf
(+) Tj ET BT 6.9738 0 0 6.9738 67.913 443.27 Tm /Ty9 1 Tf (4) Tj ET BT 6.9738 0 0 6.9738 67.555 437.182
Tm /Ty9 1 Tf (0) Tj ET BT 0.3999 Tc 9.9626 0 0 9.9626 72.382 439.655 Tm /Ty12
1 Tf (\)=) Tj 0 Tc ET BT 9.9626 0 0 9.9626 91.959 439.655 Tm /Ty7 1 Tf (O)
Tj ET BT 9.9626 0 0 9.9626 99.835 439.655 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 103.709 439.655
Tm /Ty7 1 Tf (d) Tj ET BT 6.9738 0 0 6.9738 108.895 443.27 Tm /Ty16 1 Tf (!)
Tj ET BT 6.9738 0 0 6.9738 115.121 443.27 Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 119.591 439.655
Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 123.465 439.655 Tm /Ty2 1 Tf
[ (.) -507 (Theorem) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 170.1099 439.655
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 178.2394 439.655
Tm /Ty2 1 Tf [ (considerably) -315 (simplies) -316 (the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 427.7
Tm /Ty2 1 Tf [ (optimization) -281 (problem) -281 (from) -281 (one) -281 (o)
15 (v) 15 (er) -281 (the) -281 (space) -281 (of) -281 (probabil-) ] TJ ET
BT 9.9626 0 0 9.9626 50.112 415.745 Tm /Ty2 1 Tf [ (ity) -233 (density) -234
(f) 1 (u) -1 (nc) 1 (tions) ] TJ ET BT 9.9626 0 0 9.9626 133.467 415.745 Tm
/Ty13 1 Tf (Q) Tj ET BT 9.9626 0 0 9.9626 143.927 415.745 Tm /Ty2 1 Tf [ (to)
-233 (one) -234 (o) 15 (v) 15 (er) -233 (model) -233 (weights) ] TJ ET BT
9.9626 0 0 9.9626 250.988 415.745 Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 255.942 415.745
Tm /Ty2 1 Tf [ (.) -304 (More-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 403.789
Tm /Ty2 1 Tf [ (o) 15 (v) 15 (er) 40 (,) -245 (the) -243 (resulting) -243
(bound) -243 (\(RHS) -244 (of) -243 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 203.0877 403.789
Tm /Ty2 1 Tf (5) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 208.069 403.789 Tm
/Ty2 1 Tf [ (\)) -243 (contains) -243 (the) -244 (T) 35 (race) ] TJ ET BT
9.9626 0 0 9.9626 50.112 391.834 Tm /Ty2 1 Tf [ (of) -270 (Hessian) -270 (\(T)
35 (rH\)) -270 (term) ] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 141.852 391.834
Tm /Ty12 1 Tf [ (Tr) -84 (\() ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 155.993 391.834
Tm /Ty22 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 163.189 395.45 Tm /Ty9 1 Tf (2)
Tj ET BT 6.9738 0 0 6.9738 163.189 389.013 Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 169.856 394.353
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 167.696 391.834 Tm /Ty7 1 Tf
(R) Tj ET BT 9.9626 0 0 9.9626 175.337 391.834 Tm /Ty12 1 Tf (\() Tj ET BT
0.0284 Tc 9.9626 0 0 9.9626 179.212 391.834 Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf
[ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 197.118 395.45 Tm /Ty10 1
Tf (m) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 204.686 391.834 Tm /Ty12 1 Tf
(\)\)) Tj 0 Tc ET BT 9.9626 0 0 9.9626 215.123 391.834 Tm /Ty2 1 Tf [ (of)
-270 (the) -270 (rob) 20 (ust) -270 (loss,) ] TJ ET BT 9.9626 0 0 9.9626 50.112 379.879
Tm /Ty2 1 Tf [ (which) -222 (sums) -221 (the) -222 (loss) -221 (surf) 10 (ace)
-222 (curv) 25 (atures) -221 (in) -222 (all) -221 (directions.) -301 (F) 15
(or) ] TJ ET BT 9.9626 0 0 9.9626 50.112 367.924 Tm /Ty2 1 Tf [ (a) -340 (con)
40 (v) 15 (e) 15 (x) -340 (loss,) -362 (the) -340 (Hessian) -340 (is) -340
(positi) 25 (v) 15 (e) -340 (semi-denite) -340 (\(PSD\)) ] TJ ET BT 9.9626 0 0 9.9626 50.112 355.969
Tm /Ty2 1 Tf [ (in) -285 (which) -284 (case) -285 (trace) -285 (minimization)
-284 (leads) ] TJ ET BT 9.9626 0 0 9.9626 209.343 355.969 Tm /Ty8 1 Tf (")
Tj ET BT 9.9626 0 0 9.9626 217.132 355.969 Tm /Ty2 1 Tf [ (to) -285 (a) -284
(atter) -285 (re) 15 (gion) ] TJ ET BT 9.9626 0 0 9.9626 50.112 344.014 Tm
/Ty2 1 Tf [ (of) -268 (the) -268 (loss) -269 (surf) 10 (ace.) -364 (Although)
-268 (in) -268 (general,) -273 (our) -268 (Hessian) -269 (is) -268 (not) ]
TJ ET BT 9.9626 0 0 9.9626 50.112 332.058 Tm /Ty2 1 Tf [ (PSD,) -357 (empirically)
-358 (we) -357 -357 (that) -358 (i) 1 (ts) -358 (lar) 18 (gest) -357
(eigen) 40 (v) 25 (alue) -357 (has) -358 (a) ] TJ ET BT 9.9626 0 0 9.9626 50.112 320.103
Tm /Ty2 1 Tf [ (much) -229 (lar) 18 (ger) -230 (magnitude) -229 (than) -229
(the) -229 (least) -230 (ones) -229 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 222.5248 320.103
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 227.5061 320.103
Tm /Ty2 1 Tf [ (]) -229 (and) -229 (that) -230 (trace) ] TJ ET BT 9.9626 0 0 9.9626 50.112 308.148
Tm /Ty2 1 Tf [ (minimization) -244 (correlates) -244 (with) -243 (minimizing)
-244 (the) -244 (standard) -244 (de) 25 (vi-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 296.193
Tm /Ty2 1 Tf [ (ation) -313 (of) -313 (the) -312 (eigen) 40 (v) 25 (alues)
-313 (\(see) -313 (Figure) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 197.6481 296.193
Tm /Ty2 1 Tf (5) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 205.7477 296.193
Tm /Ty2 1 Tf [ (in) -312 (the) -313 (appendix\),) -329 (so) ] TJ ET BT 9.9626 0 0 9.9626 50.112 284.238
Tm /Ty2 1 Tf [ (that) -250 (the) -250 (o) 15 (v) 15 (erall) -250 (curv) 25
(ature) -250 (is) -250 (ef) 25 (fecti) 25 (v) 15 (ely) -250 (decreases.) ]
TJ ET BT 9.9626 0 0 9.9626 62.067 272.283 Tm /Ty2 1 Tf [ (The) -283 (RHS)
-283 (of) -283 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 130.0817 272.283
Tm /Ty2 1 Tf (5) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 137.8824 272.283
Tm /Ty2 1 Tf [ (in) -283 (Theorem) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 187.2371 272.283
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 195.0378 272.283
Tm /Ty2 1 Tf [ (pro) 15 (vides) -283 (a) -284 (training) -283 (ob-) ] TJ ET
BT 9.9626 0 0 9.9626 50.112 260.327 Tm /Ty2 1 Tf [ (jecti) 25 (v) 15 (e) -353
(function) -354 (that) -353 (bounds) -353 (the) -354 (optimal) -353 (test)
-354 (error) -353 (up) -353 (to) -354 (a) ] TJ ET BT 9.9626 0 0 9.9626 50.112 248.372
Tm /Ty2 1 Tf [ (constant.) -301 (Ho) 25 (we) 25 (v) 15 (er) 40 (,) -229 (e)
25 (v) 25 (aluating) -224 (and) -224 (minimizing) -223 (the) -224 (bound)
-224 (in) ] TJ ET BT 9.9626 0 0 9.9626 50.112 236.417 Tm /Ty2 1 Tf (Eq.) Tj
ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 66.45066 236.417 Tm /Ty2 1 Tf (5)
Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 74.21153 236.417 Tm /Ty2 1 Tf [ (requires)
-279 (computing) -279 (the) -279 (T) 35 (race) -279 (of) -280 (Hessian) -279
(\(T) 35 (rH\)) -279 (term.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 224.462 Tm
/Ty2 1 Tf [ (Unfortunately) 65 (,) -290 (computing) -281 (the) -282 (Hessian)
-281 (directly) -282 (by) -282 (applying) ] TJ ET BT 9.9626 0 0 9.9626 50.112 212.507
Tm /Ty2 1 Tf [ (auto-dif) 25 (ferentiation) -276 (twice) -276 (is) -276 (infeasible)
-276 (for) -276 (a) -276 (lar) 18 (ge) -276 (deep) -276 (net-) ] TJ ET BT
9.9626 0 0 9.9626 50.112 200.552 Tm /Ty2 1 Tf [ (w) 10 (ork.) -299 (Another)
-215 (solution) -216 (is) -215 (to) -216 (apply) -216 (Hut) 1 (chinson) 55
(s) -216 (method) -216 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 278.0663 200.552
Tm /Ty2 1 Tf (5) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 283.0476 200.552
Tm /Ty2 1 Tf (]) Tj ET BT 9.9626 0 0 9.9626 50.112 188.596 Tm /Ty2 1 Tf [
(to) -249 (randomly) -250 (approximate) -249 (the) -250 (T) 35 (rH,) -249
(ho) 25 (we) 25 (v) 15 (er) 40 (,) -250 (the) -249 (v) 25 (ariance) -250 (of)
] TJ ET BT 9.9626 0 0 9.9626 50.112 176.641 Tm /Ty2 1 Tf [ (the) -292 (resulting)
-292 (estimator) -292 (is) -293 (too) -292 (high) -292 (and) -292 (it) -292
(ends) -292 (up) -293 (being) -292 (too) ] TJ ET BT 9.9626 0 0 9.9626 50.112 164.686
Tm /Ty2 1 Tf [ (noisy) -250 (for) -250 (training) -250 (in) -250 (practice.)
] TJ ET BT 9.9626 0 0 9.9626 62.067 152.731 Tm /Ty2 1 Tf [ (Instead,) -298
(we) -289 (propose) -289 (to) -288 (restrict) -289 (T) 35 (rH) -288 (re) 15
(gularization) -289 (to) -289 (the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 140.776
Tm /Ty2 1 Tf [ (top) -211 (layer) -211 (of) -211 (the) -211 (deep) -211 (netw)
10 (ork) -212 (only) 65 (.) -297 (Although) -211 (this) -211 (restriction)
] TJ ET BT 9.9626 0 0 9.9626 50.112 128.821 Tm /Ty2 1 Tf [ (brings) -216 (approximation)
-215 (error) -216 (to) -216 (the) -215 (bound,) -223 (it) -215 (has) -216
(tw) 10 (o) -216 (benets.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 116.865 Tm
/Ty2 1 Tf [ (First,) -247 (the) -246 (T) 35 (rH) -246 (on) -246 (the) -246
(top) -246 (layer) -246 (has) -247 (simple) -246 (analytical) -246 (e) 15
(xpres-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 104.91 Tm /Ty2 1 Tf [ (sions)
-222 (\(Section) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 108.2238 104.91
Tm /Ty2 1 Tf (3.1) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 120.6771 104.91
Tm /Ty2 1 Tf [ (\).) -301 (Second,) -227 (we) -222 (sho) 25 (w) -223 (that)
-222 (the) -222 (top-layer) -222 (T) 35 (rH) ] TJ ET BT 9.9626 0 0 9.9626 50.112 92.955
Tm /Ty2 1 Tf [ (re) 15 (gularization) -344 (ef) 25 (fecti) 25 (v) 15 (ely)
-344 (re) 15 (gularizes) -343 (the) -344 (T) 35 (rH) -344 (of) -344 (the)
-344 (entire) ] TJ ET BT 9.9626 0 0 9.9626 50.112 81 Tm /Ty2 1 Tf [ (netw)
10 (ork) -250 (as) -250 (well) -250 (\(Section) ] TJ ET /Cs1 cs 1 0 0 sc BT
9.9626 0 0 9.9626 151.2822 81 Tm /Ty2 1 Tf (3.2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 163.7355 81
Tm /Ty2 1 Tf (\).) Tj ET BT 10.9589 0 0 10.9589 308.862 710.037 Tm /Ty1 1
Tf [ (3.1.) -165 (T) 92 (op-Lay) 10 (er) -164 (T) 74 (rH) -165 (r) 18 (egularizers)
-164 (f) 25 (or) -165 (A) 95 (T) -164 (&) -165 (TRADES) ] TJ ET BT 9.9626 0 0 9.9626 320.817 692.104
Tm /Ty2 1 Tf [ (The) -616 (netw) 10 (ork) -615 (parameter) ] TJ ET BT 9.9626 0 0 9.9626 427.087 692.104
Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 438.174 692.104 Tm /Ty2 1 Tf [
(can) -616 (be) -615 (decomposed) -616 (into) ] TJ ET BT 9.9626 0 0 9.9626 308.862 680.149
Tm /Ty13 1 Tf ({) Tj ET BT 9.9626 0 0 9.9626 313.843 680.149 Tm /Ty8 1 Tf
(") Tj ET BT 6.9738 0 0 6.9738 318.52 678.655 Tm /Ty10 1 Tf (t) Tj ET BT 0.1678
Tc 9.9626 0 0 9.9626 322.028 680.149 Tm /Ty7 1 Tf (,) Tj /Ty8 1 Tf (") Tj
0 Tc ET BT 6.9738 0 0 6.9738 331.133 678.655 Tm /Ty10 1 Tf (b) Tj ET BT 9.9626 0 0 9.9626 335.134 680.149
Tm /Ty13 1 Tf (}) Tj ET BT 9.9626 0 0 9.9626 342.178 680.149 Tm /Ty2 1 Tf
(where) Tj ET BT 9.9626 0 0 9.9626 368.579 680.149 Tm /Ty8 1 Tf (") Tj ET
BT 6.9738 0 0 6.9738 373.256 678.655 Tm /Ty10 1 Tf (t) Tj ET BT 9.9626 0 0 9.9626 378.826 680.149
Tm /Ty2 1 Tf [ (denotes) -207 (the) -207 (weights) -207 (of) -207 (the) -207
(top) -207 (layer) -207 (and) ] TJ ET BT 9.9626 0 0 9.9626 536.433 680.149
Tm /Ty8 1 Tf (") Tj ET BT 6.9738 0 0 6.9738 541.11 678.655 Tm /Ty10 1 Tf (b)
Tj ET BT 9.9626 0 0 9.9626 308.862 668.194 Tm /Ty2 1 Tf [ (denotes) -281 (the)
-280 (weights) -281 (of) -280 (the) -281 (remaining) -280 (\(bottom\)) -281
(netw) 10 (ork.) -402 (In) ] TJ ET BT 9.9626 0 0 9.9626 308.862 656.239 Tm
/Ty2 1 Tf [ (this) -257 (case,) -260 (the) -257 (logits) -258 (can) -257 (be)
-257 (e) 15 (xpressed) -258 (as) ] TJ ET BT 9.9626 0 0 9.9626 468.416 656.239
Tm /Ty7 1 Tf (g) Tj ET BT 6.9738 0 0 6.9738 473.168 654.744 Tm /Ty11 1 Tf
(!) Tj ET BT 9.9626 0 0 9.9626 477.676 656.239 Tm /Ty12 1 Tf (\() Tj ET BT
9.9626 0 0 9.9626 481.55 656.239 Tm /Ty7 1 Tf (x) Tj ET BT 0.2929 Tc 9.9626 0 0 9.9626 487.244 656.239
Tm /Ty12 1 Tf (\)=) Tj 0 Tc ET BT 9.9626 0 0 9.9626 504.677 656.239 Tm /Ty8
1 Tf (") Tj ET BT 6.9738 0 0 6.9738 509.63 659.854 Tm /Ty16 1 Tf (%) Tj ET
BT 6.9738 0 0 6.9738 509.354 653.776 Tm /Ty10 1 Tf (t) Tj ET BT 9.9626 0 0 9.9626 516.355 656.239
Tm /Ty7 1 Tf (f) Tj ET BT 6.9738 0 0 6.9738 521.233 654.744 Tm /Ty11 1 Tf
(!) Tj ET BT 4.9813 0 0 4.9813 525.028 653.687 Tm /Ty20 1 Tf (b) Tj ET BT
9.9626 0 0 9.9626 529.179 656.239 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 533.053 656.239
Tm /Ty7 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 538.747 656.239 Tm /Ty12 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 542.621 656.239 Tm /Ty2 1 Tf (,) Tj ET BT
9.9626 0 0 9.9626 308.862 644.284 Tm /Ty2 1 Tf (where) Tj ET BT 9.9626 0 0 9.9626 335.596 644.284
Tm /Ty7 1 Tf (f) Tj ET BT 6.9738 0 0 6.9738 340.473 642.789 Tm /Ty11 1 Tf
(!) Tj ET BT 4.9813 0 0 4.9813 344.268 641.732 Tm /Ty20 1 Tf (b) Tj ET BT
9.9626 0 0 9.9626 348.419 644.284 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 352.294 644.284
Tm /Ty7 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 357.988 644.284 Tm /Ty12 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 364.257 644.284 Tm /Ty2 1 Tf [ (is) -240 (the)
-241 (penultimate) -240 (layer) -241 (feature.) -306 (Furthermore,) ] TJ ET
BT 9.9626 0 0 9.9626 308.862 632.329 Tm /Ty2 1 Tf [ (we) -400 (dene) ] TJ
ET BT 9.9626 0 0 9.9626 352.794 632.329 Tm /Ty7 1 Tf (h) Tj ET BT 9.9626 0 0 9.9626 358.534 632.329
Tm /Ty12 1 Tf (\() Tj ET BT 0.0005 Tc 9.9626 0 0 9.9626 362.408 632.329 Tm
/Ty7 1 Tf [ (x,) -167 ] TJ /Ty8 1 Tf (") Tj 0 Tc ET BT 0.5559 Tc 9.9626 0 0 9.9626 377.483 632.329
Tm /Ty12 1 Tf (\)=) Tj 0 Tc ET BT 9.9626 0 0 9.9626 400.17 632.329 Tm /Ty7
1 Tf (s) Tj ET BT 9.9626 0 0 9.9626 404.84 632.329 Tm /Ty12 1 Tf (\() Tj ET
BT 9.9626 0 0 9.9626 408.714 632.329 Tm /Ty7 1 Tf (g) Tj ET BT 6.9738 0 0 6.9738 413.466 630.834
Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 417.973 632.329 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 421.848 632.329 Tm /Ty7 1 Tf (x) Tj ET BT
0.0009 Tc 9.9626 0 0 9.9626 427.542 632.329 Tm /Ty12 1 Tf (\)\)) Tj 0 Tc ET
BT 9.9626 0 0 9.9626 438.61 632.329 Tm /Ty14 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 449.678 632.329
Tm /Ty7 1 Tf (s) Tj ET BT 9.9626 0 0 9.9626 454.348 632.329 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 458.223 632.329 Tm /Ty7 1 Tf (g) Tj ET BT
6.9738 0 0 6.9738 462.975 630.834 Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 467.482 632.329
Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 471.356 632.329 Tm /Ty7 1 Tf
(x) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 477.05 632.329 Tm /Ty12 1 Tf (\)\))
Tj 0 Tc ET BT 6.9738 0 0 6.9738 484.799 635.944 Tm /Ty9 1 Tf (2) Tj ET BT
9.9626 0 0 9.9626 489.268 632.329 Tm /Ty2 1 Tf [ (.) -760 (W) 80 (e) -399
(present) ] TJ ET BT 9.9626 0 0 9.9626 308.862 620.373 Tm /Ty2 1 Tf [ (the)
-297 (analytical) -297 (forms) -297 (of) -297 (the) -297 (top-layer) -297
(T) 35 (rH) -297 (w) 65 (.r) 55 (.t.) -451 (the) -297 (A) 111 (T) -297 (and)
] TJ ET BT 9.9626 0 0 9.9626 308.862 608.418 Tm /Ty2 1 Tf [ (TRADES) -348
(losses) -348 (in) -348 (Proposition) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 438.9736 608.418
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 447.4218 608.418
Tm /Ty2 1 Tf (and) Tj ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 465.2748 608.418
Tm /Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 473.7331 608.418
Tm /Ty2 1 Tf [ (\(additional) -348 (e) 15 (xam-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 596.463
Tm /Ty2 1 Tf [ (ples) -191 (of) -191 (other) -192 (adv) 15 (ersarial) -191
(losses) -191 (are) -191 (pro) 15 (vided) -191 (in) -191 (Appendix) ] TJ ET
/Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 532.6618 596.463 Tm /Ty2 1 Tf (B) Tj
ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 539.3069 596.463 Tm /Ty2 1 Tf (\).) Tj
ET BT 9.9626 0 0 9.9626 308.862 575.524 Tm /Ty1 1 Tf [ (Pr) 18 (oposition)
-250 (1) -250 (\(T) 74 (rH) -250 (f) 25 (or) -250 (A) 95 (T\)) ] TJ ET BT
9.9626 0 0 9.9626 427.954 575.524 Tm /Ty6 1 Tf [ (Given) -290 (a) -290 (tr)
15 (aining) -290 (dataset) ] TJ ET BT 9.9626 0 0 9.9626 529.019 575.524 Tm
/Ty7 1 Tf (D) Tj ET BT 6.9738 0 0 6.9738 537.544 579.139 Tm /Ty10 1 Tf (m)
Tj ET BT 9.9626 0 0 9.9626 308.862 563.569 Tm /Ty6 1 Tf [ (and) -333 (the)
-333 (adver) 10 (sarial) -333 (input) -333 (e) 20 (xample) ] TJ ET BT 9.9626 0 0 9.9626 451.885 563.569
Tm /Ty7 1 Tf (x) Tj ET BT 6.9738 0 0 6.9738 457.579 567.184 Tm /Ty16 1 Tf
(&) Tj ET BT 9.9626 0 0 9.9626 463.692 563.569 Tm /Ty6 1 Tf [ (for) -333 (eac)
15 (h) -333 (e) 20 (xample) ] TJ ET BT 9.9626 0 0 9.9626 536.927 563.569 Tm
/Ty7 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 542.621 563.569 Tm /Ty6 1 Tf (,)
Tj ET BT 9.9626 0 0 9.9626 308.862 551.614 Tm /Ty6 1 Tf [ (the) -336 (top-layer)
-336 (T) 55 (rH) -336 (of) -335 (the) -336 (A) 37 (T) -336 (loss) -336 (\(Denition)
] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 490.2411 551.614 Tm /Ty6 1 Tf
(1) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 495.2224 551.614 Tm /Ty6 1 Tf
[ (\)) -336 (is) -336 (equal) -336 (to) ] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 326.33 516.518
Tm /Ty12 1 Tf [ (Tr) -84 (\() ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 340.472 516.518
Tm /Ty22 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 347.667 520.632 Tm /Ty9 1 Tf
(2) Tj ET BT 6.9738 0 0 6.9738 347.667 514.055 Tm /Ty11 1 Tf (!) Tj ET BT
4.9813 0 0 4.9813 351.462 513.059 Tm /Ty20 1 Tf (t) Tj ET BT 9.9626 0 0 9.9626 357.426 519.037
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 355.266 516.518 Tm /Ty7 1 Tf
(R) Tj ET BT 6.9738 0 0 6.9738 362.83 515.024 Tm /Ty23 1 Tf (AT) Tj ET BT
9.9626 0 0 9.9626 371.697 516.518 Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 375.572 516.518
Tm /Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 393.478 520.632
Tm /Ty10 1 Tf (m) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 401.046 516.518 Tm
/Ty12 1 Tf [ (\)\)) -278 (=) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 425.156 523.258
Tm /Ty12 1 Tf (1) Tj ET q 1 0 0 1 423.273 519.009 cm 0 0 m 8.747 0 l S Q BT
9.9626 0 0 9.9626 423.273 509.685 Tm /Ty7 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 445.738 525.983
Tm /Ty19 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 434.877 504.148 Tm /Ty9 1 Tf
(\() Tj ET BT 0.0008 Tc 6.9738 0 0 6.9738 437.99 504.148 Tm /Ty10 1 Tf [ (x,)
1 (y) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 449.165 504.148 Tm /Ty9 1 Tf (\))
Tj ET BT 6.9738 0 0 6.9738 452.278 504.148 Tm /Ty16 1 Tf (#) Tj ET BT 6.9738 0 0 6.9738 457.647 504.148
Tm /Ty10 1 Tf (D) Tj ET BT 4.9813 0 0 4.9813 464.375 506.141 Tm /Ty20 1 Tf
(m) Tj ET BT -0.0828 Tc 9.9626 0 0 9.9626 472.651 516.518 Tm /Ty12 1 Tf [
(Tr) -84 (H) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 490.39 515.024 Tm /Ty23 1 Tf
(AT) Tj ET BT 9.9626 0 0 9.9626 499.257 516.518 Tm /Ty12 1 Tf (\() Tj ET BT
9.9626 0 0 9.9626 503.131 516.518 Tm /Ty7 1 Tf (x) Tj ET BT 6.9738 0 0 6.9738 508.825 520.632
Tm /Ty16 1 Tf (&) Tj ET BT 9.9626 0 0 9.9626 511.62 516.518 Tm /Ty12 1 Tf
(;) Tj ET BT 9.9626 0 0 9.9626 516.048 516.518 Tm /Ty8 1 Tf (") Tj ET BT 9.9626 0 0 9.9626 521.002 516.518
Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 524.876 516.518 Tm /Ty7 1 Tf
(,) Tj ET BT 9.9626 0 0 9.9626 331.755 488.467 Tm /Ty6 1 Tf [ (wher) 37 (e)
] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 363.76 488.467 Tm /Ty12 1 Tf [ (Tr)
-84 (H) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 381.499 486.972 Tm /Ty23 1 Tf (AT)
Tj ET BT 9.9626 0 0 9.9626 390.366 488.467 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 394.24 488.467
Tm /Ty7 1 Tf (x) Tj ET BT 6.9738 0 0 6.9738 399.934 492.58 Tm /Ty16 1 Tf (&)
