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(recently) -394.98400 (sho) 24.99220 (wn) -394.98600 (in) -394.98100 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 168.78600 128.82000 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 178.74900 128.82000 Tm [ (\135) -394.99700 (that) -395.01700 (minimization) -395.00500 (of) -394.99000 (the) ] TJ /R46 9.96260 Tf -128.63700 -11.95510 Td (top\055) Tj /R48 9.96260 Tf 16.05000 0 Td [ (k) -0.59978 ] TJ /R46 9.96260 Tf 9.93398 0 Td [ (hing) 9.98118 (e) -444.98900 (loss) ] TJ /R42 9.96260 Tf 46.40700 0 Td [ (leads) -445.01400 (to) -445.01200 (impro) 15.00360 (v) 14.98280 (ements) -445.00200 (in) -445.01200 (top\055) ] TJ /R48 9.96260 Tf 126.46800 0 Td [ (k) -0.60039 ] TJ /R42 9.96260 Tf 9.93398 0 Td [ (perfor) 19.99180 (\055) ] TJ -208.79300 -11.95510 Td [ (mance) -251.99300 (compared) -251.00600 (to) -251.98500 (O) 49.99410 (V) 135 (A) -251.01400 (SVM\054) -252.00600 (multiclass) -251.98700 (SVM) 1.00964 (\054) -251.99500 (and) -251.99200 (other) ] TJ 11.95510 TL T* [ (ranking\055based) -381.99100 (formulations\056) -707.98700 (In) -382.01300 (this) -381.98900 (paper) 39.99090 (\054) -416.00700 (we) -382.01700 (study) -383.00500 (top\055) ] TJ /R48 9.96260 Tf T* [ (k) -0.59978 ] TJ /R42 9.96260 Tf 10.21170 0 Td [ (error) -472.98900 (optimization) -473 (from) -473.00800 (a) -472.98500 (wider) -473.01200 (perspecti) 24.99090 (v) 14.98280 (e\056) -979.01600 (On) -473.01200 (the) ] TJ 248.53800 487.26700 Td [ (one) -483.99300 (hand\054) -542.99500 (we) -484 (compare) -483.99300 (O) 49.99660 (V) 135.00200 (A) -483.99300 (schemes) -483.98300 (and) -485.01200 (direct) -483.98800 (multi\055) ] TJ T* [ (class) -471.01000 (losses) -472.01200 (in) -471.00700 (e) 15.01220 (xtensi) 25.00320 (v) 14.98280 (e) -472.00500 (e) 15.01220 (xperiments\054) -525.99100 (and) -471.99500 (on) -471.01000 (the) -471.99000 (other) 40.00310 (\054) ] TJ T* [ (we) -428.99000 (present) -429.01400 (theoretical) -427.99000 (discussion) -429.01700 (re) 15.00730 (g) 4.98446 (arding) -429.01200 (their) -429.01700 (calibra\055) ] TJ T* [ (tion) -345.01600 (for) -343.98400 (the) -344.99400 (top\055) ] TJ /R48 9.96260 Tf 65.64300 0 Td [ (k) -0.60039 ] TJ /R42 9.96260 Tf 8.93398 0 Td [ (error) 55 (\056) -594.01600 (Based) -344.98700 (on) -344.01100 (these) -344.99100 (insights\054) -368.00700 (we) -345.00100 (sug\055) ] TJ -74.57700 -11.95470 Td (gest) Tj /R50 9.96260 Tf 19.98400 0 Td (4) Tj /R42 9.96260 Tf 8.91680 0 Td [ (ne) 25.01540 (w) -394.99000 (f) 9.99588 (amilies) -395 (of) -394.99000 (loss) -395.00800 (functions) -394.99800 (for) -394.99300 (the) -394.98300 (top\055) ] TJ /R48 9.96260 Tf 176.61400 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf 9.43516 0 Td [ (error) 55 (\056) ] TJ -214.95000 -11.95510 Td [ (T) 79.99160 (w) 10 (o) -311.00200 (are) -311.01900 (smoothed) -311.00400 (v) 14.98280 (ersions) -310.00700 (of) -311.00700 (the) -310.99700 (top\055) ] TJ /R48 9.96260 Tf 156.43400 