Tj ET BT 9.9626 0 0 9.9626 402.729 488.467 Tm /Ty12 1 Tf (;) Tj ET BT 9.9626 0 0 9.9626 407.157 488.467
Tm /Ty8 1 Tf (") Tj ET BT 0.2789 Tc 9.9626 0 0 9.9626 412.11 488.467 Tm /Ty12
1 Tf (\)=) Tj 0 Tc ET BT 0.0008 Tc 9.9626 0 0 9.9626 429.268 488.467 Tm /Ty13
1 Tf (||) Tj 0 Tc ET BT 9.9626 0 0 9.9626 434.803 488.467 Tm /Ty7 1 Tf (f)
Tj ET BT 6.9738 0 0 6.9738 439.681 486.972 Tm /Ty11 1 Tf (!) Tj ET BT 4.9813 0 0 4.9813 443.475 485.915
Tm /Ty20 1 Tf (b) Tj ET BT 9.9626 0 0 9.9626 447.626 488.467 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 451.501 488.467 Tm /Ty7 1 Tf (x) Tj ET BT
6.9738 0 0 6.9738 457.195 492.58 Tm /Ty16 1 Tf (&) Tj ET BT 9.9626 0 0 9.9626 459.99 488.467
Tm /Ty12 1 Tf (\)) Tj ET BT 0.0008 Tc 9.9626 0 0 9.9626 463.864 488.467 Tm
/Ty13 1 Tf (||) Tj 0 Tc ET BT 6.9738 0 0 6.9738 469.399 492.58 Tm /Ty9 1 Tf
(2) Tj ET BT 6.9738 0 0 6.9738 469.399 486.004 Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 476.082 488.467
Tm /Ty13 1 Tf Tj ET BT 9.9626 0 0 9.9626 481.063 488.467 Tm /Ty25 1 Tf
(1) Tj ET BT 6.9738 0 0 6.9738 486.792 492.58 Tm /Ty16 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 493.517 488.467
Tm /Ty7 1 Tf (h) Tj ET BT 9.9626 0 0 9.9626 499.257 488.467 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 503.131 488.467 Tm /Ty7 1 Tf (x) Tj ET BT
6.9738 0 0 6.9738 508.825 492.58 Tm /Ty16 1 Tf (&) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 511.62 488.467
Tm /Ty7 1 Tf (,) Tj /Ty8 1 Tf (") Tj 0 Tc ET BT 9.9626 0 0 9.9626 521.002 488.467
Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 524.876 488.467 Tm /Ty7 1 Tf
(.) Tj ET BT 9.9626 0 0 9.9626 308.862 467.528 Tm /Ty1 1 Tf [ (Pr) 18 (oposition)
-250 (2) -250 (\(T) 74 (rH) -250 (f) 25 (or) -250 (TRADES\)) ] TJ ET BT 9.9626 0 0 9.9626 455.471 467.528
Tm /Ty6 1 Tf [ (Under) -648 (the) -648 (same) -648 (as-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 455.573
Tm /Ty6 1 Tf [ (sumption) -191 (in) -191 (Pr) 45 (oposition) ] TJ ET /Cs1
cs 1 0 0 sc BT 9.9626 0 0 9.9626 405.4594 455.573 Tm /Ty6 1 Tf (1) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 410.4407 455.573 Tm /Ty6 1 Tf [ (,) -202 (the)
-191 (top-layer) -191 (T) 55 (rH) -191 (of) -191 (the) -191 (TRADES) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 443.617 Tm /Ty6 1 Tf [ (loss) -250 (\(Denition)
] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 372.5131 443.617 Tm /Ty6 1 Tf
(2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 377.4944 443.617 Tm /Ty6 1 Tf
[ (\)) -250 (is) -250 (equal) -250 (to) ] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 318.58 418.42
Tm /Ty12 1 Tf [ (Tr) -84 (\() ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 332.722 418.42
Tm /Ty22 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 339.917 422.533 Tm /Ty9 1 Tf
(2) Tj ET BT 6.9738 0 0 6.9738 339.917 415.957 Tm /Ty11 1 Tf (!) Tj ET BT
4.9813 0 0 4.9813 343.712 414.961 Tm /Ty20 1 Tf (t) Tj ET BT 9.9626 0 0 9.9626 349.676 420.938
Tm /Ty12 1 Tf Tj ET BT 9.9626 0 0 9.9626 347.516 418.42 Tm /Ty7 1 Tf (R)
Tj ET BT 6.9738 0 0 6.9738 355.08 416.926 Tm /Ty23 1 Tf (T) Tj ET BT 9.9626 0 0 9.9626 359.763 418.42
Tm /Ty12 1 Tf (\() Tj ET BT 0.0284 Tc 9.9626 0 0 9.9626 363.637 418.42 Tm
/Ty8 1 Tf (") Tj /Ty7 1 Tf [ (,) -138 (D) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 381.544 422.533
Tm /Ty10 1 Tf (m) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 389.111 418.42 Tm /Ty12
1 Tf [ (\)\)) -278 (=) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 413.222 425.16 Tm
/Ty12 1 Tf (1) Tj ET q 1 0 0 1 411.339 420.911 cm 0 0 m 8.747 0 l S Q BT 9.9626 0 0 9.9626 411.339 411.586
Tm /Ty7 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 433.804 427.884 Tm /Ty19 1 Tf
(!) Tj ET BT 6.9738 0 0 6.9738 422.942 406.05 Tm /Ty9 1 Tf (\() Tj ET BT 0.0008
Tc 6.9738 0 0 6.9738 426.056 406.05 Tm /Ty10 1 Tf [ (x,) 1 (y) ] TJ 0 Tc ET
BT 6.9738 0 0 6.9738 437.23 406.05 Tm /Ty9 1 Tf (\)) Tj ET BT 6.9738 0 0 6.9738 440.344 406.05
Tm /Ty16 1 Tf (#) Tj ET BT 6.9738 0 0 6.9738 445.712 406.05 Tm /Ty10 1 Tf
(D) Tj ET BT 4.9813 0 0 4.9813 452.441 408.042 Tm /Ty20 1 Tf (m) Tj ET BT
-0.0828 Tc 9.9626 0 0 9.9626 460.717 418.42 Tm /Ty12 1 Tf [ (Tr) -84 (H) ]
TJ 0 Tc ET BT 6.9738 0 0 6.9738 478.456 416.926 Tm /Ty23 1 Tf (T) Tj ET BT
9.9626 0 0 9.9626 483.138 418.42 Tm /Ty12 1 Tf (\() Tj ET BT 0.0005 Tc 9.9626 0 0 9.9626 487.012 418.42
Tm /Ty7 1 Tf [ (x,) -167 (x) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 502.828 422.533
Tm /Ty16 1 Tf (&) Tj ET BT 9.9626 0 0 9.9626 505.623 418.42 Tm /Ty12 1 Tf
(;) Tj ET BT 9.9626 0 0 9.9626 510.051 418.42 Tm /Ty8 1 Tf (%) Tj ET BT 6.9738 0 0 6.9738 515.863 416.926
Tm /Ty10 1 Tf (t) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 519.37 418.42 Tm /Ty7
1 Tf (,) Tj /Ty8 1 Tf (") Tj 0 Tc ET BT 9.9626 0 0 9.9626 528.752 418.42 Tm
/Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 532.626 418.42 Tm /Ty7 1 Tf (,)
Tj ET BT 9.9626 0 0 9.9626 318.58 390.368 Tm /Ty6 1 Tf [ (wher) 37 (e) 10
(,) ] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 350.486 390.368 Tm /Ty12 1 Tf
[ (Tr) -84 (H) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 368.225 388.874 Tm /Ty23
1 Tf (T) Tj ET BT 9.9626 0 0 9.9626 372.907 390.368 Tm /Ty12 1 Tf (\() Tj
ET BT 0.0005 Tc 9.9626 0 0 9.9626 376.782 390.368 Tm /Ty7 1 Tf [ (x,) -167
(x) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 392.597 394.482 Tm /Ty16 1 Tf (&) Tj
ET BT 9.9626 0 0 9.9626 395.392 390.368 Tm /Ty12 1 Tf (;) Tj ET BT 9.9626 0 0 9.9626 399.82 390.368
Tm /Ty8 1 Tf (%) Tj ET BT 6.9738 0 0 6.9738 405.632 388.874 Tm /Ty10 1 Tf
(t) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 409.139 390.368 Tm /Ty7 1 Tf (,)
Tj /Ty8 1 Tf (") Tj 0 Tc ET BT 0.2789 Tc 9.9626 0 0 9.9626 418.521 390.368
Tm /Ty12 1 Tf (\)=) Tj 0 Tc ET BT 0.0008 Tc 9.9626 0 0 9.9626 435.679 390.368
Tm /Ty13 1 Tf (||) Tj 0 Tc ET BT 9.9626 0 0 9.9626 441.214 390.368 Tm /Ty7
1 Tf (f) Tj ET BT 6.9738 0 0 6.9738 446.091 388.874 Tm /Ty11 1 Tf (!) Tj ET
BT 4.9813 0 0 4.9813 449.886 387.817 Tm /Ty20 1 Tf (b) Tj ET BT 9.9626 0 0 9.9626 454.037 390.368
Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 457.911 390.368 Tm /Ty7 1 Tf
(x) Tj ET BT 9.9626 0 0 9.9626 463.605 390.368 Tm /Ty12 1 Tf (\)) Tj ET BT
0.0008 Tc 9.9626 0 0 9.9626 467.48 390.368 Tm /Ty13 1 Tf (||) Tj 0 Tc ET BT
6.9738 0 0 6.9738 473.014 394.482 Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 473.014 387.905
Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 479.698 390.368 Tm /Ty13 1 Tf
Tj ET BT 9.9626 0 0 9.9626 484.679 390.368 Tm /Ty25 1 Tf (1) Tj ET BT
6.9738 0 0 6.9738 490.407 394.482 Tm /Ty16 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 497.132 390.368
Tm /Ty7 1 Tf (h) Tj ET BT 9.9626 0 0 9.9626 502.872 390.368 Tm /Ty12 1 Tf
(\() Tj ET BT 0.0005 Tc 9.9626 0 0 9.9626 506.747 390.368 Tm /Ty7 1 Tf [ (x,)
-167 ] TJ /Ty8 1 Tf (") Tj 0 Tc ET BT 9.9626 0 0 9.9626 521.822 390.368 Tm
/Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 368.393 373.84 Tm /Ty12 1 Tf (+)
Tj ET BT 9.9626 0 0 9.9626 378.355 373.84 Tm /Ty8 1 Tf (%) Tj ET BT 6.9738 0 0 6.9738 384.167 372.346
Tm /Ty10 1 Tf (t) Tj ET BT 0.0008 Tc 9.9626 0 0 9.9626 387.675 373.84 Tm /Ty13
1 Tf (||) Tj 0 Tc ET BT 9.9626 0 0 9.9626 393.209 373.84 Tm /Ty7 1 Tf (f)
Tj ET BT 6.9738 0 0 6.9738 398.087 372.346 Tm /Ty11 1 Tf (!) Tj ET BT 4.9813 0 0 4.9813 401.882 371.289
Tm /Ty20 1 Tf (b) Tj ET BT 9.9626 0 0 9.9626 406.033 373.84 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 409.907 373.84 Tm /Ty7 1 Tf (x) Tj ET BT 6.9738 0 0 6.9738 415.601 377.954
Tm /Ty16 1 Tf (&) Tj ET BT 9.9626 0 0 9.9626 418.396 373.84 Tm /Ty12 1 Tf
(\)) Tj ET BT 0.0008 Tc 9.9626 0 0 9.9626 422.271 373.84 Tm /Ty13 1 Tf (||)
Tj 0 Tc ET BT 6.9738 0 0 6.9738 427.805 377.954 Tm /Ty9 1 Tf (2) Tj ET BT
6.9738 0 0 6.9738 427.805 371.377 Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 434.489 373.84
Tm /Ty13 1 Tf Tj ET BT 9.9626 0 0 9.9626 439.47 373.84 Tm /Ty25 1 Tf (1)
Tj ET BT 6.9738 0 0 6.9738 445.198 377.954 Tm /Ty16 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 451.923 373.84
Tm /Ty7 1 Tf (h) Tj ET BT 9.9626 0 0 9.9626 457.663 373.84 Tm /Ty12 1 Tf (\()
Tj ET BT 9.9626 0 0 9.9626 461.538 373.84 Tm /Ty7 1 Tf (x) Tj ET BT 6.9738 0 0 6.9738 467.232 377.954
Tm /Ty16 1 Tf (&) Tj ET BT 0.1678 Tc 9.9626 0 0 9.9626 470.027 373.84 Tm /Ty7
1 Tf (,) Tj /Ty8 1 Tf (") Tj 0 Tc ET BT 9.9626 0 0 9.9626 479.408 373.84 Tm
/Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 483.283 373.84 Tm /Ty7 1 Tf (.)
Tj ET BT 9.9626 0 0 9.9626 533.496 373.84 Tm /Ty2 1 Tf (\(6\)) Tj ET BT 9.9626 0 0 9.9626 308.862 352.901
Tm /Ty2 1 Tf [ (T) 80 (o) -301 (obtain) -301 (Eq.) ] TJ ET /Cs1 cs 1 0 0 sc
BT 9.9626 0 0 9.9626 366.6052 352.901 Tm /Ty2 1 Tf (6) Tj ET /Cs2 cs 0 sc
BT 9.9626 0 0 9.9626 371.5865 352.901 Tm /Ty2 1 Tf [ (,) -314 (we) -301 (stopped)
-301 (the) -301 (gradient) -302 (on) -301 (the) ] TJ ET BT 9.9626 0 0 9.9626 504.777 352.901
Tm /Ty12 1 Tf [ (K) -0.8 (Ll) -0.8 (os) -0.4 (s) ] TJ ET BT 9.9626 0 0 9.9626 537.361 352.901
Tm /Ty2 1 Tf (in) Tj ET BT 9.9626 0 0 9.9626 308.862 340.946 Tm /Ty2 1 Tf
(Denition) Tj ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 352.0499 340.946 Tm
/Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 359.8207 340.946 Tm
/Ty2 1 Tf [ (with) -279 (respect) -279 (to) -279 (the) -280 (clean) -279 (logits)
] TJ ET BT 9.9626 0 0 9.9626 485.532 340.946 Tm /Ty7 1 Tf (g) Tj ET BT 6.9738 0 0 6.9738 490.284 339.452
Tm /Ty11 1 Tf (!) Tj ET BT 9.9626 0 0 9.9626 494.792 340.946 Tm /Ty12 1 Tf
(\() Tj ET BT 9.9626 0 0 9.9626 498.666 340.946 Tm /Ty7 1 Tf (x) Tj ET BT
9.9626 0 0 9.9626 504.36 340.946 Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 508.234 340.946
Tm /Ty2 1 Tf [ (,) -287 (because) ] TJ ET BT 9.9626 0 0 9.9626 308.862 328.991
Tm /Ty2 1 Tf [ (we) -222 -221 (it) -222 (is) -221 (more) -222 (stable)
-221 (for) -222 (training,) -227 (otherwise,) -227 (there) -222 (w) 10 (ould)
] TJ ET BT 9.9626 0 0 9.9626 308.862 317.036 Tm /Ty2 1 Tf [ (be) -229 (an)
-228 (additional) -229 (re) 15 (gularization) -229 (term) ] TJ ET BT 9.9626 0 0 9.9626 452.357 317.036
Tm /Ty7 1 Tf (G) Tj ET BT 9.9626 0 0 9.9626 460.19 317.036 Tm /Ty12 1 Tf (\()
Tj ET BT 0.0005 Tc 9.9626 0 0 9.9626 464.064 317.036 Tm /Ty7 1 Tf [ (x,) -167
(x) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 479.88 320.651 Tm /Ty16 1 Tf (&) Tj
ET BT 0.1678 Tc 9.9626 0 0 9.9626 482.675 317.036 Tm /Ty7 1 Tf (,) Tj /Ty8
1 Tf (") Tj 0 Tc ET BT 9.9626 0 0 9.9626 492.056 317.036 Tm /Ty12 1 Tf (\))
Tj ET BT 9.9626 0 0 9.9626 498.209 317.036 Tm /Ty2 1 Tf [ (in) -229 (the)
] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 522.69 317.036 Tm /Ty12 1 Tf [ (Tr)
-84 (H) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 540.43 315.541 Tm /Ty4 1 Tf (T)
Tj ET BT 9.9626 0 0 9.9626 308.862 305.081 Tm /Ty2 1 Tf [ (\(see) -250 (more)
-250 (details) -250 (in) -250 (the) -250 (Appendix) ] TJ ET /Cs1 cs 1 0 0
sc BT 9.9626 0 0 9.9626 445.5489 305.081 Tm /Ty2 1 Tf (A) Tj ET /Cs2 cs 0
sc BT 9.9626 0 0 9.9626 452.7419 305.081 Tm /Ty2 1 Tf (\).) Tj ET BT 9.9626 0 0 9.9626 320.817 293.125
Tm /Ty2 1 Tf [ (W) 40 (ith) -289 (Proposition) ] TJ ET /Cs1 cs 1 0 0 sc BT
9.9626 0 0 9.9626 392.0496 293.125 Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT
9.9626 0 0 9.9626 399.9001 293.125 Tm /Ty2 1 Tf (and) Tj ET /Cs1 cs 1 0 0
sc BT 9.9626 0 0 9.9626 417.1653 293.125 Tm /Ty2 1 Tf (2) Tj ET /Cs2 cs 0
sc BT 9.9626 0 0 9.9626 422.1466 293.125 Tm /Ty2 1 Tf [ (,) -299 (we) -288
(no) 25 (w) -289 (present) -289 (the) -289 (complete) ] TJ ET BT 9.9626 0 0 9.9626 308.862 281.17
Tm /Ty2 1 Tf [ (training) -469 (objecti) 25 (v) 15 (e) -470 (in) -469 (Algorithm)
] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 443.9549 281.17 Tm /Ty2 1 Tf
(1) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 448.9362 281.17 Tm /Ty2 1 Tf [
(.) -968 (Notice) -470 (that,) -524 (to) -470 (sim-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 267.976
Tm /Ty2 1 Tf [ (plify) -392 (h) 5 (yper) 20 (-parameter) -391 (notations,)
-427 (we) -392 (re-parameterize) ] TJ ET BT 9.9626 0 0 9.9626 526.271 267.976
Tm /Ty8 1 Tf (,) Tj ET BT 4.9813 0 0 4.9813 538.057 273.624 Tm /Ty2 1 Tf (def)
Tj ET BT 9.9626 0 0 9.9626 537.363 267.976 Tm /Ty12 1 Tf (=) Tj ET BT 9.9626 0 0 9.9626 308.862 254.782
Tm /Ty12 1 Tf (1) Tj ET BT 9.9626 0 0 9.9626 313.843 254.782 Tm /Ty7 1 Tf
(/) Tj ET BT 9.9626 0 0 9.9626 318.825 254.782 Tm /Ty12 1 Tf (2) Tj ET BT
0.0536 Tc 9.9626 0 0 9.9626 323.806 254.782 Tm /Ty8 1 Tf (*+) Tj 0 Tc ET BT
6.9738 0 0 6.9738 336.017 258.397 Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 335.66 252.309
Tm /Ty9 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 342.977 254.782 Tm /Ty2 1 Tf (and)
Tj ET BT 9.9626 0 0 9.9626 359.854 254.782 Tm /Ty8 1 Tf (%) Tj ET BT 4.9813 0 0 4.9813 369.127 260.43
Tm /Ty2 1 Tf (def) Tj ET BT 9.9626 0 0 9.9626 368.433 254.782 Tm /Ty12 1 Tf
(=) Tj ET BT 9.9626 0 0 9.9626 378.949 254.782 Tm /Ty8 1 Tf (+) Tj ET BT 6.9738 0 0 6.9738 384.999 258.397
Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 384.642 252.309 Tm /Ty9 1 Tf (0)
Tj ET BT 9.9626 0 0 9.9626 389.468 254.782 Tm /Ty7 1 Tf (/) Tj ET BT 9.9626 0 0 9.9626 394.45 254.782
Tm /Ty12 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 401.922 254.782 Tm /Ty2 1 Tf
[ (in) -250 (the) -250 (algorithm.) ] TJ ET BT 10.9589 0 0 10.9589 308.862 235.248
Tm /Ty1 1 Tf [ (3.2.) -250 (The) -250 (effect) -250 (of) -250 (T) 92 (op-Lay)
10 (er) -250 (T) 74 (rH) -250 (Regularization) ] TJ ET BT 9.9626 0 0 9.9626 320.817 217.315
Tm /Ty2 1 Tf [ (Although) -335 (the) -334 (T) 35 (rH) -335 (re) 15 (gularization)
-335 (is) -335 (restricted) -334 (to) -335 (the) -335 (top) ] TJ ET BT 9.9626 0 0 9.9626 308.862 205.36
Tm /Ty2 1 Tf [ (layer) -356 (only) 65 (,) -382 (the) -356 (gradient) -356
(back-propag) 5 (ates) -355 (to) -356 (the) -356 (entire) -356 (net-) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 193.405 Tm /Ty2 1 Tf [ (w) 10 (ork) -214 (through)
-214 (the) -214 (penultimate) -214 (layer) -215 (features.) -298 (This) -214
(moti) 25 (v) 25 (ates) ] TJ ET BT 9.9626 0 0 9.9626 308.862 181.45 Tm /Ty2
1 Tf [ (the) -250 (follo) 25 (wing) -250 (research) -250 (question:) ] TJ
ET /Cs2 cs 0.25 sc 308.862 135.464 m 308.862 167.6347 l 308.862 169.983 310.7656
171.8867 313.114 171.8867 c 540.8631 171.8867 l 543.2114 171.8867 545.115
169.983 545.115 167.6347 c 545.115 135.464 l 545.115 133.1156 543.2114 131.212
540.8631 131.212 c 313.114 131.212 l 310.7656 131.212 308.862 133.1156 308.862
135.464 c h f /Cs2 cs 0.95 sc 310.2793 135.464 m 310.2793 167.6347 l 310.2793
169.2002 311.5484 170.4693 313.114 170.4693 c 540.8631 170.4693 l 542.4286
170.4693 543.6977 169.2002 543.6977 167.6347 c 543.6977 135.464 l 543.6977
133.8984 542.4286 132.6293 540.8631 132.6293 c 313.114 132.6293 l 311.5484
132.6293 310.2793 133.8984 310.2793 135.464 c h f /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 324.452 155.145
Tm /Ty6 1 Tf [ (What) -280 (ef) 18 (fect) -280 (does) -280 (top-layer) -280
(T) 55 (rH) -280 (r) 37 (e) 40 (gularization) -280 (have) ] TJ ET BT 9.9626 0 0 9.9626 324.452 143.19
Tm /Ty6 1 Tf [ (on) -250 (the) -250 (T) 55 (rH) -250 (of) -250 (the) -250
(entir) 37 (e) -250 (network?) ] TJ ET BT 9.9626 0 0 9.9626 320.817 116.866
Tm /Ty2 1 Tf [ (T) 80 (o) -365 (answer) -366 (this) -365 (question,) -394
(we) -366 (tak) 10 (e) -365 (a) -365 (tw) 10 (o-step) -366 (approach.) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 104.91 Tm /Ty2 1 Tf [ (First,) -388 (we) -360
(e) 15 (xperiment) -360 (with) -360 (a) -361 (small) -360 (3-layer) -360 (netw)
10 (ork) -360 (on) -361 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 92.955
Tm /Ty2 1 Tf [ (synthetic) -379 (T) 80 (w) 10 (o-Moon) -378 (dataset) -379
(\(see) -379 (Appendix) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 491.1875 92.955
Tm /Ty2 1 Tf (C) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 501.5985 92.955 Tm
/Ty2 1 Tf [ (for) -379 (a) -379 (visu-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 81
Tm /Ty2 1 Tf [ (alization) -362 (of) -362 (the) -363 (dataset\),) -390 (pro)
15 (vided) -362 (that) -362 (computing) -362 (the) -363 (full) ] TJ ET Q
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0 0 m 495 0 l S Q BT 8.9664 0 0 8.9664 62.067 694.192 Tm /Ty1 1 Tf [ (Hyper)
37 (-parameters:) ] TJ ET BT 8.9664 0 0 8.9664 138.711 694.192 Tm /Ty2 1 Tf
(The) Tj ET BT 8.9664 0 0 8.9664 154.895 694.192 Tm /Ty27 1 Tf (!) Tj ET BT
5.9776 0 0 5.9776 158.7 693.196 Tm /Ty28 1 Tf (2) Tj ET BT 8.9664 0 0 8.9664 162.851 694.192
Tm /Ty2 1 Tf [ (-norm) -250 (penalty) -250 (for) -250 (weights) ] TJ ET BT
8.9664 0 0 8.9664 258.477 694.192 Tm /Ty27 1 Tf (") Tj ET BT 8.9664 0 0 8.9664 263.748 694.192
Tm /Ty2 1 Tf [ (,) -250 (the) -250 (TRADES) -250 (penalty) ] TJ ET BT 8.9664 0 0 8.9664 347.18 694.192
Tm /Ty27 1 Tf (#) Tj ET BT 5.9776 0 0 5.9776 352.556 693.196 Tm /Ty29 1 Tf
(t) Tj ET BT 8.9664 0 0 8.9664 358.146 694.192 Tm /Ty2 1 Tf [ (and) -250 (the)
-250 (T) 35 (rH) -250 (penalty) ] TJ ET BT 8.9664 0 0 8.9664 432.037 694.192
Tm /Ty27 1 Tf (#) Tj ET BT 8.9664 0 0 8.9664 437.413 694.192 Tm /Ty2 1 Tf
(.) Tj ET BT 8.9664 0 0 8.9664 62.067 683.233 Tm /Ty1 1 Tf (Inputs:) Tj ET
BT 8.9664 0 0 8.9664 92.75 683.233 Tm /Ty2 1 Tf [ (A) -250 (batch) ] TJ ET
BT 8.9664 0 0 8.9664 123.127 683.233 Tm /Ty26 1 Tf (B) Tj ET BT 8.9664 0 0 8.9664 132.789 683.233
Tm /Ty2 1 Tf [ (of) -250 (e) 15 (xamples,) -250 (a) ] TJ ET BT 8.9664 0 0 8.9664 186.936 683.233
Tm /Ty4 1 Tf (loss) Tj ET 0.398 w q 1 0 0 1 208.993 683.432 cm 0 0 m 2.69
0 l S Q BT 8.9664 0 0 8.9664 211.683 683.233 Tm /Ty4 1 Tf (type) Tj ET BT
8.9664 0 0 8.9664 235.444 683.233 Tm /Ty30 1 Tf (=) Tj ET BT 8.9664 0 0 8.9664 242.612 683.233
Tm /Ty2 1 Tf Tj ET BT 8.9664 0 0 8.9664 245.597 683.233 Tm /Ty4 1 Tf (AT)
Tj ET BT 8.9664 0 0 8.9664 256.357 683.233 Tm /Ty2 1 Tf [ -250 (or) -250
] TJ ET BT 8.9664 0 0 8.9664 274.281 683.233 Tm /Ty4 1 Tf (TRADES) Tj
ET BT 8.9664 0 0 8.9664 306.56 683.233 Tm /Ty2 1 Tf [ -250 (the) -250
(noise) -250 (b) 20 (udget) ] TJ ET BT 8.9664 0 0 8.9664 374.865 683.233 Tm
/Ty27 1 Tf ($) Tj ET BT 8.9664 0 0 8.9664 379.29 683.233 Tm /Ty2 1 Tf [ (,)
-250 (and) -250 (a) -250 (netw) 10 (ork) ] TJ ET BT 8.9664 0 0 8.9664 436.72 683.233
Tm /Ty26 1 Tf (g) Tj ET BT 5.9776 0 0 5.9776 441.114 682.17 Tm /Ty31 1 Tf
(!) Tj ET BT 8.9664 0 0 8.9664 447.894 683.233 Tm /Ty30 1 Tf (=) Tj ET BT
8.9664 0 0 8.9664 457.621 683.233 Tm /Ty27 1 Tf (%) Tj ET BT 5.9776 0 0 5.9776 462.191 687.042
Tm /Ty33 1 Tf (!) Tj ET BT 5.9776 0 0 5.9776 461.935 681.656 Tm /Ty29 1 Tf
(t) Tj ET BT 8.9664 0 0 8.9664 468.445 683.233 Tm /Ty26 1 Tf (f) Tj ET BT
5.9776 0 0 5.9776 472.918 682.17 Tm /Ty31 1 Tf (!) Tj ET BT 4.9813 0 0 4.9813 476.447 680.77
Tm /Ty20 1 Tf (b) Tj ET BT 8.9664 0 0 8.9664 480.598 683.233 Tm /Ty30 1 Tf
(\() Tj ET BT 8.9664 0 0 8.9664 484.181 683.233 Tm /Ty26 1 Tf (x) Tj ET BT
8.9664 0 0 8.9664 489.405 683.233 Tm /Ty30 1 Tf (\)) Tj ET BT 8.9664 0 0 8.9664 492.989 683.233
Tm /Ty2 1 Tf (.) Tj ET BT 8.9664 0 0 8.9664 62.067 672.274 Tm /Ty1 1 Tf (Output:)
Tj ET BT 8.9664 0 0 8.9664 95.735 672.274 Tm /Ty2 1 Tf [ (The) -250 (training)
-250 (objecti) 25 (v) 15 (e) -250 (at) -250 (the) -250 (current) -250 (iteration.)