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf 8.59688 0 Td [ (hinge) -310.98700 (losses) -310.98200 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 529.34500 508.49200 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 539.30700 508.49200 Tm (\135\054) Tj -230.44500 -11.95630 Td [ (and) -372.01100 (the) -372.00900 (other) -370.98700 (tw) 10.00810 (o) -372.01100 (are) -371.98900 (top\055) ] TJ /R48 9.96260 Tf 108.61000 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf 9.20508 0 Td [ (v) 14.98280 (ersions) -371.99700 (of) -370.99700 (the) -372.00700 (softmax) -371.98700 (loss\056) ] TJ -117.81500 -11.95470 Td [ (W) 79.98660 (e) -269.01900 (discuss) -268.98200 (t) 0.98758 (heir) -269.00900 (adv) 24.98110 (antages) -269.00400 (and) -269.00900 (disadv) 25 (antages\054) -272.99900 (and) -269.00900 (for) -269.01400 (the) ] TJ 11.95510 TL T* [ (con) 39.99820 (v) 14.98280 (e) 15.01220 (x) -245.01300 (losses) -244.99100 (pro) 14.98520 (vide) -245.00600 (an) -245.01800 (ef) 25.00560 <026369656e74> -246.01300 (implem) 0.98023 (entation) -246.00800 (based) -245.00800 (on) ] TJ T* [ (stochastic) -250.00500 (dual) -249.98500 (coordinate) -250.01700 (ascent) -249.99300 (\050SDCA\051) -250.01200 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 481.23500 460.67100 Tm (38) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 491.19800 460.67100 Tm (\135\056) Tj -170.38100 -14.22110 Td [ (W) 79.98660 (e) -381 (e) 25.01050 (v) 24.98110 (aluate) -380.00800 (a) -381 (battery) -380.98100 (of) -380.01500 (loss) -381.01000 (functions) -379.98100 (on) ] TJ /R50 9.96260 Tf 178.99900 0 Td (11) Tj /R42 9.96260 Tf 13.75470 0 Td (datasets) Tj -204.70900 -11.95470 Td [ (of) -374.99400 (dif) 24.98600 (ferent) -374.01800 (tasks) -375.01600 (ranging) -375.01600 (from) -374.98600 (te) 14.98280 (xt) -374.00600 <636c6173736902636174696f6e> -374.98600 (to) -374.98600 (lar) 17.99700 (ge) ] TJ 11.95510 TL T* [ (scale) -315.98600 (vision) -315.99100 (benchmarks\054) -333.01800 (including) -315.98200 <026e652d677261696e6564> -316.00600 (and) -315.98200 (scene) ] TJ T* [ <636c6173736902636174696f6e2e> -292.01700 (W) 79.98660 (e) -194.99200 (systematically) -195.99200 (optim) 1.01454 (ize) -196.00700 (and) -194.98200 (report) -196.00200 (results) ] TJ T* [ (separately) -201.01500 (for) -200.98900 (each) -200.99300 (top\055) ] TJ /R48 9.96260 Tf 92.31330 0 Td [ (k) -0.60039 ] TJ /R42 9.96260 Tf 7.50273 0 Td [ (accurac) 14.99750 (y) 65.01370 (\056) -293.98500 (One) -200.98100 (interesting) -200.98600 (message) ] TJ -99.81600 -11.95470 Td [ (that) -348.98600 (we) -349.98300 (w) 10 (ould) -349.01800 (lik) 10.01790 (e) -349.98600 (to) -348.98800 (highlight) -350.00500 (is) -348.98600 (that) -348.98600 (the) -350.01000 (softmax) -349.01000 (loss) -349.99600 (is) ] TJ 11.95630 TL T* [ (able) -356.01700 (to) -356.98700 (optimize) ] TJ /R46 9.96260 Tf 69.86910 0 Td [ (all) -356 (top\055) ] TJ /R48 9.96260 Tf 30.12110 0 Td [ (k) -0.59794 ] TJ /R46 9.96260 Tf 9.05078 0 Td [ (err) 44.98270 (or) -356.00900 (measur) 36.99380 (es) -357 (simultaneously) ] TJ /R42 9.96260 Tf 124.71800 0 Td (\056) Tj -233.75900 -11.95510 Td [ (This) -316.00400 (is) -316.01300 (in) -316.01300 (contrast) -316.00600 (to) -314.99400 (multiclass) -316.01600 (SVM) -315.99600 (and) -315.98200 (is) -316.01100 (also) -316.01100 <7265036563746564> ] TJ 11.95470 TL T* [ (in) -362.00600 (our) -362.01100 (e) 15.01220 (xperiments\056) -646.99000 (Finally) 65.00880 (\054) -390.00800 (we) -362.01800 (sho) 24.99090 (w) -362.01300 (that) -362.00300 (our) -362.01300 (ne) 25.01540 (w) -362.99300 (top\055) ] TJ /R48 9.96260 Tf 230.75000 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf -230.75000 -11.95510 Td [ (v) 24.98110 (ariants) -391.01800 (of) -390.99100 (smooth) -390.99100 (multiclass) -390.98400 (SVM) -391.00300 (and) -390.98900 (the) -390.98400 (softmax) -391.00300 (loss) ] TJ T* [ (can) -250 (further) -249.99500 (impro) 15.00480 (v) 14.98280 (e) -250.00200 (top\055) ] TJ /R48 9.96260 Tf 97.36410 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf 7.99102 0 Td [ (performance) -249.99700 (for) -249.99700 (a) -250.00200 <73706563690263> ] TJ /R48 9.96260 Tf 106.77900 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf 5.50000 0 Td (\056) Tj /R40 9.96260 Tf -205.67900 -14.22110 Td [ (Related) -219.98500 (w) 10 (ork\056) ] TJ /R42 9.96260 Tf 62.36020 0 Td [ (T) 79.99160 (op\055) ] TJ /R48 9.96260 Tf 18.56990 0 Td [ (k) -0.60039 ] TJ /R42 9.96260 Tf 7.69609 0 Td [ (optimization) -219.98300 (has) -221.01700 (recently) -219.99300 (recei) 25.00560 (v) 14.98280 (ed) ] TJ -100.58100 -11.95470 Td [ (re) 25.00810 (vi) 24.98850 (v) 14.98280 (ed) -386.99400 (attention) -386.01900 (with) -387.01100 (the) -386.98400 (adv) 14.98280 (ent) -386.98400 (of) -386.01400 (lar) 17.99700 (ge) -386.99400 (scale) -386.99400 (problems) ] TJ (\133) ' ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 312.17900 288.76800 Tm (18) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 322.14200 288.76800 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 328.24900 288.76800 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 338.21100 288.76800 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 344.31800 288.76800 Tm (24) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 354.28100 288.76800 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 360.38800 288.76800 Tm (25) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 370.35000 288.76800 Tm [ (\135\056) -648.99000 (The) -362.99300 (top\055) ] TJ /R48 9.96260 Tf 47.43750 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf 9.11680 0 Td [ (error) -363.00800 (in) -362.98800 (multiclass) -362.98800 <636c617373690263612d> ] TJ -118.04300 -11.95510 Td [ (tion\054) -286.98400 (which) -278.99800 (promotes) -280 (good) -278.99300 (ranking) -280.01200 (of) -279.01200 (class) ] TJ /R46 9.96260 Tf 177.01300 0 Td (labels) Tj /R42 9.96260 Tf 26.58480 0 Td [ (for) -279.01200 (each) ] TJ -203.59800 -11.95510 Td [ (e) 15.01220 (xample\054) -254.99400 (is) -253.98500 (closely) -254.01400 (related) -253.99200 (to) -253.98700 (the) -253.98700 (precision\100) ] TJ /R48 9.96260 Tf 178.88600 0 Td [ (k) -0.59794 ] TJ /R42 9.96260 Tf 8.03008 0 Td [ (metric) -253.98200 (in) -253.98700 (in\055) ] TJ -186.91600 -11.95590 Td [ (formation) -222.01000 (retrie) 25.01540 (v) 24.98110 (al\054) -227.01600 (which) -221.98700 (counts) -222.01700 (the) -221.01200 (fraction) -221.99200 (of) -222.00200 (positi) 25.01540 (v) 14.98280 (e) -222.00700 (in\055) ] TJ 11.95510 TL T* [ (stances) -257.98400 (among) -258.01300 (the) -257.98900 (top\055) ] TJ /R48 9.96260 Tf 91.82420 0 Td [ (k) -0.60039 ] TJ /R42 9.96260 Tf 8.06992 0 Td [ (rank) 9.99833 (ed) ] TJ /R46 9.96260 Tf 29.57890 0 Td [ (e) 19.99180 (xamples) ] TJ /R42 9.96260 Tf 36.87110 0 Td [ (\056) -333.97900 (In) -257.99600 (essence\054) -259.99600 (both) ] TJ -166.34400 -11.95510 Td [ (approaches) -249.99300 (enforce) -250.00700 (a) -250.00200 (desirable) ] TJ /R46 9.96260 Tf 125.03000 0 Td [ (r) 14.98280 (anking) ] TJ /R42 9.96260 Tf 33.33520 0 Td [ (of) -249.99700 (items) -250.00700 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 505.41400 228.99200 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 515.37600 228.99200 Tm (\135\056) Tj -194.55900 -14.21990 Td [ (The) -346.01600 (classic) -344.98700 (approaches) -346.01600 (optimize) -345.00600 (pairwise) -346.00600 (ranking) -346.00100 (with) ] TJ /R50 9.96260 Tf -11.95510 -11.95510 Td [ (S) -0.60039 (VM) -0.70086 ] TJ /R54 6.97380 Tf 22.13910 3.61523 Td [ (s) -0.60214 (t) -0.40259 (r) -0.39909 (u) -0.99774 (c) -0.89971 (t) -0.40259 ] TJ /R42 9.96260 Tf 24.20510 -3.61523 Td (\133) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 358.52300 202.81700 Tm (20) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 368.48600 202.81700 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 374.24400 202.81700 Tm (43) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 384.20700 202.81700 Tm (\135\054) Tj /R50 9.96260 Tf 9.26914 0 Td [ (R) -0.10047 (an) -0.60284 (k) -0.79889 (Ne) -0.39699 (t) -0.90181 ] TJ /R42 9.96260 Tf 42.15000 0 Td (\133) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 438.94300 202.81700 Tm (10) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 448.90600 202.81700 Tm [ (\135\054) -347 (and) ] TJ /R50 9.96260 Tf 26.92300 0 Td [ (LaR) -0.10292 (an) -0.59794 (k) -0.79889 ] TJ /R42 9.96260 Tf 37.58280 0 Td (\133) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 516.72900 202.81700 Tm (6) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R42 9.96260 Tf 1 0 0 1 521.71100 202.81700 Tm [ (\135\056) -543.98800 (An) ] TJ -212.84900 -11.95590 Td [ (alternati) 24.99340 (v) 14.98280 (e) -367.00200 (direction) -365.99300 (w) 10 (as) -366.99500 (proposed) -367.01200 (by) -366.98800 (Usunier) ] TJ /R46 9.96260 Tf 192.41000 0 Td [ (et) -366.99300 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