] TJ ET BT 6.2267 0 0 6.2267 53.972 661.315 Tm /Ty1 1 Tf (1) Tj ET BT 8.9664 0 0 8.9664 62.067 661.315
Tm /Ty26 1 Tf (R) Tj ET BT 8.9664 0 0 8.9664 71.663 661.315 Tm /Ty34 1 Tf
(!) Tj ET BT 8.9664 0 0 8.9664 83.438 661.315 Tm /Ty30 1 Tf (0) Tj ET BT 6.2267 0 0 6.2267 53.972 650.356
Tm /Ty1 1 Tf (2) Tj ET BT 8.9664 0 0 8.9664 62.067 650.356 Tm /Ty1 1 Tf [
(f) 25 (or) 18 (each) ] TJ ET BT 8.9664 0 0 8.9664 92.804 650.356 Tm /Ty30
1 Tf (\() Tj ET BT 0.0006 Tc 8.9664 0 0 8.9664 96.387 650.356 Tm /Ty26 1 Tf
[ (x,) -171 (y) ] TJ 0 Tc ET BT 8.9664 0 0 8.9664 110.567 650.356 Tm /Ty30
1 Tf (\)) Tj ET BT 8.9664 0 0 8.9664 116.71 650.356 Tm /Ty34 1 Tf (") Tj ET
BT 8.9664 0 0 8.9664 125.414 650.356 Tm /Ty26 1 Tf (B) Tj ET BT 8.9664 0 0 8.9664 135.075 650.356
Tm /Ty1 1 Tf (do) Tj ET q 1 0 0 1 67.248 544.294 cm 0 0 m 0 102.775 l S Q
BT 6.2267 0 0 6.2267 54.371 639.397 Tm /Ty1 1 Tf (3) Tj ET BT 8.9664 0 0 8.9664 77.41 639.397
Tm /Ty26 1 Tf (x) Tj ET BT 5.9776 0 0 5.9776 82.633 643.206 Tm /Ty33 1 Tf
(") Tj ET BT 8.9664 0 0 8.9664 87.559 639.397 Tm /Ty34 1 Tf (!) Tj ET BT 8.9664 0 0 8.9664 99.334 639.397
Tm /Ty4 1 Tf (PGD) Tj ET q 1 0 0 1 116.012 639.597 cm 0 0 m 2.69 0 l S Q BT
8.9664 0 0 8.9664 118.702 639.397 Tm /Ty4 1 Tf (InnerLoop) Tj ET BT 8.9664 0 0 8.9664 167.12 639.397
Tm /Ty30 1 Tf (\() Tj ET BT 0.0006 Tc 8.9664 0 0 8.9664 170.704 639.397 Tm
/Ty26 1 Tf [ (x,) -171 (y) -36 (,) -250 ] TJ /Ty27 1 Tf ($) Tj 0 Tc ET BT
8.9664 0 0 8.9664 194.11 639.397 Tm /Ty2 1 Tf (,) Tj ET BT 8.9664 0 0 8.9664 198.593 639.397
Tm /Ty4 1 Tf (loss) Tj ET q 1 0 0 1 220.65 639.597 cm 0 0 m 2.69 0 l S Q BT
8.9664 0 0 8.9664 223.34 639.397 Tm /Ty4 1 Tf (type) Tj ET BT 8.9664 0 0 8.9664 247.101 639.397
Tm /Ty2 1 Tf (\)) Tj ET BT 6.2267 0 0 6.2267 54.371 627.153 Tm /Ty1 1 Tf (4)
Tj ET BT 8.9664 0 0 8.9664 77.41 627.153 Tm /Ty26 1 Tf (z) Tj ET BT 5.9776 0 0 5.9776 82.083 630.962
Tm /Ty33 1 Tf (") Tj ET BT 8.9664 0 0 8.9664 87.009 627.153 Tm /Ty34 1 Tf
(!) Tj ET BT 8.9664 0 0 8.9664 98.784 627.153 Tm /Ty26 1 Tf (f) Tj ET BT 5.9776 0 0 5.9776 103.257 626.091
Tm /Ty31 1 Tf (!) Tj ET BT 4.9813 0 0 4.9813 106.785 624.69 Tm /Ty20 1 Tf
(b) Tj ET BT 8.9664 0 0 8.9664 110.937 627.153 Tm /Ty30 1 Tf (\() Tj ET BT
8.9664 0 0 8.9664 114.52 627.153 Tm /Ty26 1 Tf (x) Tj ET BT 5.9776 0 0 5.9776 119.744 630.962
Tm /Ty33 1 Tf (") Tj ET BT 8.9664 0 0 8.9664 122.428 627.153 Tm /Ty30 1 Tf
(\)) Tj ET BT 1.1715 Tc 8.9664 0 0 8.9664 126.012 627.153 Tm /Ty26 1 Tf (,h)
Tj 0 Tc ET BT 5.9776 0 0 5.9776 144.384 630.962 Tm /Ty33 1 Tf (") Tj ET BT
8.9664 0 0 8.9664 149.628 627.153 Tm /Ty34 1 Tf (!) Tj ET BT 8.9664 0 0 8.9664 158.843 627.153
Tm /Ty2 1 Tf (s\() Tj ET BT 8.9664 0 0 8.9664 165.317 627.153 Tm /Ty27 1 Tf
(%) Tj ET BT 5.9776 0 0 5.9776 169.887 630.962 Tm /Ty33 1 Tf (!) Tj ET BT
5.9776 0 0 5.9776 169.631 625.576 Tm /Ty29 1 Tf (t) Tj ET BT 8.9664 0 0 8.9664 176.141 627.153
Tm /Ty26 1 Tf (z) Tj ET BT 5.9776 0 0 5.9776 180.814 630.962 Tm /Ty33 1 Tf
(") Tj ET BT 8.9664 0 0 8.9664 183.499 627.153 Tm /Ty30 1 Tf (\)) Tj ET BT
8.9664 0 0 8.9664 189.13 627.153 Tm /Ty34 1 Tf (#) Tj ET BT 8.9664 0 0 8.9664 198.346 627.153
Tm /Ty26 1 Tf (s) Tj ET BT 8.9664 0 0 8.9664 202.639 627.153 Tm /Ty30 1 Tf
(\() Tj ET BT 8.9664 0 0 8.9664 206.222 627.153 Tm /Ty27 1 Tf (%) Tj ET BT
5.9776 0 0 5.9776 210.792 630.962 Tm /Ty33 1 Tf (!) Tj ET BT 5.9776 0 0 5.9776 210.536 625.576
Tm /Ty29 1 Tf (t) Tj ET BT 8.9664 0 0 8.9664 217.046 627.153 Tm /Ty26 1 Tf
(z) Tj ET BT 5.9776 0 0 5.9776 221.72 630.962 Tm /Ty33 1 Tf (") Tj ET BT 8.9664 0 0 8.9664 224.404 627.153
Tm /Ty30 1 Tf (\)) Tj ET BT 5.9776 0 0 5.9776 227.988 630.962 Tm /Ty28 1 Tf
(2) Tj ET BT 8.9664 0 0 8.9664 232.139 627.153 Tm /Ty30 1 Tf (;) Tj ET /Cs1
cs 0 0 1 sc BT 7.9701 0 0 7.9701 277.584 627.153 Tm /Ty4 1 Tf (//) Tj ET BT
7.9701 0 0 7.9701 291.931 627.153 Tm /Ty35 1 Tf (s) Tj ET BT 7.9701 0 0 7.9701 300.629 627.153
Tm /Ty4 1 Tf [ (is) -600 (the) -600 (softmax) -600 (function.) -1200 (This)
-600 (step) -600 (computes) -600 (the) ] TJ ET BT 7.9701 0 0 7.9701 82.391 616.194
Tm /Ty4 1 Tf [ (penultimate) -600 (feature) ] TJ ET BT 7.9701 0 0 7.9701 178.032 616.194
Tm /Ty35 1 Tf (z) Tj ET BT 5.9776 0 0 5.9776 182.308 619.007 Tm /Ty33 1 Tf
(") Tj ET BT 7.9701 0 0 7.9701 189.774 616.194 Tm /Ty4 1 Tf [ (and) -600 (the)
-600 (softmax) -600 (gradient) ] TJ ET BT 7.9701 0 0 7.9701 309.326 616.194
Tm /Ty35 1 Tf (h) Tj ET BT 5.9776 0 0 5.9776 314.206 619.007 Tm /Ty33 1 Tf
(") Tj ET BT 7.9701 0 0 7.9701 321.673 616.194 Tm /Ty4 1 Tf [ (on) -600 (the)
-600 (adversarial) -600 (input) ] TJ ET BT 7.9701 0 0 7.9701 441.224 616.194
Tm /Ty35 1 Tf (x) Tj ET BT 5.9776 0 0 5.9776 445.991 619.007 Tm /Ty33 1 Tf
(") Tj ET BT 7.9701 0 0 7.9701 448.676 616.194 Tm /Ty4 1 Tf (.) Tj ET /Cs2
cs 0 sc BT 6.2267 0 0 6.2267 54.371 605.235 Tm /Ty1 1 Tf (5) Tj ET BT 8.9664 0 0 8.9664 77.41 605.235
Tm /Ty1 1 Tf (if) Tj ET BT 8.9664 0 0 8.9664 85.129 605.235 Tm /Ty23 1 Tf
(loss) Tj ET q 1 0 0 1 107.187 605.435 cm 0 0 m 2.69 0 l S Q BT 8.9664 0 0 8.9664 109.877 605.235
Tm /Ty23 1 Tf (type) Tj ET BT 8.9664 0 0 8.9664 133.638 605.235 Tm /Ty6 1
Tf [ (==) -250 ] TJ ET BT 8.9664 0 0 8.9664 150.97 605.235 Tm /Ty23 1
Tf (AT) Tj ET BT 8.9664 0 0 8.9664 161.729 605.235 Tm /Ty6 1 Tf Tj ET
BT 8.9664 0 0 8.9664 166.957 605.235 Tm /Ty1 1 Tf (then) Tj ET q 1 0 0 1 82.59 590.7
cm 0 0 m 0 11.248 l S Q BT 6.2267 0 0 6.2267 54.769 593.988 Tm /Ty1 1 Tf (6)
Tj ET BT 8.9664 0 0 8.9664 92.752 593.988 Tm /Ty26 1 Tf (R) Tj ET BT 8.9664 0 0 8.9664 102.348 593.988
Tm /Ty34 1 Tf (!) Tj ET BT 8.9664 0 0 8.9664 114.123 593.988 Tm /Ty26 1 Tf
(R) Tj ET BT 0.2284 Tc 8.9664 0 0 8.9664 123.206 593.988 Tm /Ty30 1 Tf [ (+C)
228 (E) 228 (\() 228 (\() ] TJ 0 Tc ET BT 8.9664 0 0 8.9664 152.516 593.988
Tm /Ty26 1 Tf (x) Tj ET BT 5.9776 0 0 5.9776 157.739 597.797 Tm /Ty33 1 Tf
(") Tj ET BT 0.1715 Tc 8.9664 0 0 8.9664 160.424 593.988 Tm /Ty26 1 Tf (,y)
Tj 0 Tc ET BT 8.9664 0 0 8.9664 169.379 593.988 Tm /Ty30 1 Tf (\)) Tj ET BT
0.1715 Tc 8.9664 0 0 8.9664 172.963 593.988 Tm /Ty26 1 Tf (,g) Tj 0 Tc ET
BT 5.9776 0 0 5.9776 181.453 592.925 Tm /Ty31 1 Tf (!) Tj ET BT 0.2287 Tc
8.9664 0 0 8.9664 185.673 593.988 Tm /Ty30 1 Tf (\)+) Tj 0 Tc ET BT 8.9664 0 0 8.9664 200.52 593.988
Tm /Ty27 1 Tf (#) Tj ET BT 8.9664 0 0 8.9664 205.896 593.988 Tm /Ty30 1 Tf
(\() Tj ET BT 0.0005 Tc 8.9664 0 0 8.9664 209.48 593.988 Tm /Ty5 1 Tf (||)
Tj 0 Tc ET BT 8.9664 0 0 8.9664 214.599 593.988 Tm /Ty26 1 Tf (z) Tj ET BT
5.9776 0 0 5.9776 219.273 597.797 Tm /Ty33 1 Tf (") Tj ET BT 0.0005 Tc 8.9664 0 0 8.9664 221.957 593.988
Tm /Ty5 1 Tf (||) Tj 0 Tc ET BT 5.9776 0 0 5.9776 227.077 597.797 Tm /Ty28
1 Tf (2) Tj ET BT 5.9776 0 0 5.9776 227.077 592.41 Tm /Ty28 1 Tf (2) Tj ET
BT 8.9664 0 0 8.9664 233.276 593.988 Tm /Ty5 1 Tf Tj ET BT 8.9664 0 0 8.9664 237.884 593.988
Tm /Ty36 1 Tf (1) Tj ET BT 5.9776 0 0 5.9776 243.189 597.797 Tm /Ty33 1 Tf
(!) Tj ET BT 8.9664 0 0 8.9664 249.443 593.988 Tm /Ty26 1 Tf (h) Tj ET BT
5.9776 0 0 5.9776 254.753 597.797 Tm /Ty33 1 Tf (") Tj ET BT 8.9664 0 0 8.9664 257.437 593.988
Tm /Ty30 1 Tf (\)) Tj ET BT 8.9664 0 0 8.9664 261.021 593.988 Tm /Ty2 1 Tf
(;) Tj ET BT 6.2267 0 0 6.2267 54.371 583.029 Tm /Ty1 1 Tf (7) Tj ET BT 8.9664 0 0 8.9664 77.41 583.029
Tm /Ty1 1 Tf [ (else) -250 (if) ] TJ ET BT 8.9664 0 0 8.9664 101.313 583.029
Tm /Ty23 1 Tf (loss) Tj ET q 1 0 0 1 123.371 583.228 cm 0 0 m 2.69 0 l S Q
BT 8.9664 0 0 8.9664 126.061 583.029 Tm /Ty23 1 Tf (type) Tj ET BT 8.9664 0 0 8.9664 149.822 583.029
Tm /Ty6 1 Tf [ (==) -250 ] TJ ET BT 8.9664 0 0 8.9664 167.154 583.029
Tm /Ty23 1 Tf (TRADES) Tj ET BT 8.9664 0 0 8.9664 199.432 583.029 Tm /Ty6
1 Tf Tj ET BT 8.9664 0 0 8.9664 204.66 583.029 Tm /Ty1 1 Tf (then) Tj
ET q 1 0 0 1 82.59 556.249 cm 0 0 m 0 23.492 l S Q BT 6.2267 0 0 6.2267 54.769 571.781
Tm /Ty1 1 Tf (8) Tj ET BT 8.9664 0 0 8.9664 92.752 571.781 Tm /Ty26 1 Tf (z)
Tj ET BT 8.9664 0 0 8.9664 99.667 571.781 Tm /Ty34 1 Tf (!) Tj ET BT 8.9664 0 0 8.9664 111.442 571.781
Tm /Ty26 1 Tf (f) Tj ET BT 5.9776 0 0 5.9776 115.915 570.718 Tm /Ty31 1 Tf
(!) Tj ET BT 4.9813 0 0 4.9813 119.443 569.318 Tm /Ty20 1 Tf (b) Tj ET BT
8.9664 0 0 8.9664 123.595 571.781 Tm /Ty30 1 Tf (\() Tj ET BT 8.9664 0 0 8.9664 127.178 571.781
Tm /Ty26 1 Tf (x) Tj ET BT 8.9664 0 0 8.9664 132.402 571.781 Tm /Ty30 1 Tf
(\)) Tj ET BT 1.1715 Tc 8.9664 0 0 8.9664 135.986 571.781 Tm /Ty26 1 Tf (,h)
Tj 0 Tc ET BT 8.9664 0 0 8.9664 156.917 571.781 Tm /Ty34 1 Tf (!) Tj ET BT
8.9664 0 0 8.9664 166.133 571.781 Tm /Ty2 1 Tf (s\() Tj ET BT 8.9664 0 0 8.9664 172.606 571.781
Tm /Ty27 1 Tf (%) Tj ET BT 5.9776 0 0 5.9776 177.176 575.59 Tm /Ty33 1 Tf
(!) Tj ET BT 5.9776 0 0 5.9776 176.92 570.204 Tm /Ty29 1 Tf (t) Tj ET BT 8.9664 0 0 8.9664 183.43 571.781
Tm /Ty26 1 Tf (z) Tj ET BT 8.9664 0 0 8.9664 188.104 571.781 Tm /Ty30 1 Tf
(\)) Tj ET BT 8.9664 0 0 8.9664 193.735 571.781 Tm /Ty34 1 Tf (#) Tj ET BT
8.9664 0 0 8.9664 202.951 571.781 Tm /Ty26 1 Tf (s) Tj ET BT 8.9664 0 0 8.9664 207.244 571.781
Tm /Ty30 1 Tf (\() Tj ET BT 8.9664 0 0 8.9664 210.827 571.781 Tm /Ty27 1 Tf
(%) Tj ET BT 5.9776 0 0 5.9776 215.397 575.59 Tm /Ty33 1 Tf (!) Tj ET BT 5.9776 0 0 5.9776 215.141 570.204
Tm /Ty29 1 Tf (t) Tj ET BT 8.9664 0 0 8.9664 221.651 571.781 Tm /Ty26 1 Tf
(z) Tj ET BT 8.9664 0 0 8.9664 226.325 571.781 Tm /Ty30 1 Tf (\)) Tj ET BT
5.9776 0 0 5.9776 229.908 575.59 Tm /Ty28 1 Tf (2) Tj ET BT 8.9664 0 0 8.9664 234.059 571.781
Tm /Ty30 1 Tf (;) Tj ET /Cs1 cs 0 0 1 sc BT 7.9701 0 0 7.9701 291.488 571.781
Tm /Ty4 1 Tf (//) Tj ET BT 7.9701 0 0 7.9701 305.8342 571.781 Tm /Ty4 1 Tf
[ (TRADES) -600 (needs) -600 (the) ] TJ ET BT 7.9701 0 0 7.9701 387.129 571.781
Tm /Ty35 1 Tf (z) Tj ET BT 7.9701 0 0 7.9701 396.187 571.781 Tm /Ty4 1 Tf
(and) Tj ET BT 7.9701 0 0 7.9701 415.315 571.781 Tm /Ty35 1 Tf (h) Tj ET BT
7.9701 0 0 7.9701 424.977 571.781 Tm /Ty4 1 Tf [ (for) -600 (the) -600 (clean)
-600 (input) ] TJ ET BT 7.9701 0 0 7.9701 520.619 571.781 Tm /Ty35 1 Tf (x)
Tj ET BT 7.9701 0 0 7.9701 525.386 571.781 Tm /Ty4 1 Tf (.) Tj ET /Cs2 cs
0 sc BT 6.2267 0 0 6.2267 54.769 559.537 Tm /Ty1 1 Tf (9) Tj ET BT 8.9664 0 0 8.9664 92.752 559.537
Tm /Ty26 1 Tf (R) Tj ET BT 8.9664 0 0 8.9664 102.347 559.537 Tm /Ty34 1 Tf
(!) Tj ET BT 8.9664 0 0 8.9664 114.123 559.537 Tm /Ty26 1 Tf (R) Tj ET BT
0.2284 Tc 8.9664 0 0 8.9664 123.206 559.537 Tm /Ty30 1 Tf [ (+C) 228 (E) 228
(\() 228 (\() ] TJ 0 Tc ET BT 0.0006 Tc 8.9664 0 0 8.9664 152.516 559.537
Tm /Ty26 1 Tf [ (x,) -171 (y) ] TJ 0 Tc ET BT 8.9664 0 0 8.9664 166.695 559.537
Tm /Ty30 1 Tf (\)) Tj ET BT 0.1715 Tc 8.9664 0 0 8.9664 170.279 559.537 Tm
/Ty26 1 Tf (,g) Tj 0 Tc ET BT 5.9776 0 0 5.9776 178.769 558.474 Tm /Ty31 1
Tf (!) Tj ET BT 0.2287 Tc 8.9664 0 0 8.9664 182.989 559.537 Tm /Ty30 1 Tf
(\)+) Tj 0 Tc ET BT 8.9664 0 0 8.9664 197.836 559.537 Tm /Ty27 1 Tf (#) Tj
ET BT 5.9776 0 0 5.9776 203.212 558.541 Tm /Ty29 1 Tf (t) Tj ET BT 0.0002
Tc 8.9664 0 0 8.9664 206.56 559.537 Tm /Ty30 1 Tf (KL\() Tj 0 Tc ET BT 8.9664 0 0 8.9664 223.069 559.537
Tm /Ty26 1 Tf (s) Tj ET BT 8.9664 0 0 8.9664 227.362 559.537 Tm /Ty30 1 Tf
(\() Tj ET BT 8.9664 0 0 8.9664 230.946 559.537 Tm /Ty27 1 Tf (%) Tj ET BT
5.9776 0 0 5.9776 235.515 563.346 Tm /Ty33 1 Tf (!) Tj ET BT 5.9776 0 0 5.9776 235.259 557.959
Tm /Ty29 1 Tf (t) Tj ET BT 8.9664 0 0 8.9664 241.77 559.537 Tm /Ty26 1 Tf
(z) Tj ET BT 8.9664 0 0 8.9664 246.443 559.537 Tm /Ty30 1 Tf (\)) Tj ET BT
0.0005 Tc 8.9664 0 0 8.9664 250.027 559.537 Tm /Ty5 1 Tf (||) Tj 0 Tc ET BT
8.9664 0 0 8.9664 255.146 559.537 Tm /Ty26 1 Tf (s) Tj ET BT 8.9664 0 0 8.9664 259.439 559.537
Tm /Ty30 1 Tf (\() Tj ET BT 8.9664 0 0 8.9664 263.023 559.537 Tm /Ty27 1 Tf
(%) Tj ET BT 5.9776 0 0 5.9776 267.593 563.346 Tm /Ty33 1 Tf (!) Tj ET BT
5.9776 0 0 5.9776 267.337 557.96 Tm /Ty29 1 Tf (t) Tj ET BT 8.9664 0 0 8.9664 273.847 559.537
Tm /Ty26 1 Tf (z) Tj ET BT 5.9776 0 0 5.9776 278.52 563.346 Tm /Ty33 1 Tf
(") Tj ET BT 0.0007 Tc 8.9664 0 0 8.9664 281.205 559.537 Tm /Ty30 1 Tf [ (\)\))
-228 (+) ] TJ 0 Tc ET BT 8.9664 0 0 8.9664 299.636 559.537 Tm /Ty27 1 Tf (#)
Tj ET BT 8.9664 0 0 8.9664 305.011 559.537 Tm /Ty30 1 Tf (\() Tj ET BT 0.0005
Tc 8.9664 0 0 8.9664 308.595 559.537 Tm /Ty5 1 Tf (||) Tj 0 Tc ET BT 8.9664 0 0 8.9664 313.715 559.537
Tm /Ty26 1 Tf (z) Tj ET BT 0.0005 Tc 8.9664 0 0 8.9664 318.388 559.537 Tm
/Ty5 1 Tf (||) Tj 0 Tc ET BT 5.9776 0 0 5.9776 323.508 563.346 Tm /Ty28 1
Tf (2) Tj ET BT 5.9776 0 0 5.9776 323.508 557.96 Tm /Ty28 1 Tf (2) Tj ET BT
8.9664 0 0 8.9664 329.707 559.537 Tm /Ty5 1 Tf Tj ET BT 8.9664 0 0 8.9664 334.314 559.537
Tm /Ty36 1 Tf (1) Tj ET BT 5.9776 0 0 5.9776 339.619 563.346 Tm /Ty33 1 Tf
(!) Tj ET BT 8.9664 0 0 8.9664 345.874 559.537 Tm /Ty26 1 Tf (h) Tj ET BT
8.9664 0 0 8.9664 353.231 559.537 Tm /Ty30 1 Tf (+) Tj ET BT 8.9664 0 0 8.9664 362.447 559.537
Tm /Ty27 1 Tf (#) Tj ET BT 5.9776 0 0 5.9776 367.822 558.541 Tm /Ty29 1 Tf
(t) Tj ET BT 0.0005 Tc 8.9664 0 0 8.9664 371.171 559.537 Tm /Ty5 1 Tf (||)
Tj 0 Tc ET BT 8.9664 0 0 8.9664 376.291 559.537 Tm /Ty26 1 Tf (z) Tj ET BT
5.9776 0 0 5.9776 380.964 563.346 Tm /Ty33 1 Tf (") Tj ET BT 0.0005 Tc 8.9664 0 0 8.9664 383.648 559.537
Tm /Ty5 1 Tf (||) Tj 0 Tc ET BT 5.9776 0 0 5.9776 388.768 563.346 Tm /Ty28
1 Tf (2) Tj ET BT 5.9776 0 0 5.9776 388.768 557.96 Tm /Ty28 1 Tf (2) Tj ET
BT 8.9664 0 0 8.9664 394.967 559.537 Tm /Ty5 1 Tf Tj ET BT 8.9664 0 0 8.9664 399.575 559.537
Tm /Ty36 1 Tf (1) Tj ET BT 5.9776 0 0 5.9776 404.88 563.346 Tm /Ty33 1 Tf
(!) Tj ET BT 8.9664 0 0 8.9664 411.134 559.537 Tm /Ty26 1 Tf (h) Tj ET BT
5.9776 0 0 5.9776 416.444 563.346 Tm /Ty33 1 Tf (") Tj ET BT 0.0007 Tc 8.9664 0 0 8.9664 419.128 559.537
Tm /Ty30 1 Tf (\);) Tj 0 Tc ET BT 6.2267 0 0 6.2267 51.258 547.582 Tm /Ty1
1 Tf (10) Tj ET BT 8.9664 0 0 8.9664 77.41 547.582 Tm /Ty1 1 Tf (end) Tj ET
BT 6.2267 0 0 6.2267 50.859 535.627 Tm /Ty1 1 Tf (11) Tj ET BT 8.9664 0 0 8.9664 62.067 535.627
Tm /Ty1 1 Tf (end) Tj ET BT 6.2267 0 0 6.2267 50.859 524.668 Tm /Ty1 1 Tf
(12) Tj ET BT 8.9664 0 0 8.9664 62.067 524.668 Tm /Ty1 1 Tf [ (r) 18 (etur)
15 (n) ] TJ ET BT 5.9776 0 0 5.9776 91.221 528.341 Tm /Ty28 1 Tf (1) Tj ET
0.379 w q 1 0 0 1 87.866 526.909 cm 0 0 m 10.363 0 l S Q BT 5.9776 0 0 5.9776 87.866 521.625
Tm /Ty32 1 Tf (|) Tj ET BT 5.9776 0 0 5.9776 90.135 521.625 Tm /Ty29 1 Tf
(B) Tj ET BT 5.9776 0 0 5.9776 95.96 521.625 Tm /Ty32 1 Tf (|) Tj ET BT 8.9664 0 0 8.9664 99.425 524.668
Tm /Ty26 1 Tf (R) Tj ET BT 8.9664 0 0 8.9664 108.508 524.668 Tm /Ty30 1 Tf
(+) Tj ET BT 8.9664 0 0 8.9664 117.724 524.668 Tm /Ty27 1 Tf (") Tj ET BT
0.0005 Tc 8.9664 0 0 8.9664 122.995 524.668 Tm /Ty5 1 Tf (||) Tj 0 Tc ET BT
8.9664 0 0 8.9664 128.115 524.668 Tm /Ty27 1 Tf (%) Tj ET BT 0.0005 Tc 8.9664 0 0 8.9664 132.685 524.668
Tm /Ty5 1 Tf (||) Tj 0 Tc ET BT 5.9776 0 0 5.9776 137.804 528.477 Tm /Ty28
1 Tf (2) Tj ET BT 5.9776 0 0 5.9776 137.804 523.09 Tm /Ty28 1 Tf (2) Tj ET
0.797 w q 1 0 0 1 50.112 517.74 cm 0 0 m 495 0 l S Q BT 9.9626 0 0 9.9626 50.112 484.464
Tm /Ty2 1 Tf [ (netw) 10 (ork) -287 (Hessian) -286 (is) -287 (ine) 15 (xpensi)
25 (v) 15 (e.) -419 (Subsequently) 65 (,) -296 (we) -287 (pro) 15 (vide) ]
TJ ET BT 9.9626 0 0 9.9626 50.112 472.509 Tm /Ty2 1 Tf [ (a) -230 (theorem)
-229 (that) -230 (can) -229 (be) -230 (used) -229 (to) -230 (bound) -229 (the)
-230 (T) 35 (race) -230 (of) -229 (Hessian) -230 (of) ] TJ ET BT 9.9626 0 0 9.9626 50.112 460.554
Tm /Ty2 1 Tf [ (the) -250 (full) -250 (netw) 10 (ork) -250 (with) -250 (that)
-250 (of) -250 (the) -250 (top) -250 (layer) -250 (only) 65 (.) ] TJ ET BT
9.9626 0 0 9.9626 50.112 435.636 Tm /Ty1 1 Tf [ (Example) -250 (1) -250 (\(T)
74 (w) 10 (o) -250 (Moons\)) ] TJ ET BT 9.9626 0 0 9.9626 158.584 435.636
Tm /Ty6 1 Tf [ (W) 92 (e) -412 (use) ] TJ ET BT 9.9626 0 0 9.9626 191.883 435.636
Tm /Ty12 1 Tf (500) Tj ET BT 9.9626 0 0 9.9626 210.934 435.636 Tm /Ty6 1 Tf
[ (tr) 15 (aining) -412 (e) 20 (xamples,) ] TJ ET BT 9.9626 0 0 9.9626 50.112 423.681
Tm /Ty6 1 Tf [ (wher) 37 (e) ] TJ ET BT 9.9626 0 0 9.9626 79.246 423.681 Tm
/Ty7 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 92.639 423.681 Tm /Ty14 1 Tf (!)
Tj ET BT 9.9626 0 0 9.9626 106.979 423.681 Tm /Ty17 1 Tf (R) Tj ET BT 6.9738 0 0 6.9738 114.175 427.296
Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 123.798 423.681 Tm /Ty6 1 Tf (and)
Tj ET BT 9.9626 0 0 9.9626 143.896 423.681 Tm /Ty7 1 Tf (y) Tj ET BT 0.7737
Tc 9.9626 0 0 9.9626 156.837 423.681 Tm /Ty14 1 Tf (!) Tj /Ty13 1 Tf ({) Tj
0 Tc ET BT 9.9626 0 0 9.9626 176.159 423.681 Tm /Ty12 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 181.14 423.681
Tm /Ty7 1 Tf (,) Tj ET BT 9.9626 0 0 9.9626 185.568 423.681 Tm /Ty12 1 Tf
(1) Tj ET BT 9.9626 0 0 9.9626 190.549 423.681 Tm /Ty13 1 Tf (}) Tj ET BT
9.9626 0 0 9.9626 200.684 423.681 Tm /Ty6 1 Tf [ (fr) 45 (om) -517 (the) -518
(T) 74 (wo) -517 (Moon) ] TJ ET BT 9.9626 0 0 9.9626 50.112 411.725 Tm /Ty6
1 Tf [ (dataset.) -694 (W) 92 (e) -378 (tr) 15 (ain) -378 (a) -378 (3-layer)
-378 (fully-connected) -378 (network) -378 (with) ] TJ ET BT 9.9626 0 0 9.9626 50.112 399.77
Tm /Ty6 1 Tf [ (Dense\(100\)-ReLU-Dense\(100\)-ReLU-Dense\(2\)) -215 (with)
-215 (the) -216 (A) 37 (T) ] TJ ET BT 9.9626 0 0 9.9626 50.112 387.815 Tm
/Ty6 1 Tf [ (loss) -250 (under) -250 (thr) 37 (ee) -250 (settings:) ] TJ ET
BT 9.9626 0 0 9.9626 61.569 366.089 Tm /Ty2 1 Tf Tj ET BT 9.9626 0 0 9.9626 70.037 366.089
Tm /Ty6 1 Tf [ (Standar) 37 (d:) -310 (no) -250 (r) 37 (e) 40 (gularization.)
] TJ ET BT 9.9626 0 0 9.9626 61.569 343.764 Tm /Ty2 1 Tf Tj ET BT 9.9626 0 0 9.9626 70.037 343.764
Tm /Ty6 1 Tf [ (T) 92 (op:) -310 (Re) 40 (gularizing) -250 (the) -250 (T)
55 (rH) -250 (of) -250 (the) -250 (top) -250 (layer) -250 (only) 55 (.) ]
TJ ET BT 9.9626 0 0 9.9626 61.569 321.438 Tm /Ty2 1 Tf Tj ET BT 9.9626 0 0 9.9626 70.037 321.438
Tm /Ty6 1 Tf [ (Full:) -310 (Re) 40 (gularizing) -250 (the) -250 (T) 55 (rH)
-250 (of) -250 (the) -250 (entir) 37 (e) -250 (network.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 299.713
Tm /Ty6 1 Tf [ (Thr) 45 (oughout) -365 (the) -366 (tr) 15 (aining) -365 (pr)
45 (ocess) -365 (\(x-axis\),) -394 (we) -365 (e) 15 (valuate) -366 (the) ]
TJ ET BT 9.9626 0 0 9.9626 50.112 287.757 Tm /Ty6 1 Tf [ (T) 55 (rH) -437
(of) -438 (the) ] TJ ET BT 9.9626 0 0 9.9626 99.172 287.757 Tm /Ty2 1 Tf (entire)
Tj ET BT 9.9626 0 0 9.9626 126.216 287.757 Tm /Ty6 1 Tf [ (network) -438 (\(y-axis\))
-437 (with) -438 (a) -437 (numerical) -438 (ap-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 275.802
Tm /Ty6 1 Tf [ (pr) 45 (oac) 15 (h) -392 (\(twice) -391 (dif) 18 (fer) 37
(entiation\)) -392 (and) -391 (plot) -392 (the) -392 (r) 37 (esult) 1 (s)
-392 (in) -392 (F) 45 (ig-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 263.847 Tm
/Ty6 1 Tf [ (ur) 37 (e) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 65.51418 263.847
Tm /Ty6 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 70.49548 263.847
Tm /Ty6 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 62.067 239.529 Tm /Ty2 1 Tf (Figure)
Tj ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 91.02828 239.529 Tm /Ty2 1 Tf
(2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 98.95851 239.529 Tm /Ty2 1 Tf
[ (empirically) -297 (sho) 25 (ws) -296 (that) -296 (re) 15 (gularizing) -296
(the) -297 (T) 35 (rH) -296 (of) ] TJ ET BT 9.9626 0 0 9.9626 50.112 227.574
Tm /Ty2 1 Tf [ (the) -276 (top) -275 (layer) -276 (\(orange\)) -275 (indirectly)
-276 (reduces) -275 (the) -276 (T) 35 (rH) -276 (of) -275 (the) -276 (en-)
] TJ ET BT 9.9626 0 0 9.9626 50.112 215.619 Tm /Ty2 1 Tf [ (tire) -374 (netw)
10 (ork) -374 (and) -374 (is) -374 (nearly) -374 (as) -374 (ef) 25 (fecti)
25 (v) 15 (e) -374 (as) -374 (re) 15 (gularizing) -374 (the) ] TJ ET BT 9.9626 0 0 9.9626 50.112 203.663
Tm /Ty2 1 Tf [ (entire) -250 (netw) 10 (ork) -250 (\(green\)) -250 (after)
-250 (the) -250 (60-th) -250 (epoch.) ] TJ ET BT 9.9626 0 0 9.9626 62.067 191.108
Tm /Ty2 1 Tf [ (Ne) 15 (xt,) -396 (we) -367 (pro) 15 (vide) -367 (a) -367
(theoretic) 1 (al) -367 (justication) -367 (for) -367 (the) -367 (im-) ]
TJ ET BT 9.9626 0 0 9.9626 50.112 179.153 Tm /Ty2 1 Tf [ (pact) -403 (of)
-402 (top-layer) -403 (T) 35 (rH) -402 (re) 15 (gularization) -403 (on) -402
(the) -403 (layers) -403 (belo) 25 (w) 65 (.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 167.198
Tm /Ty2 1 Tf [ (Intuiti) 25 (v) 15 (ely) 65 (,) -243 (our) -242 (Theorem)
] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 149.5587 167.198 Tm /Ty2 1 Tf
(4) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 154.54 167.198 Tm /Ty2 1 Tf [
(,) -243 (establishes) -241 (an) -242 (inducti) 25 (v) 15 (e) -242 (relation)
] TJ ET BT 9.9626 0 0 9.9626 50.112 155.243 Tm /Ty2 1 Tf [ (between) -256
(the) -257 (T) 35 (rH) -256 (of) -256 (the) -257 (consecut) 1 (i) 25 (v) 15
(e) -257 (layers) -256 (in) -256 (a) -257 (feedforw) 10 (ard) ] TJ ET BT 9.9626 0 0 9.9626 50.112 143.287
Tm /Ty2 1 Tf [ (neural) -310 (netw) 10 (ork) -310 (with) -310 (ReLU) -310
(acti) 25 (v) 25 (ation) -310 (and) -310 (CE) -310 (loss,) -325 (a) -310 (com-)
] TJ ET BT 9.9626 0 0 9.9626 50.112 131.332 Tm /Ty2 1 Tf [ (mon) -250 (b)
20 (uilding) -250 (block) -250 (in) -250 (A) 111 (T) -250 (and) -250 (TRADES)
-250 (training.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 106.414 Tm /Ty1 1 Tf
[ (Theor) 18 (em) -250 (4) -250 (\(Inducti) 10 (v) 10 (e) -250 (Relation)
-250 (in) -250 (T) 74 (rH\)) ] TJ ET BT 9.9626 0 0 9.9626 220.292 106.414
Tm /Ty6 1 Tf (Suppose) Tj ET BT 9.9626 0 0 9.9626 257.49 106.414 Tm /Ty7 1
Tf (g) Tj ET BT 6.9738 0 0 6.9738 262.242 104.92 Tm /Ty11 1 Tf (!) Tj ET BT
9.9626 0 0 9.9626 270.743 106.414 Tm /Ty6 1 Tf [ (is) -401 (a) ] TJ ET BT
9.9626 0 0 9.9626 50.112 94.459 Tm /Ty6 1 Tf [ (feed-forwar) 37 (d) -374 (network)
-374 (with) -375 (ReLU) -374 (activation.) -683 (F) 105 (or) -374 (the) ]
TJ ET BT 9.9626 0 0 9.9626 271.861 94.459 Tm /Ty7 1 Tf (i) Tj ET BT 9.9626 0 0 9.9626 275.294 94.459
Tm /Ty6 1 Tf (-th) Tj ET BT 9.9626 0 0 9.9626 50.112 81 Tm /Ty6 1 Tf [ (layer)
111 (,) -281 (let) ] TJ ET BT 9.9626 0 0 9.9626 87.468 81 Tm /Ty7 1 Tf (W)
Tj ET BT 6.9738 0 0 6.9738 98.261 84.615 Tm /Ty9 1 Tf (\() Tj ET BT 6.9738 0 0 6.9738 101.374 84.615
Tm /Ty10 1 Tf (i) Tj ET BT 6.9738 0 0 6.9738 104.193 84.615 Tm /Ty9 1 Tf (\))
Tj ET BT 9.9626 0 0 9.9626 110.541 81 Tm /Ty6 1 Tf [ (be) -275 (its) -274
(weight) -275 (and) ] TJ ET BT 9.9626 0 0 9.9626 181.823 81 Tm /Ty13 1 Tf
(I) Tj ET BT 6.9738 0 0 6.9738 187.983 86.175 Tm /Ty9 1 Tf (\() Tj ET BT 6.9738 0 0 6.9738 191.096 86.175
Tm /Ty10 1 Tf (i) Tj ET BT 6.9738 0 0 6.9738 193.915 86.175 Tm /Ty9 1 Tf (\))
Tj ET BT 6.9738 0 0 6.9738 187.248 79.835 Tm /Ty10 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 200.264 81
Tm /Ty6 1 Tf [ (be) -275 (its) -274 (input) -275 (e) 15 (valuated) ] TJ ET
Q q 0 0 612 792 re W n /Fm1 Do BT 8.9664 0 0 8.9664 308.862 307.077 Tm /Ty2
1 Tf [ (Figure) -222 (2.) -301 (T) 35 (ra) 1 (ce) -222 (of) -222 (the) -222
(Hessian) -222 (\(T) 35 (rH\)) -222 (of) -222 (the) -222 (entire) -222 (netw)
10 (ork) -221 (\(y-axis\)) ] TJ ET BT 8.9664 0 0 8.9664 308.862 296.118 Tm
/Ty2 1 Tf [ (o) 15 (v) 15 (er) -248 (training) -248 (epochs) -247 (\(x-axis\))
-248 (with) -248 (\(1\)) -248 (no) -248 (re) 15 (gularization) -247 (\(Standard,)
] TJ ET BT 8.9664 0 0 8.9664 308.862 285.159 Tm /Ty2 1 Tf [ (in) -253 (blue\);)
-255 (\(2\)) -254 (top) -253 (layer) -253 (T) 35 (rH) -253 (re) 15 (gularization)
-254 (\(T) 80 (op,) -254 (in) -253 (orange\);) -255 (and) -253 (\(3\)) ] TJ
ET BT 8.9664 0 0 8.9664 308.862 274.2 Tm /Ty2 1 Tf [ (re) 15 (gularization)
-215 (the) -216 (T) 35 (rH) -215 (of) -216 (all) -215 (layers) -215 (\(Full,)
-223 (in) -215 (green\).) -299 (See) -215 (Example) ] TJ ET /Cs1 cs 1 0 0
sc BT 8.9664 0 0 8.9664 540.6255 274.2 Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc
BT 8.9664 0 0 8.9664 308.862 263.241 Tm /Ty2 1 Tf [ (for) -250 (the) -250
(e) 15 (xperimental) -250 (setup.) ] TJ ET BT 9.9626 0 0 9.9626 308.862 228.666
Tm /Ty6 1 Tf (at) Tj ET BT 9.9626 0 0 9.9626 319.332 228.666 Tm /Ty7 1 Tf
(x) Tj ET BT 9.9626 0 0 9.9626 325.025 228.666 Tm /Ty6 1 Tf [ (.) -379 (Thus,)
] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 355.933 228.666 Tm /Ty12 1 Tf [ (Tr)
-84 (H) ] TJ 0 Tc ET BT 0.0005 Tc 6.9738 0 0 6.9738 373.672 233.011 Tm /Ty9
1 Tf (CE) Tj 0 Tc ET BT 6.9738 0 0 6.9738 373.672 226.203 Tm /Ty10 1 Tf (x)
Tj ET BT 9.9626 0 0 9.9626 385.212 228.666 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 389.086 228.666
Tm /Ty7 1 Tf (W) Tj ET BT 6.9738 0 0 6.9738 399.879 232.281 Tm /Ty9 1 Tf (\()
Tj ET BT 6.9738 0 0 6.9738 402.992 232.281 Tm /Ty10 1 Tf (i) Tj ET BT 6.9738 0 0 6.9738 405.811 232.281
Tm /Ty16 1 Tf (!) Tj ET BT 0.0005 Tc 6.9738 0 0 6.9738 412.038 232.281 Tm
/Ty9 1 Tf (1\)) Tj 0 Tc ET BT 9.9626 0 0 9.9626 419.62 228.666 Tm /Ty12 1
Tf (\)) Tj ET BT 9.9626 0 0 9.9626 423.495 228.666 Tm /Ty6 1 Tf [ (,) -279
(i.e) 15 (.) -378 (T) 55 (rH) -273 (e) 15 (valuated) -273 (at) ] TJ ET BT
9.9626 0 0 9.9626 515.11 228.666 Tm /Ty7 1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 523.523 228.666
Tm /Ty6 1 Tf (using) Tj ET BT 9.9626 0 0 9.9626 308.862 216.711 Tm /Ty6 1
Tf [ (a) -250 (CE) -250 (loss) -250 (w) 74 (.r) 111 (.t) ] TJ ET BT 9.9626 0 0 9.9626 368.468 216.711
Tm /Ty7 1 Tf (W) Tj ET BT 6.9738 0 0 6.9738 379.261 220.326 Tm /Ty9 1 Tf (\()
Tj ET BT 6.9738 0 0 6.9738 382.374 220.326 Tm /Ty10 1 Tf (i) Tj ET BT 6.9738 0 0 6.9738 385.193 220.326
Tm /Ty16 1 Tf (!) Tj ET BT 0.0005 Tc 6.9738 0 0 6.9738 391.419 220.326 Tm
/Ty9 1 Tf (1\)) Tj 0 Tc ET BT 9.9626 0 0 9.9626 399.002 216.711 Tm /Ty6 1
Tf [ (,) -250 (is) -250 (equal) -250 (to) ] TJ ET BT -0.0828 Tc 9.9626 0 0 9.9626 324.825 191.834
Tm /Ty12 1 Tf [ (Tr) -84 (H) ] TJ 0 Tc ET BT 0.0005 Tc 6.9738 0 0 6.9738 342.564 196.179
Tm /Ty9 1 Tf (CE) Tj 0 Tc ET BT 6.9738 0 0 6.9738 342.564 189.371 Tm /Ty10
1 Tf (x) Tj ET BT 9.9626 0 0 9.9626 354.104 191.834 Tm /Ty12 1 Tf (\() Tj
ET BT 9.9626 0 0 9.9626 357.979 191.834 Tm /Ty7 1 Tf (W) Tj ET BT 6.9738 0 0 6.9738 368.771 195.947
Tm /Ty9 1 Tf (\() Tj ET BT 6.9738 0 0 6.9738 371.885 195.947 Tm /Ty10 1 Tf
(i) Tj ET BT 6.9738 0 0 6.9738 374.704 195.947 Tm /Ty16 1 Tf (!) Tj ET BT
0.0005 Tc 6.9738 0 0 6.9738 380.93 195.947 Tm /Ty9 1 Tf (1\)) Tj 0 Tc ET BT
0.2789 Tc 9.9626 0 0 9.9626 388.513 191.834 Tm /Ty12 1 Tf (\)=) Tj 0 Tc ET
BT 9.9626 0 0 9.9626 405.671 191.834 Tm /Ty13 1 Tf [ (|) -0.8 (|) -0.8 ({I)
] TJ ET BT 6.9738 0 0 6.9738 422.347 195.947 Tm /Ty9 1 Tf (\() Tj ET BT 6.9738 0 0 6.9738 425.46 195.947
Tm /Ty10 1 Tf (i) Tj ET BT 6.9738 0 0 6.9738 428.279 195.947 Tm /Ty16 1 Tf
(!) Tj ET BT 0.0005 Tc 6.9738 0 0 6.9738 434.506 195.947 Tm /Ty9 1 Tf (1\))
Tj 0 Tc ET BT 6.9738 0 0 6.9738 421.612 189.371 Tm /Ty10 1 Tf (x) Tj ET BT
9.9626 0 0 9.9626 442.089 191.834 Tm /Ty13 1 Tf [ (}|) -0.8 (|) ] TJ ET BT
6.9738 0 0 6.9738 452.605 195.947 Tm /Ty9 1 Tf (2) Tj ET BT 6.9738 0 0 6.9738 452.605 189.371
Tm /Ty9 1 Tf (2) Tj ET BT 9.9626 0 0 9.9626 467.031 201.298 Tm /Ty19 1 Tf
(!) Tj ET BT 0.0243 Tc 6.9738 0 0 6.9738 458.735 178.962 Tm /Ty10 1 Tf [ (k,)
24 (d) ] TJ 0 Tc ET BT 6.9738 0 0 6.9738 469.652 178.962 Tm /Ty16 1 Tf (#)
Tj ET BT 6.9738 0 0 6.9738 475.02 178.962 Tm /Ty10 1 Tf (P) Tj ET BT 4.9813 0 0 4.9813 481.165 180.958
Tm /Ty37 1 Tf (\() Tj ET BT 4.9813 0 0 4.9813 483.863 180.958 Tm /Ty20 1 Tf
(i) Tj ET BT 4.9813 0 0 4.9813 486.521 180.958 Tm /Ty37 1 Tf (\)) Tj ET BT
9.9626 0 0 9.9626 489.718 191.834 Tm /Ty13 1 Tf ({H) Tj ET BT 6.9738 0 0 6.9738 503.209 195.947
Tm /Ty9 1 Tf (\() Tj ET BT 6.9738 0 0 6.9738 506.322 195.947 Tm /Ty10 1 Tf
(i) Tj ET BT 6.9738 0 0 6.9738 509.141 195.947 Tm /Ty9 1 Tf (\)) Tj ET BT
9.9626 0 0 9.9626 512.752 191.834 Tm /Ty13 1 Tf (}) Tj ET BT 0.0243 Tc 6.9738 0 0 6.9738 517.734 190.339
Tm /Ty10 1 Tf [ (k,) 24 (d) ] TJ 0 Tc ET BT 9.9626 0 0 9.9626 329.558 132.426
Tm /Ty6 1 Tf [ (wher) 37 (e) ] TJ ET BT 9.9626 0 0 9.9626 356.029 132.426
Tm /Ty13 1 Tf ({H) Tj ET BT 6.9738 0 0 6.9738 369.52 136.54 Tm /Ty9 1 Tf (\()
Tj ET BT 6.9738 0 0 6.9738 372.633 136.54 Tm /Ty10 1 Tf (i) Tj ET BT 6.9738 0 0 6.9738 375.452 136.54
Tm /Ty9 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 379.063 132.426 Tm /Ty13 1 Tf
(}) Tj ET BT 0.0243 Tc 6.9738 0 0 6.9738 384.045 130.932 Tm /Ty10 1 Tf [ (k,)
24 (d) ] TJ 0 Tc ET BT 4.9813 0 0 4.9813 394.962 129.935 Tm /Ty20 1 Tf (i)
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1 Tf (=0) Tj 0 Tc ET BT 9.9626 0 0 9.9626 252.046 276.75 Tm /Ty7 1 Tf (.)
Tj ET BT 9.9626 0 0 9.9626 254.814 276.75 Tm /Ty12 1 Tf (0157\() Tj ET BT
9.9626 0 0 9.9626 278.613 276.75 Tm /Ty14 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 50.112 264.794
Tm /Ty12 1 Tf (4) Tj ET BT 9.9626 0 0 9.9626 55.093 264.794 Tm /Ty7 1 Tf (/)
Tj ET BT 9.9626 0 0 9.9626 60.075 264.794 Tm /Ty12 1 Tf (255\)) Tj ET BT 9.9626 0 0 9.9626 82.77 264.794
Tm /Ty2 1 Tf [ (for) -389 (the) ] TJ ET BT 9.9626 0 0 9.9626 114.315 264.794
Tm /Ty8 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 118.466 263.3 Tm /Ty16 1 Tf (')
Tj ET BT 9.9626 0 0 9.9626 130.784 264.794 Tm /Ty2 1 Tf [ (ball,) -424 (respecti)
25 (v) 15 (ely) 65 (.) -727 (W) 80 (e) -390 (do) -389 (not) -389 (use) -389
(e) 15 (x-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 252.839 Tm /Ty2 1 Tf [ (tra)
-331 (data) -331 (for) -330 (ImageNet.) -553 (The) -331 (chosen) ] TJ ET BT
9.9626 0 0 9.9626 195.749 252.839 Tm /Ty8 1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 199.793 252.839
Tm /Ty2 1 Tf [ (s) -331 (follo) 25 (w) -331 (the) -330 (common) ] TJ ET BT
9.9626 0 0 9.9626 50.112 240.884 Tm /Ty2 1 Tf [ (choices) -307 (in) -307 (the)
-306 (literature) -307 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 151.4217 240.884
Tm /Ty2 1 Tf (21) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 161.3843 240.884
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 165.5486 240.884
Tm /Ty2 1 Tf (26) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 175.5112 240.884
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 179.6756 240.884
Tm /Ty2 1 Tf (32) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 189.6382 240.884
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 193.8026 240.884
Tm /Ty2 1 Tf (49) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 203.7652 240.884
Tm /Ty2 1 Tf [ (].) -480 (W) 80 (e) -307 (report) -307 (the) -307 (test) ]
TJ ET BT 9.9626 0 0 9.9626 50.112 228.929 Tm /Ty2 1 Tf [ (accurac) 15 (y)
-265 (e) 25 (v) 25 (aluated) -265 (with) -265 (benign) -265 (images) -266
(and) -265 (adv) 15 (ersarial) -265 (im-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 216.974
Tm /Ty2 1 Tf [ (ages) -248 (generated) -247 (by) -248 (AutoAttack) -247 ([)
] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 176.1688 216.974 Tm /Ty2 1 Tf
(11) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 186.1314 216.974 Tm /Ty2 1 Tf
[ (]) -248 (\(AutoPGD+AutoDLR\),) ] TJ ET BT 9.9626 0 0 9.9626 50.112 205.018
Tm /Ty2 1 Tf [ (which) -250 (is) -250 (widely) -250 (used) -250 (in) -250
(the) -250 (literature) -250 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 203.1276 205.018
Tm /Ty2 1 Tf (21) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 213.0902 205.018
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 216.876 205.018
Tm /Ty2 1 Tf (26) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 226.8386 205.018
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 230.6243 205.018
Tm /Ty2 1 Tf (49) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 240.5869 205.018
Tm /Ty2 1 Tf (].) Tj ET BT 9.9626 0 0 9.9626 50.112 176.641 Tm /Ty1 1 Tf [
(Netw) 10 (ork) -687 (Ar) 18 (chitectur) 18 (es.) ] TJ ET BT 9.9626 0 0 9.9626 164.111 176.641
Tm /Ty2 1 Tf [ (W) 80 (e) -687 (use) -686 (V) 60 (ision) -687 (T) 35 (ransformer)
] TJ ET BT 9.9626 0 0 9.9626 50.112 164.686 Tm /Ty2 1 Tf [ (\(V) 60 (iT\))
-363 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 79.13305 164.686 Tm
/Ty2 1 Tf (14) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 89.09565 164.686 Tm
/Ty2 1 Tf [ (]) -363 (through) -363 (all) -363 (e) 15 (xperiments) -363 (because)
-364 (of) -363 (its) -363 (success) ] TJ ET BT 9.9626 0 0 9.9626 50.112 152.731
Tm /Ty2 1 Tf [ (on) -332 (multiple) -332 (tasks) -332 (o) 15 (v) 15 (er) -331
(e) 15 (xisting) -332 (architectures.) -556 (Specically) 65 (,) ] TJ ET BT
9.9626 0 0 9.9626 50.112 140.776 Tm /Ty2 1 Tf [ (we) -334 (report) -334 (the)
-334 (results) -334 (of) -334 (V) 60 (iT) 92 (-L16,) -356 (Hybrid-L16) -334
(for) -334 (CIF) 74 (AR-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 128.82 Tm /Ty2
1 Tf [ (10/100) -261 (and) -260 (V) 60 (iT) 92 (-B16,) -264 (V) 60 (iT) 92
(-L16) -261 (for) -260 (ImageNet) -261 (\(additional) -261 (re-) ] TJ ET BT
9.9626 0 0 9.9626 50.112 116.865 Tm /Ty2 1 Tf [ (sults) -268 (and) -268 (architecture)
-268 (details) -268 (can) -268 (be) -268 (found) -269 (in) -268 (Appendix)
] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 273.3639 116.865 Tm /Ty2 1 Tf
(G) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 280.5569 116.865 Tm /Ty2 1 Tf
(\).) Tj ET BT 9.9626 0 0 9.9626 50.112 104.91 Tm /Ty2 1 Tf [ (W) 80 (e) -301
(initialize) -301 (the) -302 (weights) -301 (from) -301 (a) -301 (pre-trained)
-301 (checkpoint) -302 (on) ] TJ ET BT 9.9626 0 0 9.9626 50.112 92.955 Tm
/Ty2 1 Tf [ (ImageNet21K) -276 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 112.6174 92.955
Tm /Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 117.5987 92.955 Tm
/Ty2 1 Tf [ (].) -388 (Noti) 1 (ce) -276 (that) -276 (the) -276 (resolution)
-276 (of) -276 (the) -276 (CIF) 74 (AR) ] TJ ET BT 9.9626 0 0 9.9626 50.112 81
Tm /Ty2 1 Tf [ (images) -321 (\() ] TJ ET BT 9.9626 0 0 9.9626 84.852 81 Tm
/Ty12 1 Tf (32) Tj ET BT 9.9626 0 0 9.9626 97.552 81 Tm /Ty14 1 Tf (\)) Tj
ET BT 9.9626 0 0 9.9626 108.039 81 Tm /Ty12 1 Tf (32) Tj ET BT 9.9626 0 0 9.9626 118.002 81
Tm /Ty2 1 Tf [ (\)) -321 (are) -321 (too) -321 (small) -321 (to) -321 (correctly)
-321 (align) -321 (with) -321 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 710.037
Tm /Ty2 1 Tf [ (pre-trained) -341 (k) 10 (ernel) -340 (of) -341 (the) -341
-340 (layer) 55 (.) -583 (T) 80 (o) -340 (address) -341 (this) -341
(issue,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 698.082 Tm /Ty2 1 Tf [ (we)
-253 (do) 25 (wn-sample) -253 (the) -253 (k) 10 (ernel) -253 (of) -253 (the)
-253 (input) -254 (layer) -253 (follo) 25 (wing) -253 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 686.127
Tm /Ty2 1 Tf [ (receipt) -250 (proposed) -250 (by) -250 (Mahmood) -250 (et)
-250 (al.) -250 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 458.5501 686.127
Tm /Ty2 1 Tf (33) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 468.5127 686.127
Tm /Ty2 1 Tf (].) Tj ET BT 9.9626 0 0 9.9626 308.862 654.116 Tm /Ty1 1 Tf
(Methods.) Tj ET BT 9.9626 0 0 9.9626 358.396 654.116 Tm /Ty2 1 Tf [ (W) 80
(e) -395 (train) -396 (the) -395 (models) -396 (using) -395 (A) 111 (T) -395
(and) -396 (TRADES) ] TJ ET BT 9.9626 0 0 9.9626 308.862 642.161 Tm /Ty2 1
Tf [ (losses,) -356 (together) -335 (with) -335 (the) -335 (follo) 25 (wing)
-335 (defenses:) -481 (\(1\)) -335 (base:) -480 (no) ] TJ ET BT 9.9626 0 0 9.9626 308.862 630.206
Tm /Ty2 1 Tf [ (re) 15 (gularization;) -293 (\(2\)) -280 (A) 90 (WP) -279
([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 411.4768 630.206 Tm /Ty2
1 Tf (49) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 421.4394 630.206 Tm /Ty2
1 Tf [ (];) -293 (\(3\)) -279 (SW) 120 (A) -279 ([) ] TJ ET /Cs1 cs 0 1 0
sc BT 9.9626 0 0 9.9626 471.88 630.206 Tm /Ty2 1 Tf (24) Tj ET /Cs2 cs 0 sc
BT 9.9626 0 0 9.9626 481.8426 630.206 Tm /Ty2 1 Tf [ (];) -294 (\(4\)) -279
(S2O) -279 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 529.0653 630.206
Tm /Ty2 1 Tf (26) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 539.0279 630.206
Tm /Ty2 1 Tf (];) Tj ET BT 9.9626 0 0 9.9626 308.862 618.251 Tm /Ty2 1 Tf
[ (and) -414 (\(5\)) -414 (our) -414 (Algorithm) ] TJ ET /Cs1 cs 1 0 0 sc
BT 9.9626 0 0 9.9626 406.1568 618.251 Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc
BT 9.9626 0 0 9.9626 415.2626 618.251 Tm /Ty2 1 Tf [ (\(T) 35 (rH\).) -414
(W) 80 (e) -414 (are) -414 (interested) -414 (in) -414 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 606.296
Tm /Ty2 1 Tf [ (baselines) -231 (defenses) -232 (because) -231 (of) -231 (their)
-232 (connections) -231 (to) -231 (the) -232 (P) 92 (A) 40 (C-) ] TJ ET BT
9.9626 0 0 9.9626 308.862 594.341 Tm /Ty2 1 Tf [ (Bayesian) -368 (bound) -368
(or) -368 (the) -368 (loss) -369 (atness.) -664 (During) -368 (training,)
-398 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 582.385 Tm /Ty2 1 Tf [ (model)
-521 (w) 10 (as) -520 (partitioned) -521 (o) 15 (v) 15 (er) -521 (four) -520
(Google) -521 (Cloud) -521 (TPUv4) ] TJ ET BT 9.9626 0 0 9.9626 308.862 570.43
Tm /Ty2 1 Tf [ (chips) -212 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 335.3227 570.43
Tm /Ty2 1 Tf (27) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 345.2853 570.43
Tm /Ty2 1 Tf [ (]) -211 (for) -212 (the) -212 (base) -212 (and) -211 (T) 35
(rH) -212 (methods,) -219 (and) -212 (eight) -212 (chips) -212 (for) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 558.475 Tm /Ty2 1 Tf [ (A) 90 (WP) 111 (,)
-214 (S2O,) -213 (and) -214 (SW) 120 (A) -214 (as) -213 (the) 15 (y) -214
(consume) -213 (more) -214 (HBM) -214 (memory) 65 (.) ] TJ ET BT 9.9626 0 0 9.9626 308.862 526.465
Tm /Ty1 1 Tf [ (Hyper) 10 (parameter) -252 (Selection.) ] TJ ET BT 9.9626 0 0 9.9626 433.842 526.465
Tm /Ty2 1 Tf [ (T) 35 (raining) -252 (rob) 20 (ust) -252 (V) 60 (iTs) -252
(can) -252 (be) ] TJ ET BT 9.9626 0 0 9.9626 308.862 514.509 Tm /Ty2 1 Tf
[ (challenging) -239 (due) -240 (to) -239 (a) -240 (lar) 18 (ge) -239 (number)
-240 (of) -239 (h) 5 (yper) 20 (-parameters.) -307 (W) 80 (e) ] TJ ET BT 9.9626 0 0 9.9626 308.862 502.554
Tm /Ty2 1 Tf [ (use) -288 (tw) 10 (o) -289 (steps) -288 (for) -288 (h) 5 (yperparameter)
-289 (selection.) -425 (F) 15 (or) -288 (the) -289 (choice) ] TJ ET BT 9.9626 0 0 9.9626 308.862 490.599
Tm /Ty2 1 Tf [ (of) -351 (common) -352 (h) 5 (yper) 20 (-parameters,) -376
(e.g.) -614 (batch) -352 (size,) -376 (patch) -352 (size,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 478.644
Tm /Ty2 1 Tf [ (training) -362 (iterations,) -391 (and) -362 (etc.) -648 (\(a)
-362 (full) -363 (list) -362 (is) -363 (included) -362 (in) -363 (Ap-) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 466.689 Tm /Ty2 1 Tf (pendix) Tj ET /Cs1 cs
1 0 0 sc BT 9.9626 0 0 9.9626 338.8096 466.689 Tm /Ty2 1 Tf (D) Tj ET /Cs2
cs 0 sc BT 9.9626 0 0 9.9626 346.0026 466.689 Tm /Ty2 1 Tf [ (\),) -284 (we)
-284 -284 (do) -284 (a) -284 (lar) 18 (ge) -284 (grid) -284 (search)
-284 (and) -284 (select) -284 (v) 25 (alues) ] TJ ET BT 9.9626 0 0 9.9626 308.862 454.734
Tm /Ty2 1 Tf [ (that) -236 (produce) -235 (the) -236 (best) -236 (results)
-235 (on) -236 (TRADES\() ] TJ ET BT 9.9626 0 0 9.9626 476.242 454.734 Tm
/Ty4 1 Tf (base) Tj ET BT 9.9626 0 0 9.9626 500.152 454.734 Tm /Ty2 1 Tf [
(\).) -305 (This) -236 (step) ] TJ ET BT 9.9626 0 0 9.9626 308.862 442.778
Tm /Ty2 1 Tf [ (is) -250 (referred) -250 (to) -250 (as) -250 (pre-tuning)
-250 (and) -250 (is) -250 (done) -250 (per) -250 (dataset.) ] TJ ET BT 9.9626 0 0 9.9626 320.817 429.826
Tm /Ty2 1 Tf [ (After) -232 (the) -232 -232 (step,) -236 (where) -232
(the) -232 (common) -232 (h) 5 (yper) 20 (-parameters) ] TJ ET BT 9.9626 0 0 9.9626 308.862 417.871
Tm /Ty2 1 Tf [ (are) -318 (lock) 10 (ed,) -336 (we) -319 (tune) -318 (and)
-318 (report) -319 (the) -318 (best) -319 (results) -318 (after) -319 (trying)
] TJ ET BT 9.9626 0 0 9.9626 308.862 405.916 Tm /Ty2 1 Tf [ (dif) 25 (ferent)
-239 (sets) -238 (of) -239 (method-specic) -239 (h) 5 (yper) 20 (-parameters,)
-241 (e.g.,) -241 (the) ] TJ ET BT 9.9626 0 0 9.9626 308.862 393.96 Tm /Ty2
1 Tf [ (norm) -319 (bound) -319 (of) -319 (weight) -319 (noises) -319 (in)
-319 (A) 90 (WP) -319 (and) ] TJ ET BT 9.9626 0 0 9.9626 483.92 393.96 Tm
/Ty8 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 492.909 393.96 Tm /Ty2 1 Tf [ (for)
-319 (T) 35 (rH.) -319 (Ap-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 382.005
Tm /Ty2 1 Tf (pendix) Tj ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 338.7797 382.005
Tm /Ty2 1 Tf (E) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 347.6763 382.005
Tm /Ty2 1 Tf [ (pro) 15 (vides) -281 (a) -281 (full) -282 (list) -281 (of)
-282 (h) 5 (yper) 20 (-parameters) -281 (we) -281 (use) -282 (to) ] TJ ET
BT 9.9626 0 0 9.9626 308.862 370.05 Tm /Ty2 1 Tf [ (produce) -250 (our) -250
(main) -250 (results) -250 (in) -250 (T) 80 (able) ] TJ ET /Cs1 cs 1 0 0 sc
BT 9.9626 0 0 9.9626 444.7519 370.05 Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT
9.9626 0 0 9.9626 449.7332 370.05 Tm /Ty2 1 Tf (.) Tj ET BT 10.9589 0 0 10.9589 308.862 347.133
Tm /Ty1 1 Tf [ (4.2.) -250 (Main) -250 (Results) ] TJ ET BT 9.9626 0 0 9.9626 320.817 328.203
Tm /Ty2 1 Tf [ (In) -293 (T) 80 (able) ] TJ ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 356.8418 328.203
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 361.8231 328.203
Tm /Ty2 1 Tf [ (,) -303 (we) -293 (report) -293 (the) -293 (rob) 20 (ust)
-293 (test) -293 (accurac) 15 (y) -293 (using) -293 (dif-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 316.248
Tm /Ty2 1 Tf [ (ferent) -396 (types) -397 (of) -396 (defenses.) -749 (The)
-397 (top) -396 (results) -396 (are) -397 (highlighted) ] TJ ET BT 9.9626 0 0 9.9626 308.862 304.293
Tm /Ty2 1 Tf [ (in) -360 (bold) -360 (font.) -641 (T) 80 (o) -360 (measure)
-360 (the) -360 (signicance) -360 (of) -361 (an) -360 (impro) 15 (v) 15 (e-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 292.338 Tm /Ty2 1 Tf [ (ment,) -234 (we)
-230 (calculate) -229 (the) -230 (maximum) -230 (standard) -229 (error) -230
(\(SE\)) -230 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 523.9246 292.338
Tm /Ty2 1 Tf (44) Tj ET /Cs2 cs 0 sc BT 0.23 Tc 9.9626 0 0 9.9626 533.8872 292.338
Tm /Ty2 1 Tf (]=) Tj 0 Tc ET BT 9.9626 0 0 9.9626 308.862 288.9 Tm /Ty19 1
Tf (') Tj ET 0.398 w q 1 0 0 1 318.825 289.1 cm 0 0 m 73.504 0 l S Q BT 9.9626 0 0 9.9626 318.825 280.383
Tm /Ty12 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 323.806 280.383 Tm /Ty7 1 Tf
(.) Tj ET BT 9.9626 0 0 9.9626 326.573 280.383 Tm /Ty12 1 Tf (5) Tj ET BT
9.9626 0 0 9.9626 333.769 280.383 Tm /Ty14 1 Tf (*) Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 340.964 280.383
Tm /Ty12 1 Tf (\(1) Tj 0 Tc ET BT 9.9626 0 0 9.9626 352.033 280.383 Tm /Ty14
1 Tf (#) Tj ET BT 9.9626 0 0 9.9626 361.996 280.383 Tm /Ty12 1 Tf (0) Tj ET
BT 9.9626 0 0 9.9626 366.977 280.383 Tm /Ty7 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 369.745 280.383
Tm /Ty12 1 Tf (5\)) Tj ET BT 9.9626 0 0 9.9626 378.6 280.383 Tm /Ty7 1 Tf
(/m) Tj ET BT 9.9626 0 0 9.9626 395.357 280.383 Tm /Ty2 1 Tf (\(where) Tj
ET BT 9.9626 0 0 9.9626 426.042 280.383 Tm /Ty7 1 Tf (m) Tj ET BT 9.9626 0 0 9.9626 437.817 280.383
Tm /Ty2 1 Tf [ (denotes) -304 (the) -304 (number) -304 (of) -304 (test) ]
TJ ET BT 9.9626 0 0 9.9626 308.862 268.428 Tm /Ty2 1 Tf [ (e) 15 (xamples\))
-380 (for) -380 (each) -380 (dataset.) -700 (Thus,) -413 (the) -380 (accurac)
15 (y) -380 (of) -380 (a) -380 (cer) 20 (-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 256.472
Tm /Ty2 1 Tf [ (tain) -350 (model) -351 (is) -350 (re) 15 (g) 5 (arded) -351
(a) ] TJ ET BT 9.9626 0 0 9.9626 411.89 256.472 Tm /Ty6 1 Tf (silver) Tj ET
BT 9.9626 0 0 9.9626 437.748 256.472 Tm /Ty2 1 Tf (result) Tj ET BT 9.9626 0 0 9.9626 463.376 256.472
Tm /Ty7 1 Tf (a) Tj ET BT 6.9738 0 0 6.9738 468.642 254.978 Tm /Ty10 1 Tf
[ (s) -0.2 (i) -0.2 (l) -6.3 (v) -36.4 (er) ] TJ ET BT 9.9626 0 0 9.9626 490.208 256.472
Tm /Ty2 1 Tf [ (,) -376 (if) -350 (its) -351 (SE) -350 (in-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 244.517
Tm /Ty2 1 Tf [ (terv) 25 (al) -267 (o) 15 (v) 15 (erlaps) -266 (with) -267
(the) -267 (that) -266 (of) -267 (the) -267 (top) -266 (result) ] TJ ET BT
9.9626 0 0 9.9626 488.837 244.517 Tm /Ty7 1 Tf (a) Tj ET BT 0.0006 Tc 6.9738 0 0 6.9738 494.103 243.023
Tm /Ty10 1 Tf (top) Tj 0 Tc ET BT 9.9626 0 0 9.9626 505.65 244.517 Tm /Ty2
1 Tf [ (.) -360 (Namely) 65 (,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 232.562
Tm /Ty7 1 Tf (a) Tj ET BT 0.0006 Tc 6.9738 0 0 6.9738 314.128 231.068 Tm /Ty10
1 Tf (top) Tj 0 Tc ET BT 9.9626 0 0 9.9626 327.889 232.562 Tm /Ty14 1 Tf (#)
Tj ET BT 0.0582 Tc 9.9626 0 0 9.9626 337.852 232.562 Tm /Ty7 1 Tf (SE) Tj
0 Tc ET BT 9.9626 0 0 9.9626 355.231 232.562 Tm /Ty14 1 Tf (%) Tj ET BT 9.9626 0 0 9.9626 365.747 232.562
Tm /Ty7 1 Tf (a) Tj ET BT 6.9738 0 0 6.9738 371.013 231.068 Tm /Ty10 1 Tf
[ (s) -0.2 (i) -0.2 (l) -6.3 (v) -36.4 (er) ] TJ ET BT 9.9626 0 0 9.9626 394.793 232.562
Tm /Ty12 1 Tf (+) Tj ET BT 0.0582 Tc 9.9626 0 0 9.9626 404.755 232.562 Tm
/Ty7 1 Tf (SE) Tj 0 Tc ET BT 9.9626 0 0 9.9626 419.367 232.562 Tm /Ty2 1 Tf
(.) Tj ET BT 9.9626 0 0 9.9626 308.862 200.552 Tm /Ty1 1 Tf [ (CIF) 90 (AR-10/100.)
] TJ ET BT 9.9626 0 0 9.9626 382.954 200.552 Tm /Ty2 1 Tf [ (In) -241 (CIF)
74 (AR-10/100,) -242 (a) -241 (signicant) -241 (impro) 15 (v) 15 (e-) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 188.596 Tm /Ty2 1 Tf [ (ment) -353 (is) -352
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BT 9.9626 0 0 9.9626 494.882 494.086 Tm /Ty7 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 497.65 494.086
Tm /Ty12 1 Tf (0\)) Tj ET BT 9.9626 0 0 9.9626 69.234 482.131 Tm /Ty2 1 Tf
(Defense) Tj ET BT 9.9626 0 0 9.9626 150.479 482.131 Tm /Ty4 1 Tf (Clean)
Tj ET BT 9.9626 0 0 9.9626 180.367 482.131 Tm /Ty2 1 Tf (\(%\)) Tj ET BT 9.9626 0 0 9.9626 207.256 482.131
Tm /Ty4 1 Tf (AA) Tj ET BT 9.9626 0 0 9.9626 219.211 482.131 Tm /Ty2 1 Tf
(\(%\)) Tj ET BT 9.9626 0 0 9.9626 246.1 482.131 Tm /Ty4 1 Tf (Clean) Tj ET
BT 9.9626 0 0 9.9626 278.479 482.131 Tm /Ty2 1 Tf (\(%\)) Tj ET BT 9.9626 0 0 9.9626 305.368 482.131
Tm /Ty4 1 Tf (AA) Tj ET BT 9.9626 0 0 9.9626 317.323 482.131 Tm /Ty2 1 Tf
(\(%\)) Tj ET q 1 0 0 1 338.234 478.544 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 344.212 482.131
Tm /Ty4 1 Tf (Clean) Tj ET BT 9.9626 0 0 9.9626 374.1 482.131 Tm /Ty2 1 Tf
(\(%\)) Tj ET BT 9.9626 0 0 9.9626 400.989 482.131 Tm /Ty4 1 Tf (AA) Tj ET
BT 9.9626 0 0 9.9626 412.944 482.131 Tm /Ty2 1 Tf (\(%\)) Tj ET BT 9.9626 0 0 9.9626 439.833 482.131
Tm /Ty4 1 Tf (Clean) Tj ET BT 9.9626 0 0 9.9626 472.212 482.131 Tm /Ty2 1
Tf (\(%\)) Tj ET BT 9.9626 0 0 9.9626 499.101 482.131 Tm /Ty4 1 Tf (AA) Tj
ET BT 9.9626 0 0 9.9626 511.056 482.131 Tm /Ty2 1 Tf (\(%\)) Tj ET 0.498 w
q 1 0 0 1 63.256 476.58 cm 0 0 m 468.711 0 l S Q BT 9.9626 0 0 9.9626 69.234 465.174
Tm /Ty2 1 Tf [ (A) 111 (T\() ] TJ ET BT 9.9626 0 0 9.9626 84.726 465.174 Tm
/Ty4 1 Tf (base) Tj ET BT 9.9626 0 0 9.9626 108.636 465.174 Tm /Ty2 1 Tf [
(\)) -5242 (72.2) -3049 (39.0) ] TJ ET 0.398 w q 1 0 0 1 240.123 461.587 cm
0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 261.039 465.174 Tm /Ty2 1 Tf [ (71.0)
-3174 (39.3) ] TJ ET q 1 0 0 1 338.234 461.587 cm 0 0 m 0 11.955 l S Q BT
9.9626 0 0 9.9626 357.906 465.174 Tm /Ty2 1 Tf [ (75.4) -3049 (44.1) ] TJ
ET q 1 0 0 1 433.856 461.587 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 465.174
Tm /Ty2 1 Tf [ (73.9) -3174 (43.5) ] TJ ET BT 9.9626 0 0 9.9626 69.234 453.219
Tm /Ty2 1 Tf [ (A) 111 (T\() ] TJ ET BT 9.9626 0 0 9.9626 84.726 453.219 Tm
/Ty4 1 Tf (SWA) Tj ET BT 9.9626 0 0 9.9626 102.659 453.219 Tm /Ty2 1 Tf [
(\)) -5841 (72.3) -3049 (40.0) ] TJ ET q 1 0 0 1 240.123 449.632 cm 0 0 m
0 11.955 l S Q BT 9.9626 0 0 9.9626 261.039 453.219 Tm /Ty2 1 Tf [ (71.5)
-3174 (39.8) ] TJ ET q 1 0 0 1 338.234 449.632 cm 0 0 m 0 11.955 l S Q BT
9.9626 0 0 9.9626 357.906 453.219 Tm /Ty2 1 Tf [ (75.2) -3049 (44.3) ] TJ
ET q 1 0 0 1 433.856 449.632 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 453.219
Tm /Ty2 1 Tf [ (74.3) -3174 (43.8) ] TJ ET BT 9.9626 0 0 9.9626 69.234 441.264
Tm /Ty2 1 Tf [ (A) 111 (T\() ] TJ ET BT 9.9626 0 0 9.9626 84.726 441.264 Tm
/Ty4 1 Tf (S2O) Tj ET BT 9.9626 0 0 9.9626 102.659 441.264 Tm /Ty2 1 Tf [
(\)) -5841 (72.0) -3049 (39.0) ] TJ ET q 1 0 0 1 240.123 437.677 cm 0 0 m
0 11.955 l S Q BT 9.9626 0 0 9.9626 261.039 441.264 Tm /Ty2 1 Tf [ (71.4)
-3174 (39.3) ] TJ ET q 1 0 0 1 338.234 437.677 cm 0 0 m 0 11.955 l S Q BT
9.9626 0 0 9.9626 357.906 441.264 Tm /Ty2 1 Tf [ (75.4) -3049 (46.2) ] TJ
ET q 1 0 0 1 433.856 437.677 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 441.264
Tm /Ty2 1 Tf [ (76.3) -3174 (46.4) ] TJ ET BT 9.9626 0 0 9.9626 69.234 429.308
Tm /Ty2 1 Tf [ (A) 111 (T\() ] TJ ET BT 9.9626 0 0 9.9626 84.726 429.308 Tm
/Ty4 1 Tf (AWP) Tj ET BT 9.9626 0 0 9.9626 102.659 429.308 Tm /Ty2 1 Tf [
(\)) -5841 (71.3) -3049 (39.5) ] TJ ET q 1 0 0 1 240.123 425.722 cm 0 0 m
0 11.955 l S Q BT 9.9626 0 0 9.9626 261.039 429.308 Tm /Ty2 1 Tf [ (70.5)
-3174 (39.3) ] TJ ET q 1 0 0 1 338.234 425.722 cm 0 0 m 0 11.955 l S Q BT
9.9626 0 0 9.9626 357.906 429.308 Tm /Ty2 1 Tf [ (74.5) -3049 (44.0) ] TJ
ET q 1 0 0 1 433.856 425.722 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 429.308
Tm /Ty2 1 Tf [ (73.8) -3174 (44.0) ] TJ ET BT 9.9626 0 0 9.9626 69.234 417.353
Tm /Ty2 1 Tf [ (A) 111 (T\() ] TJ ET BT 9.9626 0 0 9.9626 84.726 417.353 Tm
/Ty4 1 Tf (TrH) Tj ET BT 9.9626 0 0 9.9626 102.659 417.353 Tm /Ty2 1 Tf [
(\)) -5841 (71.3) ] TJ ET BT 9.9626 0 0 9.9626 211.983 417.353 Tm /Ty1 1 Tf
(42.2) Tj ET q 1 0 0 1 240.123 413.767 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 261.039 417.353
Tm /Ty2 1 Tf (71.6) Tj ET BT 9.9626 0 0 9.9626 310.095 417.353 Tm /Ty1 1 Tf
(42.4) Tj ET q 1 0 0 1 338.234 413.767 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 357.906 417.353
Tm /Ty2 1 Tf (75.8) Tj ET BT 9.9626 0 0 9.9626 405.716 417.353 Tm /Ty1 1 Tf
(48.8) Tj ET q 1 0 0 1 433.856 413.767 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 417.353
Tm /Ty2 1 Tf (74.2) Tj ET BT 9.9626 0 0 9.9626 503.828 417.353 Tm /Ty1 1 Tf
(47.0) Tj ET 0.498 w q 1 0 0 1 63.256 411.802 cm 0 0 m 468.711 0 l S Q BT
9.9626 0 0 9.9626 69.234 400.396 Tm /Ty2 1 Tf (TRADES\() Tj ET BT 9.9626 0 0 9.9626 111.296 400.396
Tm /Ty4 1 Tf (base) Tj ET BT 9.9626 0 0 9.9626 135.206 400.396 Tm /Ty2 1 Tf
[ (\)) -2575 (69.2) -3049 (39.3) ] TJ ET 0.398 w q 1 0 0 1 240.123 396.809
cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 261.039 400.396 Tm /Ty2 1 Tf
[ (67.8) -3174 (39.7) ] TJ ET q 1 0 0 1 338.234 396.809 cm 0 0 m 0 11.955
l S Q BT 9.9626 0 0 9.9626 357.906 400.396 Tm /Ty2 1 Tf [ (77.8) -3049 (40.9)
] TJ ET q 1 0 0 1 433.856 396.809 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 400.396
Tm /Ty2 1 Tf [ (77.1) -3174 (41.5) ] TJ ET BT 9.9626 0 0 9.9626 69.234 388.441
Tm /Ty2 1 Tf (TRADES\() Tj ET BT 9.9626 0 0 9.9626 111.296 388.441 Tm /Ty4
1 Tf (SWA) Tj ET BT 9.9626 0 0 9.9626 129.229 388.441 Tm /Ty2 1 Tf [ (\))
-3174 (69.5) -3049 (39.7) ] TJ ET q 1 0 0 1 240.123 384.854 cm 0 0 m 0 11.955
l S Q BT 9.9626 0 0 9.9626 261.039 388.441 Tm /Ty2 1 Tf [ (68.1) -3174 (40.0)
] TJ ET q 1 0 0 1 338.234 384.854 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 357.906 388.441
Tm /Ty2 1 Tf [ (72.7) -3049 (44.5) ] TJ ET q 1 0 0 1 433.856 384.854 cm 0
0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 388.441 Tm /Ty2 1 Tf [ (71.1)
-3174 (44.2) ] TJ ET BT 9.9626 0 0 9.9626 69.234 376.486 Tm /Ty2 1 Tf (TRADES\()
Tj ET BT 9.9626 0 0 9.9626 111.296 376.486 Tm /Ty4 1 Tf (S2O) Tj ET BT 9.9626 0 0 9.9626 129.229 376.486
Tm /Ty2 1 Tf [ (\)) -3174 (70.6) -3049 (39.3) ] TJ ET q 1 0 0 1 240.123 372.899
cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 261.039 376.486 Tm /Ty2 1 Tf
[ (69.8) -3174 (39.7) ] TJ ET q 1 0 0 1 338.234 372.899 cm 0 0 m 0 11.955
l S Q BT 9.9626 0 0 9.9626 357.906 376.486 Tm /Ty2 1 Tf [ (73.7) -3049 (43.6)
] TJ ET q 1 0 0 1 433.856 372.899 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 376.486
Tm /Ty2 1 Tf [ (72.5) -3174 (44.0) ] TJ ET BT 9.9626 0 0 9.9626 69.234 364.531
Tm /Ty2 1 Tf (TRADES\() Tj ET BT 9.9626 0 0 9.9626 111.296 364.531 Tm /Ty4
1 Tf (AWP) Tj ET BT 9.9626 0 0 9.9626 129.229 364.531 Tm /Ty2 1 Tf [ (\))
-3174 (65.8) -3049 (38.6) ] TJ ET q 1 0 0 1 240.123 360.944 cm 0 0 m 0 11.955
l S Q BT 9.9626 0 0 9.9626 261.039 364.531 Tm /Ty2 1 Tf [ (64.5) -3174 (38.3)
] TJ ET q 1 0 0 1 338.234 360.944 cm 0 0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 357.906 364.531
Tm /Ty2 1 Tf [ (68.5) -3049 (43.2) ] TJ ET q 1 0 0 1 433.856 360.944 cm 0
0 m 0 11.955 l S Q BT 9.9626 0 0 9.9626 454.772 364.531 Tm /Ty2 1 Tf [ (67.2)
-3174 (42.7) ] TJ ET BT 9.9626 0 0 9.9626 69.234 352.575 Tm /Ty2 1 Tf (TRADES\()
Tj ET BT 9.9626 0 0 9.9626 111.296 352.575 Tm /Ty4 1 Tf (TrH) Tj ET BT 9.9626 0 0 9.9626 129.229 352.575
Tm /Ty2 1 Tf [ (\)) -3174 (65.3) ] TJ ET BT 9.9626 0 0 9.9626 211.983 352.575
Tm /Ty1 1 Tf (41.9) Tj ET q 1 0 0 1 240.123 348.989 cm 0 0 m 0 11.955 l S
Q BT 9.9626 0 0 9.9626 261.039 352.575 Tm /Ty2 1 Tf (66.4) Tj ET BT 9.9626 0 0 9.9626 310.095 352.575
Tm /Ty1 1 Tf (41.6) Tj ET q 1 0 0 1 338.234 348.989 cm 0 0 m 0 11.955 l S
Q BT 9.9626 0 0 9.9626 357.906 352.575 Tm /Ty2 1 Tf (70.1) Tj ET BT 9.9626 0 0 9.9626 405.716 352.575
Tm /Ty1 1 Tf (48.9) Tj ET q 1 0 0 1 433.856 348.989 cm 0 0 m 0 11.955 l S
Q BT 9.9626 0 0 9.9626 454.772 352.575 Tm /Ty2 1 Tf (68.9) Tj ET BT 9.9626 0 0 9.9626 503.828 352.575
Tm /Ty1 1 Tf (47.3) Tj ET 0.797 w q 1 0 0 1 63.256 346.874 cm 0 0 m 468.711
0 l S Q BT 8.9664 0 0 8.9664 50.112 328.842 Tm /Ty2 1 Tf [ (T) 80 (able) -232
(1.) ] TJ ET BT 8.9664 0 0 8.9664 81.341 328.842 Tm /Ty4 1 Tf (Clean) Tj ET
BT 8.9664 0 0 8.9664 108.241 328.842 Tm /Ty2 1 Tf [ (:) -301 (%) -232 (of)
-232 (T) 80 (op-1) -232 (correct) -232 (predictions.) ] TJ ET BT 8.9664 0 0 8.9664 227.59 328.842
Tm /Ty4 1 Tf (AA) Tj ET BT 8.9664 0 0 8.9664 238.35 328.842 Tm /Ty2 1 Tf [
(:) -232 (%) -232 (of) -232 (T) 80 (op-1) -232 (correct) -232 (predictions)
-232 (under) -232 (AutoAttack.) -304 (A) -232 (max) -232 (Standard) -232 (Error)
-232 (\(SE\)) -232 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 8.9664 0 0 8.9664 526.028 328.842
Tm /Ty2 1 Tf (44) Tj ET /Cs2 cs 0 sc BT 0.231 Tc 8.9664 0 0 8.9664 534.9944 328.842
Tm /Ty2 1 Tf (]=) Tj 0 Tc ET BT 8.9664 0 0 8.9664 50.112 325.552 Tm /Ty40
1 Tf (!) Tj ET 0.379 w q 1 0 0 1 59.327 325.741 cm 0 0 m 68.019 0 l S Q BT
8.9664 0 0 8.9664 59.327 317.883 Tm /Ty30 1 Tf (0) Tj ET BT 8.9664 0 0 8.9664 63.935 317.883
Tm /Ty26 1 Tf (.) Tj ET BT 8.9664 0 0 8.9664 66.495 317.883 Tm /Ty30 1 Tf
(5) Tj ET BT 8.9664 0 0 8.9664 73.15 317.883 Tm /Ty34 1 Tf ($) Tj ET BT 0.0007
Tc 8.9664 0 0 8.9664 79.806 317.883 Tm /Ty30 1 Tf (\(1) Tj 0 Tc ET BT 8.9664 0 0 8.9664 90.045 317.883
Tm /Ty34 1 Tf (#) Tj ET BT 8.9664 0 0 8.9664 99.261 317.883 Tm /Ty30 1 Tf
(0) Tj ET BT 8.9664 0 0 8.9664 103.868 317.883 Tm /Ty26 1 Tf (.) Tj ET BT
0.0009 Tc 8.9664 0 0 8.9664 106.428 317.883 Tm /Ty30 1 Tf (5\)) Tj 0 Tc ET
BT 0.0009 Tc 8.9664 0 0 8.9664 114.62 317.883 Tm /Ty26 1 Tf (/m) Tj 0 Tc ET
BT 8.9664 0 0 8.9664 129.498 317.883 Tm /Ty2 1 Tf (\() Tj ET BT 8.9664 0 0 8.9664 132.484 317.883
Tm /Ty26 1 Tf (m) Tj ET BT 8.9664 0 0 8.9664 142.755 317.883 Tm /Ty2 1 Tf
[ (as) -240 (the) -240 (number) -240 (of) -240 (test) -240 (e) 15 (xamples\))
-240 (is) -240 (computed) -240 (for) -240 (each) -240 (dataset.) -306 (The)
-240 (best) -240 (results) -240 (appear) -240 (in) -240 (bold.) -307 (Underlined)
-240 (results) ] TJ ET BT 8.9664 0 0 8.9664 50.112 306.924 Tm /Ty2 1 Tf [
(are) -250 (those) -250 (that) -250 (f) 10 (all) -250 (within) -250 (the)
-250 (SE) -250 (range) -250 (of) -250 (the) -250 (result) -250 (and) -250
(are) -250 (re) 15 (g) 5 (arded) -250 (roughly) -250 (equal) -250 (to) -250
(the) -250 (best) -250 (result.) ] TJ ET BT 9.9626 0 0 9.9626 50.112 273.749
Tm /Ty1 1 Tf (ImageNet.) Tj ET BT 9.9626 0 0 9.9626 104.059 273.749 Tm /Ty2
1 Tf [ (On) -263 (ImageNet,) -266 (a) -263 (signicant) -263 (impro) 15 (v)
15 (ement) -263 (is) -263 (at) ] TJ ET BT 9.9626 0 0 9.9626 50.112 261.794
Tm /Ty2 1 Tf [ (least) -201 (0.4%) -201 (according) -201 (to) -201 (SE.) -201
(W) 80 (e) -202 (obs) 1 (erv) 14 (e) -201 (that) -201 (T) 35 (rH) -201 (re)
15 (gulariza-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 249.838 Tm /Ty2 1 Tf [
(tion) -200 (out) 1 (performs) -200 (the) -200 (other) -199 (baselines) -200
(acros) 1 (s) -200 (the) -200 (board.) -293 (Using) ] TJ ET BT 9.9626 0 0 9.9626 50.112 237.883
Tm /Ty2 1 Tf [ (A) 111 (T\() ] TJ ET BT 9.9626 0 0 9.9626 65.604 237.883 Tm
/Ty4 1 Tf (TrH) Tj ET BT 9.9626 0 0 9.9626 83.536 237.883 Tm /Ty2 1 Tf [ (\),)
-311 (we) -311 (set) -312 (a) -311 (ne) 25 (w) ] TJ ET BT 9.9626 0 0 9.9626 148.304 237.883
Tm /Ty6 1 Tf (state-of-the-art) Tj ET BT 9.9626 0 0 9.9626 211.907 237.883
Tm /Ty2 1 Tf [ (rob) 20 (ust) -311 (accurac) 15 (y) -311 (of) ] TJ ET BT 9.9626 0 0 9.9626 50.112 225.928
Tm /Ty2 1 Tf [ (48.8%,) -260 (at) ] TJ ET BT 9.9626 0 0 9.9626 90.685 225.928
Tm /Ty8 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 94.836 224.434 Tm /Ty16 1 Tf (')
Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 103.277 225.928 Tm /Ty12 1 Tf (\(4) Tj
0 Tc ET BT 9.9626 0 0 9.9626 112.132 225.928 Tm /Ty7 1 Tf (/) Tj ET BT 9.9626 0 0 9.9626 117.114 225.928
Tm /Ty12 1 Tf (255\)) Tj ET BT 9.9626 0 0 9.9626 138.501 225.928 Tm /Ty2 1
Tf [ (and) -258 (47.0%) -258 (at) ] TJ ET BT 9.9626 0 0 9.9626 193.518 225.928
Tm /Ty8 1 Tf (!) Tj ET BT 6.9738 0 0 6.9738 197.669 224.434 Tm /Ty9 1 Tf (2)
Tj ET BT 0.0009 Tc 9.9626 0 0 9.9626 202.138 225.928 Tm /Ty12 1 Tf (\(3) Tj
0 Tc ET BT 9.9626 0 0 9.9626 210.994 225.928 Tm /Ty7 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 213.762 225.928
Tm /Ty12 1 Tf (0\)) Tj ET BT 9.9626 0 0 9.9626 225.186 225.928 Tm /Ty2 1 Tf
[ (with) -258 (a) -258 (V) 60 (iT) 92 (-L16) ] TJ ET BT 9.9626 0 0 9.9626 50.112 213.973
Tm /Ty2 1 Tf [ (model.) -753 (Specically) 65 (,) -435 (in) -397 (the) -398
(case) -398 (of) ] TJ ET BT 9.9626 0 0 9.9626 199.443 213.973 Tm /Ty8 1 Tf
(!) Tj ET BT 6.9738 0 0 6.9738 203.595 212.478 Tm /Ty16 1 Tf (') Tj ET BT
9.9626 0 0 9.9626 212.035 213.973 Tm /Ty2 1 Tf [ (,) -435 (48.8%) -397 (is)
-398 (an) -398 (im-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 202.018 Tm /Ty2 1
Tf [ (pro) 15 (v) 15 (ement) -238 (of) -238 (4.7%) -238 (compared) -238 (to)
-238 (the) -238 (basic) -238 (setup) -238 (A) 111 (T\() ] TJ ET BT 9.9626 0 0 9.9626 256.643 202.018
Tm /Ty4 1 Tf (base) Tj ET BT 9.9626 0 0 9.9626 280.554 202.018 Tm /Ty2 1 Tf
(\).) Tj ET BT 9.9626 0 0 9.9626 50.112 190.062 Tm /Ty2 1 Tf [ (In) -432 (TRADES\()
] TJ ET BT 9.9626 0 0 9.9626 104.772 190.062 Tm /Ty4 1 Tf (TrH) Tj ET BT 9.9626 0 0 9.9626 122.705 190.062
Tm /Ty2 1 Tf [ (\),) -432 (a) 1 (lthough) -432 (the) -432 (rob) 20 (ust) -431
(accurac) 15 (y) -432 (is) -431 (e) 25 (v) 15 (en) ] TJ ET BT 9.9626 0 0 9.9626 50.112 178.107
Tm /Ty2 1 Tf [ (slightly) -254 (higher) -254 (than) -254 (A) 111 (T) 74 (,)
-254 (the) -254 (clean) -254 (accurac) 15 (y) -254 (is) -254 (lo) 25 (wer)
55 (.) -323 (This) -254 (is) ] TJ ET BT 9.9626 0 0 9.9626 50.112 166.152 Tm
/Ty2 1 Tf [ (due) -294 (to) -295 (the) -294 (choice) -294 (of) ] TJ ET BT
9.9626 0 0 9.9626 133.385 166.152 Tm /Ty8 1 Tf (%) Tj ET BT 6.9738 0 0 6.9738 139.196 164.658
Tm /Ty10 1 Tf (t) Tj ET BT 0.3608 Tc 9.9626 0 0 9.9626 146.289 166.152 Tm
/Ty12 1 Tf (=6) Tj 0 Tc ET BT 9.9626 0 0 9.9626 162.604 166.152 Tm /Ty2 1
Tf [ (,) -305 (which) -295 (strongly) -294 (f) 10 (a) 20 (v) 20 (ors) -294
(rob) 20 (ust-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 154.197 Tm /Ty2 1 Tf [
(ness) -290 (o) 15 (v) 15 (er) -290 (clean) -290 (accurac) 15 (y) 65 (.) -430
(As) -290 (we) -290 (reduce) ] TJ ET BT 9.9626 0 0 9.9626 213.64 154.197 Tm
/Ty8 1 Tf (%) Tj ET BT 6.9738 0 0 6.9738 219.451 152.703 Tm /Ty10 1 Tf (t)
Tj ET BT 9.9626 0 0 9.9626 225.849 154.197 Tm /Ty2 1 Tf [ (to) -290 (1,) -300
(we) -290 (obtain) ] TJ ET BT 9.9626 0 0 9.9626 50.112 142.242 Tm /Ty2 1 Tf
[ (a) -238 (better) -239 (balance) -238 (of) -239 (\(clean,) -240 (AA\)) -239
(accurac) 15 (y) -238 (of) -239 (TRADES\() ] TJ ET BT 9.9626 0 0 9.9626 265.112 142.242
Tm /Ty4 1 Tf (TrH) Tj ET BT 9.9626 0 0 9.9626 283.044 142.242 Tm /Ty2 1 Tf
(\)) Tj ET BT 9.9626 0 0 9.9626 50.112 130.287 Tm /Ty2 1 Tf [ (at) -250 (\(78.7,)
-250 (46.7\)) -250 (for) ] TJ ET BT 9.9626 0 0 9.9626 122.879 130.287 Tm /Ty7
1 Tf (l) Tj ET BT 6.9738 0 0 6.9738 125.851 128.792 Tm /Ty16 1 Tf (') Tj ET
BT 9.9626 0 0 9.9626 136.783 130.287 Tm /Ty2 1 Tf [ (and) -250 (\(77.1,) -250
(45.2\)) -250 (for) ] TJ ET BT 9.9626 0 0 9.9626 216.743 130.287 Tm /Ty7 1
Tf (l) Tj ET BT 6.9738 0 0 6.9738 219.715 128.792 Tm /Ty9 1 Tf (2) Tj ET BT
9.9626 0 0 9.9626 224.185 130.287 Tm /Ty2 1 Tf (.) Tj ET BT 9.9626 0 0 9.9626 50.112 92.955
Tm /Ty1 1 Tf (Summary) Tj ET BT 9.9626 0 0 9.9626 102.137 92.955 Tm /Ty2 1
Tf [ (The) -328 (results) -328 (in) -328 (T) 80 (able) ] TJ ET /Cs1 cs 1 0
0 sc BT 9.9626 0 0 9.9626 186.3509 92.955 Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0
sc BT 9.9626 0 0 9.9626 194.6099 92.955 Tm /Ty2 1 Tf [ (dem) 1 (onstrate)
-329 (that) -328 (train-) ] TJ ET BT 9.9626 0 0 9.9626 50.112 81 Tm /Ty2 1
Tf [ (ing) -316 (with) -316 (T) 35 (rH) -316 (re) 15 (gularization) -316 (either)
-316 (matches) -317 (or) -316 (outperforms) ] TJ ET BT 9.9626 0 0 9.9626 308.862 273.749
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Tm /Ty2 1 Tf [ (On) -194 (the) -193 (contrary) 65 (,) -205 (we) -193 (used)
-194 (dif) 25 (ferent) ] TJ ET BT 9.9626 0 0 9.9626 443.858 662.217 Tm /Ty8
1 Tf (+) Tj ET BT 6.9738 0 0 6.9738 449.908 665.832 Tm /Ty9 1 Tf (2) Tj ET
BT 6.9738 0 0 6.9738 449.551 659.754 Tm /Ty10 1 Tf (q) Tj ET BT 9.9626 0 0 9.9626 454.378 662.217
Tm /Ty2 1 Tf [ 55 (s) -193 (for) -194 (dif) 25 (ferent) -193 (parame-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 650.261 Tm /Ty2 1 Tf [ (ters.) -297 (Secondly)
65 (,) -219 (in) -210 (P) 92 (A) 40 (CT) 35 (ran) -211 (the) -211 (optimization)
-211 (of) -211 (the) -211 (posterior) ] TJ ET BT 9.9626 0 0 9.9626 308.862 638.306
Tm /Ty2 1 Tf (mean) Tj ET BT 9.9626 0 0 9.9626 333.076 638.306 Tm /Ty8 1 Tf
(") Tj ET BT 6.9738 0 0 6.9738 337.753 636.812 Tm /Ty10 1 Tf (q) Tj ET BT
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-264 (the) -265 (RER) -264 (term) -265 (only) 65 (,) -268 (while) -264 (our)
-265 (optimization) ] TJ ET BT 9.9626 0 0 9.9626 308.862 626.351 Tm /Ty2 1
Tf [ (is) -365 (o) 15 (v) 15 (er) -365 (both) -364 (RER) -365 (and) -365 (FR.)
-364 (These) -365 (tw) 10 (o) -365 (changes) -365 (potentially) ] TJ ET BT
9.9626 0 0 9.9626 308.862 614.396 Tm /Ty2 1 Tf [ (mak) 10 (e) -264 (our) -265
(bound) -264 (tighter) -264 (than) -265 (the) -264 (one) -265 (in) -264 (the)
-264 (P) 92 (A) 40 (CT) 35 (ran) -265 (paper) 55 (.) ] TJ ET BT 9.9626 0 0 9.9626 308.862 602.441
Tm /Ty2 1 Tf [ (In) -323 (addition,) -341 (we) -323 (also) -323 (study) -323
(and) -323 (e) 15 (xplicitly) -323 (include) -323 (the) -323 (high-) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 590.486 Tm /Ty2 1 Tf [ (order) -250 (terms)
-250 (in) ] TJ ET BT 9.9626 0 0 9.9626 367.242 590.486 Tm /Ty7 1 Tf (O) Tj
ET BT 9.9626 0 0 9.9626 375.118 590.486 Tm /Ty12 1 Tf (\() Tj ET BT 9.9626 0 0 9.9626 378.993 590.486
Tm /Ty8 1 Tf (+) Tj ET BT 6.9738 0 0 6.9738 385.043 594.101 Tm /Ty9 1 Tf (4)
Tj ET BT 6.9738 0 0 6.9738 384.686 588.013 Tm /Ty9 1 Tf (0) Tj ET BT 9.9626 0 0 9.9626 389.512 590.486
Tm /Ty12 1 Tf (\)) Tj ET BT 9.9626 0 0 9.9626 393.387 590.486 Tm /Ty2 1 Tf
[ (,) -250 (which) -250 (w) 10 (as) -250 (ne) 15 (glected) -250 (in) -250
(P) 92 (A) 40 (CT) 35 (ran.) ] TJ ET BT 9.9626 0 0 9.9626 320.817 578.53 Tm
/Ty2 1 Tf [ (The) -538 (main) -538 (dif) 25 (ference) -538 (between) -538
(our) -539 (m) 1 (ethod) -539 (and) -538 (other) ] TJ ET BT 9.9626 0 0 9.9626 308.862 566.575
Tm /Ty2 1 Tf [ (sharpness-a) 15 (w) 10 (are) -669 (and) -668 (P) 92 (A) 40
(C-Bayesian) -669 (moti) 25 (v) 25 (ated) -669 (method,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 554.62
Tm /Ty2 1 Tf [ (such) -209 (as) -209 (SAM) -208 ([) ] TJ ET /Cs1 cs 0 1 0
sc BT 9.9626 0 0 9.9626 366.5654 554.62 Tm /Ty2 1 Tf (15) Tj ET /Cs2 cs 0
sc BT 9.9626 0 0 9.9626 376.528 554.62 Tm /Ty2 1 Tf [ (]) -209 (and) -209
(A) 90 (WP) -209 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 425.0359 554.62
Tm /Ty2 1 Tf (49) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 434.9985 554.62
Tm /Ty2 1 Tf [ (],) -217 (lies) -208 (on) -209 (ho) 25 (w) -209 (sharpness)
-209 (and) ] TJ ET BT 9.9626 0 0 9.9626 308.862 542.665 Tm /Ty2 1 Tf [ (P)
92 (A) 40 (C-Bayesian) -342 (theory) -342 (are) -343 (positioned.) -586 (SAM/A)
90 (WP) -342 (is) -343 (moti-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 530.71
Tm /Ty2 1 Tf [ (v) 25 (ated) -280 (by) -281 (empirically) -280 (reducing)
-280 (the) -281 (sharpness) -280 (of) -280 (the) -281 (training) ] TJ ET BT
9.9626 0 0 9.9626 308.862 518.755 Tm /Ty2 1 Tf [ (loss) -242 (landscape,)
-243 (whereas) -242 (our) -242 (w) 10 (ork) -242 (is) -242 (theoretically)
-242 (moti) 25 (v) 25 (ated) ] TJ ET BT 9.9626 0 0 9.9626 308.862 506.799
Tm /Ty2 1 Tf [ (and) -287 (directly) -286 (minimizes) -287 (the) -286 (P)
92 (A) 40 (C-Baysian) -287 (bound) -287 (of) -286 (the) -287 (\(ad-) ] TJ
ET BT 9.9626 0 0 9.9626 308.862 494.844 Tm /Ty2 1 Tf [ (v) 15 (ersarial\))
-342 (loss) -341 (w) 65 (.r) 55 (.t) -342 (the) -342 (Gaussian) -342 (posterior)
-341 (so) -342 (as) -342 (to) -342 (reduce) ] TJ ET BT 9.9626 0 0 9.9626 308.862 482.889
Tm /Ty2 1 Tf [ (the) -385 (generalization) -385 (error) 55 (.) -714 (Specically)
65 (,) -419 (the) -385 (sharpness) -385 (mea-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 470.934
Tm /Ty2 1 Tf [ (sure) -235 (T) 35 (rH) -235 (emer) 18 (ges) -236 (as) -235
(a) -235 (result) -235 (of) -235 (that) -236 (optimization.) -305 (Although)
] TJ ET BT 9.9626 0 0 9.9626 308.862 458.979 Tm /Ty2 1 Tf [ (a) -351 (P) 92
(A) 40 (C-Bayesian) -350 (bound) -351 (w) 10 (as) -350 (also) -351 (considered)
-351 (as) -350 (a) -351 (theoreti-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 447.023
Tm /Ty2 1 Tf [ (cal) -240 (moti) 25 (v) 25 (ation) -240 (for) -240 (SAM/A)
90 (WP) 111 (,) -240 (it) -240 (is) -240 (unclear) -241 (whether) -240 (its)
-240 (opti-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 435.068 Tm /Ty2 1 Tf [ (mization)
-250 (indeed) -250 (reduces) -250 (the) -250 (P) 92 (A) 40 (C-Bayesian) -250
(bound.) ] TJ ET BT 9.9626 0 0 9.9626 320.817 423.113 Tm /Ty2 1 Tf [ (Be)
15 (yond) -389 (the) -388 (P) 92 (A) 40 (C-Bayesian) -389 (inspired) -388
(approaches) -389 (for) -389 (ro-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 411.158
Tm /Ty2 1 Tf [ (b) 20 (ust) -436 (training,) -482 (a) -436 (dif) 25 (f) 1
(erent) -436 (line) -436 (of) -436 (w) 10 (ork) -435 (focuses) -436 (on) -436
(adapt-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 399.203 Tm /Ty2 1 Tf [ (ing)
-554 (P) 92 (A) 40 (C-Bayesian) -553 (bounds) -554 (for) -554 (an) -553 (ensemble)
-554 (of) -554 (models,) ] TJ ET BT 9.9626 0 0 9.9626 308.862 387.248 Tm /Ty2
1 Tf [ (to) -501 (impro) 15 (v) 15 (e) -501 (either) -500 (adv) 15 (ersarial)
-501 (rob) 20 (ustness) -501 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 485.8874 387.248
Tm /Ty2 1 Tf (45) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 495.85 387.248 Tm
/Ty2 1 Tf [ (]) -501 (or) -501 (out-of-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 375.292
Tm /Ty2 1 Tf [ (distrib) 20 (ution) -491 (\(OOD\)) -492 (rob) 20 (ustness)
-491 (data) -492 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 464.1889 375.292
Tm /Ty2 1 Tf (52) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 474.1515 375.292
Tm /Ty2 1 Tf [ (].) -1034 (Se) 25 (v) 15 (eral) -492 (other) ] TJ ET BT 9.9626 0 0 9.9626 308.862 363.337
Tm /Ty2 1 Tf [ (w) 10 (orks) -313 (ha) 20 (v) 15 (e) -313 (focused) -313 (on)
-313 (methods) -313 (for) -313 (nding) -313 -313 (local) -313 (min-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 351.382 Tm /Ty2 1 Tf [ (ima) -220 (of)
-221 (the) -220 (loss) -220 (surf) 10 (ace) -220 (in) -221 (order) -220 (to)
-220 (impro) 15 (v) 15 (e) -220 (\(standard\)) -221 (model) ] TJ ET BT 9.9626 0 0 9.9626 308.862 339.427
Tm /Ty2 1 Tf [ (performance) -303 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 365.5392 339.427
Tm /Ty2 1 Tf (12) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 375.5018 339.427
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 379.6363 339.427
Tm /Ty2 1 Tf (15) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 389.5989 339.427
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 393.7334 339.427
Tm /Ty2 1 Tf (25) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 403.696 339.427
Tm /Ty2 1 Tf [ (].) -469 (Also) -302 (outside) -303 (the) -303 (scope) -303
(of) -303 (adv) 15 (er) 20 (-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 327.472
Tm /Ty2 1 Tf [ (sarial) -382 (rob) 20 (ustness,) -414 (Ju) -382 (et) -381
(al.) -382 ([) ] TJ ET /Cs1 cs 0 1 0 sc BT 9.9626 0 0 9.9626 423.1828 327.472
Tm /Ty2 1 Tf (28) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 433.1454 327.472
Tm /Ty2 1 Tf [ (]) -381 -382 (that) -382 (trace) -381 (of) -382 (Hessian)
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-386 (leads) -386 (to) -387 (rob) 20 (ustness) -386 (ag) 5 (ainst) -386 (noise)
-386 (in) -386 (the) ] TJ ET BT 9.9626 0 0 9.9626 534.044 315.517 Tm /Ty6
1 Tf (la-) Tj ET BT 9.9626 0 0 9.9626 308.862 303.561 Tm /Ty6 1 Tf (bels)
Tj ET BT 9.9626 0 0 9.9626 324.912 303.561 Tm /Ty2 1 Tf [ (.) -479 (Their)
-306 (Hessian) -306 (re) 15 (gularization) -307 (is) -306 (based) -306 (on)
-307 (randomized) ] TJ ET BT 9.9626 0 0 9.9626 308.862 291.606 Tm /Ty2 1 Tf
[ (estimation) -225 (and) -226 (is) -226 (done) -225 (for) -226 (all) -225
(layers,) -231 (whereas) -225 (we) -226 (ef) 25 (fecti) 25 (v) 15 (ely) ]
TJ ET BT 9.9626 0 0 9.9626 308.862 279.651 Tm /Ty2 1 Tf [ (apply) -193 (T)
35 (rH) -194 (re) 15 (gularization) -193 (on) -194 (the) -193 (top) -194 (layer)
-193 (only) -194 (and) -193 (with) -194 (The-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 267.696
Tm /Ty2 1 Tf (orem) Tj ET /Cs1 cs 1 0 0 sc BT 9.9626 0 0 9.9626 331.8258 267.696
Tm /Ty2 1 Tf (4) Tj ET /Cs2 cs 0 sc BT 9.9626 0 0 9.9626 339.2977 267.696
Tm /Ty2 1 Tf [ (as) -250 (theoretical) -250 (justication.) ] TJ ET BT 11.9552 0 0 11.9552 308.862 243.786
Tm /Ty1 1 Tf [ (6.) -250 (Conclusion) ] TJ ET BT 9.9626 0 0 9.9626 320.817 224.857
Tm /Ty2 1 Tf [ (In) -256 (summary) 65 (,) -257 (we) -256 (alle) 25 (viate)
-255 (o) 15 (v) 15 (ertting) -256 (in) -256 (adv) 15 (ersarial) -256 (train-)
] TJ ET BT 9.9626 0 0 9.9626 308.862 212.901 Tm /Ty2 1 Tf [ (ing) -337 (with)
-337 (P) 92 (A) 40 (C-Bayesian) -337 (theory) 65 (.) -571 (Using) -337 (a)
-337 (linear) 20 (-form) -337 (P) 92 (A) 40 (C-) ] TJ ET BT 9.9626 0 0 9.9626 308.862 200.946
Tm /Ty2 1 Tf [ (Bayesian) -372 (bound) -371 (o) 15 (v) 15 (erlook) 10 (ed)
-372 (by) -371 (the) -372 (prior) -371 (w) 10 (ork,) -402 (we) -372 (deri)
25 (v) 15 (e) ] TJ ET BT 9.9626 0 0 9.9626 308.862 188.991 Tm /Ty2 1 Tf [
(a) -358 (2nd-order) -358 (estimation) -358 (that) -358 (includes) -358 (the)
-359 (T) 35 (race) -358 (of) -358 (Hessian) ] TJ ET BT 9.9626 0 0 9.9626 308.862 177.036
Tm /Ty2 1 Tf [ (\(T) 35 (rH\)) -314 (of) -313 (the) -314 (model.) -502 (W)
80 (e) -313 (focus) -314 (on) -314 (the) -314 (T) 35 (rH) -313 (of) -314 (the)
-314 (top) -314 (layer) ] TJ ET BT 9.9626 0 0 9.9626 308.862 165.081 Tm /Ty2
1 Tf [ (only) 65 (,) -240 (sho) 25 (wing) -238 (both) -238 (empirically) -238
(and) -238 (theoretically) -238 (\(for) -238 (ReLU) ] TJ ET BT 9.9626 0 0 9.9626 308.862 153.125
Tm /Ty2 1 Tf [ (netw) 10 (orks\)) -296 (that) -295 (it) -296 (leads) -296
(to) -295 (an) -296 (ef) 25 (fecti) 25 (v) 15 (e) -295 (minimization) -296
(of) -296 (T) 35 (rH) ] TJ ET BT 9.9626 0 0 9.9626 308.862 141.17 Tm /Ty2
1 Tf [ (of) -272 (the) -272 (full) -271 (netw) 10 (ork,) -278 (thereby) -271
(pro) 15 (viding) -272 (a) -272 (sound) -272 (atness) -272 (re) 15 (g-) ]
TJ ET BT 9.9626 0 0 9.9626 308.862 129.215 Tm /Ty2 1 Tf [ (ularization) -291
(technique) -290 (for) -291 (adv) 15 (ersarial) -291 (training.) -432 (Experiments)
] TJ ET BT 9.9626 0 0 9.9626 308.862 117.26 Tm /Ty2 1 Tf [ (sho) 25 (w) -256
(that) -256 (T) 35 (rH) -255 (re) 15 (gularization) -256 (method) -256 (is)
-256 (consistently) -256 (among) ] TJ ET BT 9.9626 0 0 9.9626 308.862 105.305
Tm /Ty2 1 Tf [ (the) -252 (top) -251 (performers) -252 (on) -252 (CIF) 74
(AR-10/100) -252 (benchmark) -251 (as) -252 (well) -252 (as) ] TJ ET BT 9.9626 0 0 9.9626 308.862 93.35
Tm /Ty2 1 Tf [ (achie) 25 (v) 15 (es) -284 (a) -285 (s) 1 (ignicant) -285
(impro) 15 (v) 15 (ement) -284 (on) -284 (rob) 20 (ust) -284 (test) -285 (accurac)
15 (y) ] TJ ET BT 9.9626 0 0 9.9626 308.862 81.394 Tm /Ty2 1 Tf [ (on) -250
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-576 (In) ] TJ ET BT 8.9664 0 0 8.9664 196.636 524.375 Tm /Ty6 1 Tf [ (2017)
-318 (ieee) -317 (symposium) -318 (on) ] TJ ET BT 8.9664 0 0 8.9664 70.031 513.416
Tm /Ty6 1 Tf [ (security) -250 (and) -250 (privacy) -250 (\(sp\)) ] TJ ET
BT 8.9664 0 0 8.9664 159.425 513.416 Tm /Ty2 1 Tf [ (,) -250 (pages) -250
(3957.) -250 (Ieee,) -250 (2017.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 256.2801 513.416
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 54.595 501.9 Tm /Ty2
1 Tf ([8]) Tj ET BT 8.9664 0 0 8.9664 70.03514 501.9 Tm /Ty2 1 Tf [ (Y) 100
(air) -300 (Carmon,) -314 (Aditi) -301 (Raghunathan,) -313 (Ludwig) -301 (Schmidt,)
-314 (John) -300 (C) ] TJ ET BT 8.9664 0 0 8.9664 70.031 490.941 Tm /Ty2 1
Tf [ (Duchi,) -457 (and) -416 (Perc) 15 (y) -416 (S) -416 (Liang.) -890 (Unlabeled)
-416 (data) -416 (impro) 15 (v) 15 (es) -416 (ad-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 479.982
Tm /Ty2 1 Tf [ (v) 15 (ersarial) -519 (rob) 20 (ustness.) -1221 (In) -519
(H.) -519 (W) 80 (allach,) -587 (H.) -519 (Larochelle,) -586 (A.) ] TJ ET
BT 8.9664 0 0 8.9664 70.031 469.023 Tm /Ty2 1 Tf [ (Be) 15 (ygelzimer) 40
(,) -430 (F) 80 (.) -394 (d'Alch) ] TJ ET BT 8.9664 0 0 8.9664 155.518 469.068
Tm /Ty2 1 Tf Tj ET BT 8.9664 0 0 8.9664 155.021 469.023 Tm /Ty2 1 Tf [
(e-Buc,) -430 (E.) -394 (F) 15 (ox,) -430 (and) -393 (R.) -394 (Garnett,)
-430 (ed-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 458.064 Tm /Ty2 1 Tf (itors,)
Tj ET BT 8.9664 0 0 8.9664 91.592 458.064 Tm /Ty6 1 Tf [ (Advances) -351 (in)
-352 (Ne) 1 (ur) 15 (al) -352 (Information) -351 (Pr) 45 (ocessing) -351 (Systems)
] TJ ET BT 8.9664 0 0 8.9664 284.12 458.064 Tm /Ty2 1 Tf (,) Tj ET BT 8.9664 0 0 8.9664 70.031 447.105
Tm /Ty2 1 Tf [ (v) 20 (olume) -250 (32.) -250 (Curran) -250 (Associates,)
-250 (Inc.,) -250 (2019.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 223.9931 447.105
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 54.595 435.589 Tm
/Ty2 1 Tf ([9]) Tj ET BT 8.9664 0 0 8.9664 70.03514 435.589 Tm /Ty2 1 Tf [
(Oli) 25 (vier) -277 (Catoni.) -449 (A) -277 (pac-bayesian) -278 (approach)
-277 (to) -278 (adapti) 25 (v) 15 (e) -277 (classi-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 424.63
Tm /Ty2 1 Tf [ (cation.) -360 (2004.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 125.802 424.63
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 130.2852 424.63 Tm
/Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 134.7684 424.63
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 413.113 Tm
/Ty2 1 Tf ([10]) Tj ET BT 8.9664 0 0 8.9664 70.03534 413.113 Tm /Ty2 1 Tf
[ (Thomas) -317 (Cilloni,) -334 (Charles) -317 (W) 80 (alter) 40 (,) -334
(and) -318 (Charles) -317 (Fleming.) -575 (F) 15 (o-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 402.154
Tm /Ty2 1 Tf [ (cused) -250 (adv) 15 (ersarial) -250 (attacks.) ] TJ ET BT
8.9664 0 0 8.9664 164.5 402.154 Tm /Ty6 1 Tf (ArXiv) Tj ET BT 8.9664 0 0 8.9664 185.418 402.154
Tm /Ty2 1 Tf [ (,) -250 (abs/2205.09624,) -250 (2022.) ] TJ ET /Cs1 cs 1 0
0 sc BT 8.9664 0 0 8.9664 274.822 402.154 Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0
sc BT 8.9664 0 0 8.9664 50.112 390.638 Tm /Ty2 1 Tf ([11]) Tj ET BT 8.9664 0 0 8.9664 70.03534 390.638
Tm /Ty2 1 Tf [ (France) 1 (sco) -581 (Croce) -581 (and) -580 (Matthias) -581
(Hein.) -1418 (Reliable) -580 (e) 25 (v) 25 (alua-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 379.679
Tm /Ty2 1 Tf [ (tion) -373 (of) -373 (adv) 15 (ersarial) -373 (rob) 20 (ustness)
-373 (with) -373 (an) -373 (ensemble) -373 (of) -373 (di) 25 (v) 15 (erse)
] TJ ET BT 8.9664 0 0 8.9664 70.031 368.72 Tm /Ty2 1 Tf [ (parameter) 20 (-free)
-324 (attacks.) -598 (In) ] TJ ET BT 8.9664 0 0 8.9664 168.403 368.72 Tm /Ty6
1 Tf [ (International) -324 (confer) 37 (ence) -324 (on) -325 (ma-) ] TJ ET
BT 8.9664 0 0 8.9664 70.031 357.761 Tm /Ty6 1 Tf [ (c) 15 (hine) -250 (learning)
] TJ ET BT 8.9664 0 0 8.9664 121.946 357.761 Tm /Ty2 1 Tf [ (,) -250 (pages)
-250 (22062216.) -250 (PMLR,) -250 (2020.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 246.2203 357.761
Tm /Ty2 1 Tf (6) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 346.244 Tm
/Ty2 1 Tf ([12]) Tj ET BT 8.9664 0 0 8.9664 70.03534 346.244 Tm /Ty2 1 Tf
[ (Nan) -364 (Ding,) -393 (Xi) -365 (Chen,) -393 (T) 80 (omer) -365 (Le) 25
(vinboim,) -393 (Beer) -364 (Changpin) 15 (yo,) ] TJ ET BT 8.9664 0 0 8.9664 70.031 335.285
Tm /Ty2 1 Tf [ (and) -205 (Radu) -206 (Soricut.) -263 (P) 15 (actran:) -288
(P) 15 (ac-bayesian) -205 (metrics) -206 (for) -205 (estimat-) ] TJ ET BT
8.9664 0 0 8.9664 70.031 324.327 Tm /Ty2 1 Tf [ (ing) -320 (the) -320 (transferability)
-320 (of) -321 (pretrained) -320 (models) -320 (to) -320 (classication) ]
TJ ET BT 8.9664 0 0 8.9664 70.031 313.368 Tm /Ty2 1 Tf [ (tasks.) -360 (In)
] TJ ET BT 8.9664 0 0 8.9664 103.143 313.368 Tm /Ty6 1 Tf (ECCV) Tj ET BT
8.9664 0 0 8.9664 126.061 313.368 Tm /Ty2 1 Tf [ (,) -250 (2022.) ] TJ ET
/Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 153.9465 313.368 Tm /Ty2 1 Tf (2) Tj
ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 158.4297 313.368 Tm /Ty2 1 Tf (,) Tj
ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 162.9129 313.368 Tm /Ty2 1 Tf (3)
Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 167.3961 313.368 Tm /Ty2 1 Tf (,)
Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 171.8793 313.368 Tm /Ty2 1 Tf
(4) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 176.3625 313.368 Tm /Ty2 1 Tf
(,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 180.8457 313.368 Tm /Ty2 1
Tf (8) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 301.851 Tm /Ty2 1 Tf
([13]) Tj ET BT 8.9664 0 0 8.9664 70.03534 301.851 Tm /Ty2 1 Tf [ (Nan) -230
(Ding,) -234 (Xi) -230 (Chen,) -234 (T) 80 (omer) -230 (Le) 25 (vinboim,)
-234 (Sebastian) -230 (Goodman,) ] TJ ET BT 8.9664 0 0 8.9664 70.031 290.892
Tm /Ty2 1 Tf [ (and) -364 (Radu) -364 (Soricut.) -726 (Bridging) -364 (the)
-364 (g) 5 (ap) -365 (betwee) 1 (n) -365 (practice) -364 (and) ] TJ ET BT
8.9664 0 0 8.9664 70.031 279.933 Tm /Ty2 1 Tf [ (pac-bayes) -267 (theory)
-268 (in) -267 (fe) 25 (w-shot) -267 (meta-learning.) -415 (In) -268 (M.)
-267 (Ranzato,) ] TJ ET BT 8.9664 0 0 8.9664 70.031 268.974 Tm /Ty2 1 Tf [
(A.) -416 (Be) 15 (ygelzimer) 40 (,) -457 (Y) 129 (.) -415 (Dauphin,) -457
(P) 111 (.S.) -416 (Liang,) -457 (and) -415 (J.) -416 (W) 80 (ortman) ] TJ
ET BT 8.9664 0 0 8.9664 70.031 258.015 Tm /Ty2 1 Tf [ (V) 111 (aughan,) -308
(editors,) ] TJ ET BT 8.9664 0 0 8.9664 135.815 258.015 Tm /Ty6 1 Tf [ (Advances)
-296 (in) -297 (Neur) 15 (al) -296 (Information) -296 (Pr) 45 (ocess-) ] TJ
ET BT 8.9664 0 0 8.9664 70.031 247.057 Tm /Ty6 1 Tf [ (ing) -292 (Systems)
] TJ ET BT 8.9664 0 0 8.9664 112.496 247.057 Tm /Ty2 1 Tf [ (,) -303 (v) 20
(olume) -292 (34,) -303 (pages) -292 (2950629516.) -292 (Curran) -292 (Asso-)
] TJ ET BT 8.9664 0 0 8.9664 70.031 236.098 Tm /Ty2 1 Tf [ (ciates,) -250
(Inc.,) -250 (2021.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 136.5079 236.098
Tm /Ty2 1 Tf (4) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 224.581 Tm
/Ty2 1 Tf ([14]) Tj ET BT 8.9664 0 0 8.9664 70.03534 224.581 Tm /Ty2 1 Tf
[ (Ale) 15 (x) 15 (e) 15 (y) -463 (Doso) 15 (vitskiy) 65 (,) -516 (Lucas)
-464 (Be) 15 (yer) 40 (,) -516 (Ale) 15 (xander) -463 (K) 35 (olesnik) 10
(o) 15 (v) 65 (,) ] TJ ET BT 8.9664 0 0 8.9664 70.031 213.622 Tm /Ty2 1 Tf
[ (Dirk) -639 (W) 80 (eissenborn,) -736 (Xiaohua) -639 (Zhai,) -737 (Thomas)
-639 (Unterthiner) 40 (,) ] TJ ET BT 8.9664 0 0 8.9664 70.031 202.663 Tm /Ty2
1 Tf [ (Mostaf) 10 (a) -275 (Dehghani,) -282 (Matthias) -275 (Minderer) 40
(,) -282 (Geor) 18 (g) -275 (Heigold,) -282 (Syl-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 191.704
Tm /Ty2 1 Tf [ (v) 25 (ain) -262 (Gelly) 65 (,) -265 (Jak) 10 (ob) -262 (Uszk)
10 (oreit,) -264 (and) -262 (Neil) -262 (Houlsby) 65 (.) -398 (An) -262 (image)
-262 (is) ] TJ ET BT 8.9664 0 0 8.9664 70.031 180.745 Tm /Ty2 1 Tf [ (w) 10
(orth) -318 (16x16) -318 (w) 10 (ords:) -446 (T) 35 (ra) 1 (nsformers) -318
(for) -318 (image) -318 (recognition) -318 (at) ] TJ ET BT 8.9664 0 0 8.9664 70.031 169.787
Tm /Ty2 1 Tf [ (scale.) -408 (In) ] TJ ET BT 8.9664 0 0 8.9664 103.695 169.787
Tm /Ty6 1 Tf [ (International) -265 (Confer) 37 (ence) -265 (on) -265 (Learning)
-264 (Repr) 37 (esenta-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 158.828 Tm /Ty6
1 Tf (tions) Tj ET BT 8.9664 0 0 8.9664 87.47 158.828 Tm /Ty2 1 Tf [ (,) -250
(2021.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 115.3555 158.828 Tm
/Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 119.8387 158.828 Tm
/Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 124.3219 158.828
Tm /Ty2 1 Tf (6) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 128.8051 158.828
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 133.2883 158.828
Tm /Ty2 1 Tf (32) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 147.311 Tm
/Ty2 1 Tf ([15]) Tj ET BT 8.9664 0 0 8.9664 70.03534 147.311 Tm /Ty2 1 Tf
[ (Pie) 1 (rre) -382 (F) 15 (oret,) -414 (Ariel) -382 (Kleiner) 40 (,) -414
(Hossein) -382 (Mobahi,) -414 (and) -381 (Behnam) ] TJ ET BT 8.9664 0 0 8.9664 70.031 136.352
Tm /Ty2 1 Tf [ (Ne) 15 (yshab) 20 (ur) 55 (.) -1003 (Sharpness-a) 15 (w) 10
(are) -450 (minimization) -451 (for) -451 (ef) 25 (ciently) ] TJ ET BT 8.9664 0 0 8.9664 70.031 125.393
Tm /Ty2 1 Tf [ (impro) 15 (ving) -391 (generalization.) -812 (In) ] TJ ET
BT 8.9664 0 0 8.9664 182.055 125.393 Tm /Ty6 1 Tf [ (International) -391 (Confer)
37 (ence) -391 (on) ] TJ ET BT 8.9664 0 0 8.9664 70.031 114.434 Tm /Ty6 1
Tf [ (Learning) -250 (Repr) 37 (esentations) ] TJ ET BT 8.9664 0 0 8.9664 162.599 114.434
Tm /Ty2 1 Tf [ (,) -250 (2021.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 190.4845 114.434
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 194.9677 114.434
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 199.4509 114.434
Tm /Ty2 1 Tf (8) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 102.918 Tm
/Ty2 1 Tf ([16]) Tj ET BT 8.9664 0 0 8.9664 70.03534 102.918 Tm /Ty2 1 Tf
[ (P) 15 (asca) 1 (l) -343 (Germain,) -366 (Francis) -343 (Bach,) -365 (Ale)
15 (xandre) -343 (Lacoste,) -366 (and) -342 (Si-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 91.959
Tm /Ty2 1 Tf [ (mon) -236 (Lacoste-Julien.) -329 (P) 15 (ac-bayesian) -236
(theory) -235 (meets) -236 (bayesian) -236 (in-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 81
Tm /Ty2 1 Tf [ (ference.) -309 (In) -226 (D.) -226 (Lee,) -232 (M.) -226 (Sugiyama,)
-231 (U.) -226 (Luxb) 20 (ur) 18 (g,) -231 (I.) -227 (Guyon,) -231 (and) ]
TJ ET BT 8.9664 0 0 8.9664 328.781 710.037 Tm /Ty2 1 Tf [ (R.) -195 (Garnett,)
-205 (editors,) ] TJ ET BT 8.9664 0 0 8.9664 398.215 710.037 Tm /Ty6 1 Tf
[ (Advances) -195 (i) 1 (n) -195 (Neur) 15 (al) -195 (Information) -194 (Pr)
45 (ocess-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 699.078 Tm /Ty6 1 Tf [ (ing)
-250 (Systems) ] TJ ET BT 8.9664 0 0 8.9664 370.869 699.078 Tm /Ty2 1 Tf [
(,) -250 (v) 20 (olume) -250 (29.) -250 (Curran) -250 (Associates,) -250 (Inc.,)
-250 (2016.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 529.3143 699.078
Tm /Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 686.725 Tm
/Ty2 1 Tf ([17]) Tj ET BT 8.9664 0 0 8.9664 328.7853 686.725 Tm /Ty2 1 Tf
[ (P) 15 (asca) 1 (l) -343 (Germain,) -366 (Francis) -343 (Bach,) -365 (Ale)
15 (xandre) -343 (Lacoste,) -366 (and) -342 (Si-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 675.766
Tm /Ty2 1 Tf [ (mon) -236 (Lacoste-Julien.) -329 (P) 15 (ac-bayesian) -236
(theory) -235 (meets) -236 (bayesian) -236 (in-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 664.807
Tm /Ty2 1 Tf [ (ference.) -360 (v) 20 (olume) -250 (29,) -250 (2016.) ] TJ
ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 426.443 664.807 Tm /Ty2 1 Tf (3)
Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 430.9262 664.807 Tm /Ty2 1 Tf (,)
Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 435.4094 664.807 Tm /Ty2 1 Tf
(4) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 652.454 Tm /Ty2 1 Tf ([18])
Tj ET BT 8.9664 0 0 8.9664 328.7853 652.454 Tm /Ty2 1 Tf [ (P) 15 (asca) 1
(l) -486 (Germain,) -544 (Ale) 15 (xandre) -485 (Lacasse,) -544 (Franc) 388
-55 (ois) -485 (La) 20 (violette,) ] TJ ET BT 8.9664 0 0 8.9664 328.781 641.495
Tm /Ty2 1 Tf [ (and) -234 (Mario) -235 (Marchand.) -326 (P) 15 (ac-bayesian)
-234 (learning) -234 (of) -235 (linear) -234 (classi-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 630.536
Tm /Ty2 1 Tf [ (ers.) -458 (In) ] TJ ET BT 8.9664 0 0 8.9664 360.557 630.536
Tm /Ty6 1 Tf [ (Pr) 45 (oceedings) -281 (of) -280 (the) -281 (26th) -281 (Annual)
-280 (International) -281 (Con-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 619.577
Tm /Ty6 1 Tf [ (fer) 37 (ence) -430 (on) -430 (Mac) 15 (hine) -430 (Learning)
] TJ ET BT 8.9664 0 0 8.9664 439.485 619.577 Tm /Ty2 1 Tf [ (,) -475 (ICML)
-430 -474 (page) -430 (353360,) ] TJ ET BT 8.9664 0 0 8.9664 328.781 608.618
Tm /Ty2 1 Tf [ (Ne) 25 (w) -243 (Y) 110 (ork,) -245 (NY) 129 (,) -244 (USA,)
-243 (2009.) -244 (Association) -243 (for) -243 (Computing) -244 (Ma-) ] TJ
ET BT 8.9664 0 0 8.9664 328.781 597.659 Tm /Ty2 1 Tf [ (chinery) 65 (.) ]
TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 360.5579 597.659 Tm /Ty2 1 Tf
(1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 365.0411 597.659 Tm /Ty2 1 Tf
(,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 369.5243 597.659 Tm /Ty2 1
Tf (2) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 374.0075 597.659 Tm /Ty2 1
Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 378.4907 597.659 Tm /Ty2
1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 585.306 Tm /Ty2 1
Tf ([19]) Tj ET BT 8.9664 0 0 8.9664 328.7853 585.306 Tm /Ty2 1 Tf [ (Ian)
-293 (J.) -294 (Goodfello) 25 (w) 65 (,) -304 (Jonathon) -294 (Shlens,) -304
(and) -294 (Christian) -293 (Sze) 15 (gedy) 65 (.) ] TJ ET BT 8.9664 0 0 8.9664 328.781 574.347
Tm /Ty2 1 Tf [ (Explaining) -477 (and) -477 (harnessing) -477 (adv) 15 (ersarial)
-477 (e) 15 (xamples.) ] TJ ET BT 8.9664 0 0 8.9664 521.45 574.347 Tm /Ty6
1 Tf (CoRR) Tj ET BT 8.9664 0 0 8.9664 542.87 574.347 Tm /Ty2 1 Tf (,) Tj
ET BT 8.9664 0 0 8.9664 328.781 563.388 Tm /Ty2 1 Tf [ (abs/1412.6572,) -250
(2015.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 409.2186 563.388 Tm
/Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 551.035 Tm /Ty2
1 Tf ([20]) Tj ET BT 8.9664 0 0 8.9664 328.7853 551.035 Tm /Ty2 1 Tf [ (Sv)
15 (en) -245 (Go) 25 (w) 10 (al,) -246 (Chongli) -245 (Q) 1 (in,) -246 (Jonathan)
-245 (Uesato,) -246 (T) 35 (imoth) 5 (y) -245 (Mann,) ] TJ ET BT 8.9664 0 0 8.9664 328.781 540.076
Tm /Ty2 1 Tf [ (and) -363 (Pushmeet) -364 (K) 35 (ohli.) -723 (Unco) 15 (v)
15 (ering) -364 (the) -363 (limits) -363 (of) -364 (adv) 15 (ersarial) ] TJ
ET BT 8.9664 0 0 8.9664 328.781 529.117 Tm /Ty2 1 Tf [ (training) -329 (ag)
5 (ainst) -329 (norm-bounded) -330 (adv) 15 (ersarial) -329 (e) 15 (xamples,)
-349 (2020.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 328.781 518.158
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 505.805 Tm
/Ty2 1 Tf ([21]) Tj ET BT 8.9664 0 0 8.9664 328.7853 505.805 Tm /Ty2 1 Tf
[ (Sv) 15 (en) -249 (Go) 25 (w) 10 (al,) -250 (Sylv) 15 (estre-Alvise) -249
(Reb) 20 (uf) 25 -250 (Oli) 25 (via) -250 (W) 40 (iles,) -249 (Florian)
] TJ ET BT 8.9664 0 0 8.9664 328.781 494.846 Tm /Ty2 1 Tf [ (Stimber) 18 (g,)
-298 (Dan) -288 (Andrei) -288 (Calian,) -298 (and) -288 (T) 35 (imoth) 5 (y)
-288 (Mann.) -482 (Impro) 15 (v-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 483.887
Tm /Ty2 1 Tf [ (ing) -244 (rob) 20 (ustness) -243 (using) -244 (generated)
-244 (data.) -346 (In) ] TJ ET BT 8.9664 0 0 8.9664 470.879 483.887 Tm /Ty6
1 Tf (NeurIPS) Tj ET BT 8.9664 0 0 8.9664 501.759 483.887 Tm /Ty2 1 Tf [ (,)
-244 (2021.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 529.4652 483.887
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 533.9484 483.887
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 538.3867 483.887
Tm /Ty2 1 Tf (2) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 542.8699 483.887
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 328.781 472.928
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 333.2642 472.928
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 337.7474 472.928
Tm /Ty2 1 Tf (6) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 342.2306 472.928
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 346.7138 472.928
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(T) 35 (imur) -211 (Garipo) 15 (v) 65 (,) -218 (Dmitry) ] TJ ET BT 8.9664 0 0 8.9664 328.781 348.197
Tm /Ty2 1 Tf [ (V) 111 (etro) 15 (v) 65 (,) -493 (and) -445 (Andre) 25 (w)
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[ (,) -407 (34th) -375 (Conference) -375 (on) -375 (Uncertainty) -375 (in)
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1 Tf [ (,) -301 (pages) -290 (47734783.) ] TJ ET BT 8.9664 0 0 8.9664 328.781 226.255
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1 Tf [ (,) -250 (pages) -250 (1527315283,) -250 (June) -250 (2022.) ] TJ
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10 (a,) -385 (Sarah) ] TJ ET BT 8.9664 0 0 8.9664 328.781 135.795 Tm /Ty2
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(Vladu.) -773 (T) 80 (o) 25 (w) 10 (ards) -379 (deep) -379 (learn-) ] TJ ET
BT 8.9664 0 0 8.9664 70.031 352.961 Tm /Ty2 1 Tf [ (ing) -373 (models) -372
(resistant) -372 (to) -373 (adv) 15 (ersarial) -372 (attacks.) ] TJ ET BT
8.9664 0 0 8.9664 234.039 352.961 Tm /Ty6 1 Tf [ (arXiv) -373 (pr) 38 (eprint)
] TJ ET BT 8.9664 0 0 8.9664 70.031 342.002 Tm /Ty6 1 Tf (arXiv:1706.06083)
Tj ET BT 8.9664 0 0 8.9664 135.53 342.002 Tm /Ty2 1 Tf [ (,) -250 (2017.)
] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 163.4155 342.002 Tm /Ty2 1 Tf
(1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 167.8987 342.002 Tm /Ty2 1 Tf
(,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 172.3819 342.002 Tm /Ty2 1
Tf (2) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 176.8651 342.002 Tm /Ty2 1
Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 181.3483 342.002 Tm /Ty2
1 Tf (6) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 329.765 Tm /Ty2 1
Tf ([33]) Tj ET BT 8.9664 0 0 8.9664 70.03534 329.765 Tm /Ty2 1 Tf [ (Kaleel)
-396 (Mahmood,) -433 (Rigel) -397 (Mahmood,) -433 (and) -396 (Marten) -397
(v) 25 (an) -396 (Dijk.) ] TJ ET BT 8.9664 0 0 8.9664 70.031 318.806 Tm /Ty2
1 Tf [ (On) -342 (the) -342 (rob) 20 (ustness) -342 (of) -343 (vi) 1 (sion)
-343 (transformers) -342 (to) -342 (adv) 15 (ersarial) -342 (e) 15 (x-) ]
TJ ET BT 8.9664 0 0 8.9664 70.031 307.847 Tm /Ty2 1 Tf [ (amples.) -303 (In)
] TJ ET BT 8.9664 0 0 8.9664 109.869 307.847 Tm /Ty6 1 Tf [ (Pr) 45 (oceedings)
-224 (of) -224 (the) -223 (IEEE/CVF) -224 (International) -224 (Con-) ] TJ
ET BT 8.9664 0 0 8.9664 70.031 296.889 Tm /Ty6 1 Tf [ (fer) 37 (ence) -287
(on) -287 (Computer) -287 (V) 74 (ision) -287 (\(ICCV\)) ] TJ ET BT 8.9664 0 0 8.9664 199.867 296.889
Tm /Ty2 1 Tf [ (,) -287 (pages) -287 (78387847,) -297 (Oc-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 285.93
Tm /Ty2 1 Tf [ (tober) -250 (2021.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 114.1009 285.93
Tm /Ty2 1 Tf (6) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 118.5841 285.93 Tm
/Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 123.0673 285.93
Tm /Ty2 1 Tf (27) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 132.0337 285.93
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 136.5169 285.93
Tm /Ty2 1 Tf (32) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 273.693 Tm
/Ty2 1 Tf ([34]) Tj ET BT 8.9664 0 0 8.9664 70.03534 273.693 Tm /Ty2 1 Tf
[ (Da) 20 (vid) -400 (A.) -400 (McAllester) 55 (.) -842 (P) 15 (ac-bayesian)
-400 (model) -401 (a) 20 (v) 15 (eraging.) -841 (In) ] TJ ET BT 8.9664 0 0 8.9664 70.031 262.734
Tm /Ty6 1 Tf [ (COL) 20 (T) -250 ] TJ ET BT 8.9664 0 0 8.9664 106.47 262.734
Tm /Ty2 1 Tf [ (,) -250 (1999.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 134.3555 262.734
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 138.8387 262.734
Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 143.3219 262.734
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 250.497 Tm
/Ty2 1 Tf ([35]) Tj ET BT 8.9664 0 0 8.9664 70.03534 250.497 Tm /Ty2 1 Tf
[ (Behnam) -1225 (Ne) 15 (yshab) 20 (ur) 40 (,) -1470 (Srinadh) -1226 (Bhojanapalli,)
-1469 (Da) 20 (vid) ] TJ ET BT 8.9664 0 0 8.9664 70.031 239.538 Tm /Ty2 1
Tf [ (McAllester) 40 (,) -638 (and) -560 (Nati) -560 (Srebro.) -1353 (Exploring)
-560 (generalization) ] TJ ET BT 8.9664 0 0 8.9664 70.031 228.579 Tm /Ty2
1 Tf [ (in) -233 (dee) 1 (p) -233 (learning.) ] TJ ET BT 8.9664 0 0 8.9664 132.617 228.579
Tm /Ty6 1 Tf [ (Advances) -232 (in) -233 (neur) 15 (al) -232 (information)
-233 (pr) 45 (ocessing) ] TJ ET BT 8.9664 0 0 8.9664 70.031 217.62 Tm /Ty6
1 Tf (systems) Tj ET BT 8.9664 0 0 8.9664 97.423 217.62 Tm /Ty2 1 Tf [ (,)
-250 (30,) -250 (2017.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 138.7581 217.62
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 205.383 Tm
/Ty2 1 Tf ([36]) Tj ET BT 8.9664 0 0 8.9664 70.03534 205.383 Tm /Ty2 1 Tf
[ (T) 35 (ian) 15 (yu) -202 (P) 15 (ang,) -213 (Min) -203 (Lin,) -212 (Xiao)
-203 (Y) 100 (ang,) -212 (Jun) 15 (yi) -203 (Zhu,) -213 (and) -202 (Shuicheng)
] TJ ET BT 8.9664 0 0 8.9664 70.031 194.424 Tm /Ty2 1 Tf [ (Y) 100 (an.) -1014
(Rob) 20 (ustness) -454 (and) -455 (accurac) 15 (y) -454 (could) -454 (be)
-455 (reconcilable) -454 (by) ] TJ ET BT 8.9664 0 0 8.9664 70.031 183.465
Tm /Ty2 1 Tf [ (\(proper\)) -250 (denition.) -360 (In) ] TJ ET BT 8.9664 0 0 8.9664 151.203 183.465
Tm /Ty6 1 Tf (ICML) Tj ET BT 8.9664 0 0 8.9664 172.624 183.465 Tm /Ty2 1 Tf
[ (,) -250 (2022.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 200.5095 183.465
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 171.228 Tm
/Ty2 1 Tf ([37]) Tj ET BT 8.9664 0 0 8.9664 70.03534 171.228 Tm /Ty2 1 Tf
[ (Siyuan) -504 (Qiao,) -568 (Huiyu) -504 (W) 80 (ang,) -568 (Chenxi) -504
(Liu,) -568 (W) 80 (ei) -505 (Shen,) -567 (and) ] TJ ET BT 8.9664 0 0 8.9664 70.031 160.269
Tm /Ty2 1 Tf [ (Alan) -353 (Y) 111 (uille.) -691 (Micro-batch) -353 (training)
-353 (with) -354 (batch-channel) -353 (nor) 20 (-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 149.31
Tm /Ty2 1 Tf [ (malization) -605 (and) -605 (weight) -605 (standardization.)
] TJ ET BT 8.9664 0 0 8.9664 231.954 149.31 Tm /Ty6 1 Tf [ (arXiv) -605 (pr)
37 (eprint) ] TJ ET BT 8.9664 0 0 8.9664 70.031 138.351 Tm /Ty6 1 Tf (arXiv:1903.10520)
Tj ET BT 8.9664 0 0 8.9664 135.53 138.351 Tm /Ty2 1 Tf [ (,) -250 (2019.)
] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 163.4155 138.351 Tm /Ty2 1 Tf
(32) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 126.114 Tm /Ty2 1 Tf ([38])
Tj ET BT 8.9664 0 0 8.9664 70.03534 126.114 Tm /Ty2 1 Tf [ (Lesli) 1 (e) -351
(Rice,) -376 (Eric) -350 (W) 80 (ong,) -376 (and) -351 (J.) -350 (Zico) -351
(K) 35 (olter) 55 (.) -682 (Ov) 15 (ertting) -350 (in) ] TJ ET BT 8.9664 0 0 8.9664 70.031 115.155
Tm /Ty2 1 Tf [ (adv) 15 (ersarially) -250 (rob) 20 (ust) -250 (deep) -250
(learning.) -360 (In) ] TJ ET BT 8.9664 0 0 8.9664 206.659 115.155 Tm /Ty6
1 Tf (ICML) Tj ET BT 8.9664 0 0 8.9664 228.08 115.155 Tm /Ty2 1 Tf [ (,) -250
(2020.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 255.9655 115.155 Tm
/Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 260.4487 115.155 Tm
/Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 264.9319 115.155
Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 50.112 102.918 Tm
/Ty2 1 Tf ([39]) Tj ET BT 8.9664 0 0 8.9664 70.03534 102.918 Tm /Ty2 1 Tf
[ (K) 25 (e) 25 (vin) -269 (Roth,) -275 (Y) 100 (annic) -269 (Kilcher) 40
(,) -275 (and) -270 (Thomas) -269 (Hofmann.) -423 (Adv) 15 (er) 20 (-) ] TJ
ET BT 8.9664 0 0 8.9664 70.031 91.959 Tm /Ty2 1 Tf [ (sarial) -202 (training)
-201 (is) -202 (a) -202 (form) -201 (of) -202 (data-dependent) -202 (operator)
-201 (norm) -202 (re) 15 (g-) ] TJ ET BT 8.9664 0 0 8.9664 70.031 81 Tm /Ty2
1 Tf [ (ularization.) -479 (In) -287 (H.) -287 (Larochelle,) -296 (M.) -287
(Ranzato,) -297 (R.) -287 (Hadsell,) -296 (M.F) 80 (.) ] TJ ET BT 8.9664 0 0 8.9664 328.781 710.037
Tm /Ty2 1 Tf [ (Balcan,) -242 (and) -239 (H.) -239 (Lin,) -242 (editors,)
] TJ ET BT 8.9664 0 0 8.9664 429.721 710.037 Tm /Ty6 1 Tf [ (Advances) -239
(in) -240 (Neur) 15 (al) -239 (Information) ] TJ ET BT 8.9664 0 0 8.9664 328.781 699.079
Tm /Ty6 1 Tf [ (Pr) 45 (ocessing) -210 (Systems) ] TJ ET BT 8.9664 0 0 8.9664 398.497 699.079
Tm /Ty2 1 Tf [ (,) -218 (v) 20 (olume) -211 (33,) -218 (pages) -210 (1497314985.)
-211 (Curran) ] TJ ET BT 8.9664 0 0 8.9664 328.781 688.12 Tm /Ty2 1 Tf [ (Associates,)
-250 (Inc.,) -250 (2020.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 413.1907 688.12
Tm /Ty2 1 Tf (6) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 675.981 Tm
/Ty2 1 Tf ([40]) Tj ET BT 8.9664 0 0 8.9664 328.7853 675.981 Tm /Ty2 1 Tf
[ (Jonas) -319 (Rothfuss,) -336 (V) 60 (incent) -319 (F) 15 (ortuin,) -337
(Martin) -319 (Josifoski,) -336 (and) -319 (An-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 665.022
Tm /Ty2 1 Tf [ (dreas) -201 (Krause.) -253 (P) 15 (acoh:) -286 (Bayes-optimal)
-200 (meta-learning) -201 (with) -201 (pac-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 654.063
Tm /Ty2 1 Tf [ (guarantees.) -399 (In) ] TJ ET BT 8.9664 0 0 8.9664 382.765 654.063
Tm /Ty6 1 Tf [ (International) -262 (Confer) 37 (ence) -263 (on) -262 (Mac)
15 (hine) -262 (Learn-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 643.104 Tm /Ty6
1 Tf (ing) Tj ET BT 8.9664 0 0 8.9664 340.24 643.104 Tm /Ty2 1 Tf [ (,) -250
(pages) -250 (91169126.) -250 (PMLR,) -250 (2021.) ] TJ ET /Cs1 cs 1 0 0
sc BT 8.9664 0 0 8.9664 464.5143 643.104 Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0
sc BT 8.9664 0 0 8.9664 308.862 630.965 Tm /Ty2 1 Tf ([41]) Tj ET BT 8.9664 0 0 8.9664 328.7853 630.965
Tm /Ty2 1 Tf [ (V) 60 (ikash) -279 (Sehw) 10 (ag,) -288 (Saeed) -280 (Mahloujif)
10 (ar) 40 (,) -287 (T) 35 (inashe) -280 (Handina,) -287 (Sihui) ] TJ ET BT
8.9664 0 0 8.9664 328.781 620.006 Tm /Ty2 1 Tf [ (Dai,) -341 (Chong) -323
(Xiang,) -340 (Mung) -323 (Chiang,) -341 (and) -323 (Prateek) -322 (Mittal.)
-593 (Ro-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 609.048 Tm /Ty2 1 Tf [ (b)
20 (ust) -307 (learning) -307 (meets) -307 (generati) 25 (v) 15 (e) -306 (models:)
-424 (Can) -307 (proxy) -307 (distrib) 20 (u-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 598.089
Tm /Ty2 1 Tf [ (tions) -250 (impro) 15 (v) 15 (e) -250 (adv) 15 (ersarial)
-250 (rob) 20 (ustness?) -420 (In) ] TJ ET BT 8.9664 0 0 8.9664 476.895 598.089
Tm /Ty6 1 Tf (ICLR) Tj ET BT 8.9664 0 0 8.9664 496.325 598.089 Tm /Ty2 1 Tf
[ (,) -250 (2022.) ] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 524.2105 598.089
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 585.95 Tm
/Ty2 1 Tf ([42]) Tj ET BT 8.9664 0 0 8.9664 328.7853 585.95 Tm /Ty2 1 Tf [
(John) -248 (Sha) 15 (we-T) 80 (aylor) -249 (and) -249 (Robert) -249 (C.)
-248 (W) 40 (illiamson.) -358 (A) -249 (pac) -248 (analy-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 574.991
Tm /Ty2 1 Tf [ (sis) -279 (of) -279 (a) -278 (bayesian) -279 (estimator) 55
(.) -452 (In) ] TJ ET BT 8.9664 0 0 8.9664 440.214 574.991 Tm /Ty6 1 Tf [
(Pr) 45 (oceedings) -279 (of) -279 (t) 1 (he) -279 (T) 92 (enth) -279 (An-)
] TJ ET BT 8.9664 0 0 8.9664 328.781 564.032 Tm /Ty6 1 Tf [ (nual) -251 (Confer)
37 (ence) -251 (on) -251 (Computational) -251 (Learning) -251 (Theory) ] TJ
ET BT 8.9664 0 0 8.9664 518.032 564.032 Tm /Ty2 1 Tf [ (,) -251 (COL) 92 (T)
] TJ ET BT 8.9664 0 0 8.9664 328.781 553.073 Tm /Ty2 1 Tf [ -333 (page)
-316 <32d0392c> -333 (Ne) 25 (w) -316 (Y) 110 (ork,) -332 (NY) 129 (,) -317 (USA,)
-316 (1997.) -316 (Association) -316 (for) ] TJ ET BT 8.9664 0 0 8.9664 328.781 542.114
Tm /Ty2 1 Tf [ (Computing) -250 (Machinery) 65 (.) ] TJ ET /Cs1 cs 1 0 0 sc
BT 8.9664 0 0 8.9664 415.1095 542.114 Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc
BT 8.9664 0 0 8.9664 419.5927 542.114 Tm /Ty2 1 Tf (,) Tj ET /Cs1 cs 1 0 0
sc BT 8.9664 0 0 8.9664 424.0759 542.114 Tm /Ty2 1 Tf (3) Tj ET /Cs2 cs 0
sc BT 8.9664 0 0 8.9664 308.862 529.975 Tm /Ty2 1 Tf ([43]) Tj ET BT 8.9664 0 0 8.9664 328.7853 529.975
Tm /Ty2 1 Tf [ (Da) 15 (wn) -236 (Song,) -239 (K) 25 (e) 25 (vin) -236 (Eykholt,)
-239 (Iv) 25 (an) -236 (Evtimo) 15 (v) 65 (,) -239 (Earlence) -236 (Fernan-)
] TJ ET BT 8.9664 0 0 8.9664 328.781 519.017 Tm /Ty2 1 Tf [ (des,) -429 (Bo)
-393 (Li,) -429 (Ami) 1 (r) -394 (R) 1 (ahmati,) -429 (Florian) -393 (T) 35
(ram) ] TJ ET BT 8.9664 0 0 8.9664 482.82 519.061 Tm /Ty2 1 Tf (`) Tj ET BT
8.9664 0 0 8.9664 482.323 519.017 Tm /Ty2 1 Tf [ (er) 40 (,) -429 (Atul) -393
(Prakash,) ] TJ ET BT 8.9664 0 0 8.9664 328.781 508.058 Tm /Ty2 1 Tf [ (and)
-223 (T) 80 (adayoshi) -224 (K) 35 (ohno.) -302 (Ph) 5 (ysical) -224 (adv)
15 (ersarial) -223 (e) 15 (xamples) -223 (for) -224 (ob-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 497.099
Tm /Ty2 1 Tf [ (ject) -224 (detectors.) -305 (In) ] TJ ET BT 8.9664 0 0 8.9664 390.565 497.099
Tm /Ty6 1 Tf [ (12th) -224 (USENIX) -225 (W) 92 (orkshop) -224 (on) -225 (Of)
18 (fensive) -224 (T) 92 (ec) 15 (h-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 486.14
Tm /Ty6 1 Tf [ (nolo) 10 (gies) -292 (\(W) 25 (OO) 40 (T) -292 (18\)) ] TJ
ET BT 8.9664 0 0 8.9664 404.071 486.14 Tm /Ty2 1 Tf [ (,) -303 (Bal) 1 (timore,)
-303 (MD,) -292 (Aug.) -292 (2018.) -292 (USENIX) ] TJ ET BT 8.9664 0 0 8.9664 328.781 475.181
Tm /Ty2 1 Tf (Association.) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 376.5898 475.181
Tm /Ty2 1 Tf (1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 463.042 Tm
/Ty2 1 Tf ([44]) Tj ET BT 8.9664 0 0 8.9664 328.7853 463.042 Tm /Ty2 1 Tf
[ (P) 111 (.B.) -424 (Stark) -425 (and) -425 (Berk) 10 (ele) 15 (y) 65 (.)
-425 (Department) -425 (of) -425 (Statistics) -424 (Uni) 25 (v) 15 (er) 20
(-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 452.083 Tm /Ty2 1 Tf [ (sity) -267
(of) -266 (California.) ] TJ ET BT 8.9664 0 0 8.9664 396.296 452.083 Tm /Ty6
1 Tf [ (SticiGui:) -343 (Statistics) -267 (T) 92 (ools) -267 (for) -266 (Internet)
-267 (and) ] TJ ET BT 8.9664 0 0 8.9664 328.781 441.124 Tm /Ty6 1 Tf [ (Classr)
45 (oom) -283 (Instruction) ] TJ ET BT 8.9664 0 0 8.9664 409.132 441.124 Tm
/Ty2 1 Tf [ (.) -467 (Department) -284 (of) -283 (Statistics.) -284 (Uni)
25 (v) 15 (ersity) ] TJ ET BT 8.9664 0 0 8.9664 328.781 430.165 Tm /Ty2 1
Tf [ (of) -250 (California,) -250 (Berk) 10 (ele) 15 (y) 65 (,) -250 (2005.)
] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 438.7808 430.165 Tm /Ty2 1 Tf
(6) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 443.264 430.165 Tm /Ty2 1 Tf (,)
Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 447.7472 430.165 Tm /Ty2 1 Tf
(7) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 452.2304 430.165 Tm /Ty2 1 Tf
(,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 456.7136 430.165 Tm /Ty2 1
Tf (31) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 465.68 430.165 Tm /Ty2 1 Tf
(,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 470.1632 430.165 Tm /Ty2 1
Tf (32) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 418.027 Tm /Ty2 1
Tf ([45]) Tj ET BT 8.9664 0 0 8.9664 328.7853 418.027 Tm /Ty2 1 Tf [ (P) 15
(aul) -214 (V) 60 (iallard,) -222 (Eric) -214 (Guillaume) -215 (VIDO) 40 (T)
74 (,) -214 (Amaury) -215 (Habrard,) -221 (and) ] TJ ET BT 8.9664 0 0 8.9664 328.781 407.068
Tm /Ty2 1 Tf [ (Emilie) -426 (Morv) 25 (ant.) -923 (A) -425 (pac-bayes) -426
(analysis) -426 (of) -426 (adv) 15 (ersarial) -426 (ro-) ] TJ ET BT 8.9664 0 0 8.9664 328.781 396.109
Tm /Ty2 1 Tf [ (b) 20 (ustness.) -531 (In) -303 (M.) -303 (Ranzato,) -317
(A.) -303 (Be) 15 (ygelzimer) 40 (,) -317 (Y) 129 (.) -303 (Dauphin,) -317
(P) 111 (.S.) ] TJ ET BT 8.9664 0 0 8.9664 328.781 385.15 Tm /Ty2 1 Tf [ (Liang,)
-214 (and) -206 (J.) -205 (W) 80 (ortman) -206 (V) 111 (aughan,) -214 (editors,)
] TJ ET BT 8.9664 0 0 8.9664 475.32 385.15 Tm /Ty6 1 Tf [ (Advances) -205
(in) -206 (Neur) 15 (al) ] TJ ET BT 8.9664 0 0 8.9664 328.781 374.191 Tm /Ty6
1 Tf [ (Information) -331 (Pr) 45 (ocessing) -331 (Systems) ] TJ ET BT 8.9664 0 0 8.9664 445.389 374.191
Tm /Ty2 1 Tf [ (,) -351 (v) 20 (olume) -331 (34,) -352 (pages) -331 (14421)
] TJ ET BT 8.9664 0 0 8.9664 328.781 363.232 Tm /Ty2 1 Tf [ (14433.) -250
(Curran) -250 (Associates,) -250 (Inc.,) -250 (2021.) ] TJ ET /Cs1 cs 1 0
0 sc BT 8.9664 0 0 8.9664 467.2312 363.232 Tm /Ty2 1 Tf (8) Tj ET /Cs2 cs
0 sc BT 8.9664 0 0 8.9664 308.862 351.093 Tm /Ty2 1 Tf ([46]) Tj ET BT 8.9664 0 0 8.9664 328.7853 351.093
Tm /Ty2 1 Tf [ (Y) 55 (isen) -307 (W) 80 (ang,) -323 (Dif) 10 (an) -308 (Zou,)
-322 (Jinfeng) -308 (Y) 55 (i,) -322 (James) -308 (Baile) 15 (y) 65 (,) -322
(Xingjun) ] TJ ET BT 8.9664 0 0 8.9664 328.781 340.134 Tm /Ty2 1 Tf [ (Ma,)
-417 (and) -383 (Quanquan) -383 (Gu.) -787 (Impro) 15 (ving) -384 (adv) 15
(ersarial) -383 (rob) 20 (ustness) ] TJ ET BT 8.9664 0 0 8.9664 328.781 329.175
Tm /Ty2 1 Tf [ (requires) -320 (re) 25 (visiting) -320 (misclassied) -319
(e) 15 (xamples.) -584 (In) ] TJ ET BT 8.9664 0 0 8.9664 497.788 329.175 Tm
/Ty6 1 Tf (International) Tj ET BT 8.9664 0 0 8.9664 328.781 318.217 Tm /Ty6
1 Tf [ (Confer) 37 (ence) -250 (on) -250 (Learning) -250 (Repr) 37 (esentations)
] TJ ET BT 8.9664 0 0 8.9664 475.801 318.217 Tm /Ty2 1 Tf [ (,) -250 (2020.)
] TJ ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 503.6865 318.217 Tm /Ty2 1 Tf
(1) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 508.1697 318.217 Tm /Ty2 1 Tf
(,) Tj ET /Cs1 cs 1 0 0 sc BT 8.9664 0 0 8.9664 512.6529 318.217 Tm /Ty2 1
Tf (24) Tj ET /Cs2 cs 0 sc BT 8.9664 0 0 8.9664 308.862 306.078 Tm /Ty2 1
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