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5042.21 4169.21 262.059 73.9609 re W n q 262.501 0 0 74.3582 5041.98 4169.14 cm /R63 Do Q Q q 5039.32 4163.59 268.234 85.4063 re W n /R61 cs 0 scn 5042.21 4163.39 262.055 5.82031 re f* Q q 4368.16 4246.89 640.402 75.0742 re W n q 640.883 0 0 75.257 4367.91 4246.73 cm /R66 Do Q Q q 4365.24 4241.96 647.133 85.918 re W n /R61 cs 0 scn 4368.16 4240.96 640.402 5.91797 re f* Q q 3803.46 4201.13 275.23 77.6758 re W n q 275.683 0 0 77.9533 3803.18 4200.9 cm /R63 Do Q Q q 3800.42 4195.23 281.719 89.6992 re W n /R61 cs 0 scn 3803.46 4195.02 275.227 6.11328 re f* Q q 3151.9 3934.29 2210.98 1563.97 re W n /R61 cs 1 scn q 10 0 0 10 0 0 cm BT /R67 7.1901 Tf 1 0 0 1 362.429 463.784 Tm [ (\050) 0.0781 (a) -0.34974 (\051) -15362.1 (\050) 0.0747 (b\051) ] TJ 0.59922 -66.7336 Td [ (\050) 0.0781 (c) -0.34974 (\051) -15362.1 (\050) 0.0747 (d\051) ] TJ ET Q /R69 gs 8.9877 w 1 J 1 j 0.88281 0.76953 0 0 K 3933.83 5217.82 m 3793.44 5303.26 l S 0.88281 0.76953 0 0 k 3772.05 5316.26 m 3808.9 5313.21 l 3799.04 5307 3792.66 5296.55 3791.7 5284.96 c 3772.05 5316.26 l f* 0 0.99414 1 0 K 3866.42 4906.42 m 3702.16 4941.59 l S 0 0.99414 1 0 k 3677.68 4946.87 m 3713.48 4956.09 l 3706.2 4947.02 3703.66 4935.04 3706.56 4923.74 c 3677.68 4946.87 l f* 0.88281 0.76953 0 0 K 4580.95 4964.54 m 4720.02 5029.32 l S 0.88281 0.76953 0 0 k 4742.72 5039.89 m 4719.71 5010.92 l 4720.04 5022.57 4714.86 5033.69 4705.75 5040.91 c 4742.72 5039.89 l f* 0 0.99414 1 0 K 5120.21 5248.86 m 5003.55 5359.67 l S 0 0.99414 1 0 k 4985.39 5376.93 m 5020.77 5366.14 l 5009.81 5362.19 5001.39 5353.29 4997.97 5342.15 c 4985.39 5376.93 l f* 0.88281 0.76953 0 0 K 3441.75 4272.16 m 3550.18 4357.79 l S 0.88281 0.76953 0 0 k 3569.83 4373.27 m 3554.13 4339.81 l 3551.76 4351.2 3544.15 4360.84 3533.61 4365.79 c 3569.83 4373.27 l f* 0 0.99414 1 0 K 3913.61 4284.93 m 3808.57 4407.49 l S 0 0.99414 1 0 k 3792.27 4426.48 m 3826.37 4412.13 l 3815.07 4409.31 3805.75 4401.34 3801.23 4390.62 c 3792.27 4426.48 l f* 0.88281 0.76953 0 0 K 4607.91 4336.21 m 4709.68 4417.58 l S 0.88281 0.76953 0 0 k 4729.24 4433.22 m 4713.72 4399.64 l 4711.3 4411.02 4703.66 4420.61 4693.08 4425.49 c 4729.24 4433.22 l f* 0 0.99414 1 0 K 5180.88 4232.46 m 5175.09 4381.24 l S 0 0.99414 1 0 k 5174.13 4406.26 m 5191.93 4373.84 l 5181.32 4378.64 5169.1 4378.19 5158.88 4372.55 c 5174.13 4406.26 l f* Q q 10 0 0 10 0 0 cm BT /R46 8.9664 Tf 1 0 0 1 308.862 382.471 Tm [ (Figure) -402.986 (1\056) -403.002 (Illustration) -403.979 (of) -402.994 (the) -402.991 (objecti) 24.9957 (v) 14.9865 (e) -402.996 (discrepanc) 14.9974 (y) -403.982 (mi) 1.01834 (nimization) ] TJ 10.959 TL T* [ (through) -373.013 (series) -372.996 (e) 15.011 (xpansion\056) -677.995 (\050a\051) -373.013 (The) -372.985 (sign) -372.996 (function) ] TJ /R70 8.9664 Tf 181.65 0 Td [ (b) -0.39753 ] TJ /R72 8.9664 Tf 8.60586 0 Td [ (\075) -0.39753 ] TJ /R46 8.9664 Tf 11.825 0 Td (sgn) Tj /R72 8.9664 Tf 12.4539 0 Td [ (\050) -0.70249 ] TJ /R70 8.9664 Tf 3.58398 0 Td [ (x) -0.59903 ] TJ /R72 8.9664 Tf 5.22305 0 Td [ (\051) -0.70249 ] TJ /R46 8.9664 Tf 6.92812 0 Td (is) Tj -230.27 -10.959 Td [ (usually) -329.003 (relax) 14.9865 (ed) -328.982 (as) ] TJ /R70 8.9664 Tf 68.4816 0 Td [ (h) -0.20149 ] TJ /R72 8.9664 Tf 9.22109 0 Td [ (\075) -0.40026 ] TJ /R46 8.9664 Tf 11.0801 0 Td (tanh) Tj /R72 8.9664 Tf 15.4398 0 Td [ (\050) -0.70249 ] TJ /R70 8.9664 Tf 3.58438 0 Td [ (x) -0.59903 ] TJ /R72 8.9664 Tf 5.22266 0 Td [ (\051) -0.70249 ] TJ /R46 8.9664 Tf 6.53633 0 Td [ (for) -328.99 (gradient) -328.995 (based) -329.997 (optimization\056) ] TJ -119.566 -10.959 Td [ (\050b\051) -274.01 (The) -274.007 (objecti) 24.9957 (v) 14.9865 (e\054) -279.992 (e\056g\056) ] TJ /R70 8.9664 Tf 82.9398 0 Td [ (f) -0.80051 ] TJ /R72 8.9664 Tf 5.44805 0 Td [ (\050) -0.69977 ] TJ /R70 8.9664 Tf 3.58398 0 Td [ (b) -0.40026 ] TJ /R72 8.9664 Tf 3.94883 0 Td [ (\051) -331.68 (\075) -0.39753 ] TJ /R70 8.9664 Tf 16.6863 0 Td [ (b) -0.39753 ] TJ /R74 5.9776 Tf 3.94883 3.80898 Td [ (2) -0.10619 ] TJ /R46 8.9664 Tf 4.15117 -3.80898 Td [ (\054) -280.017 (is) -274.016 (then) -273.994 (relax) 14.9865 (ed) -273.003 (as) ] TJ /R70 8.9664 Tf 69.716 0 Td [ (g) -0.09802 ] TJ /R74 5.9776 Tf 4.39375 -0.99609 Td [ (1) -0.10619 ] TJ /R72 8.9664 Tf 4.15117 0.99609 Td [ (\050) -0.70249 ] TJ /R70 8.9664 Tf 3.58398 0 Td [ (h) -0.20149 ] TJ /R72 8.9664 Tf 5.30977 0 Td [ (\051) -331.68 (\075) -0.39753 ] TJ /R70 8.9664 Tf 16.6852 0 Td [ (h) -0.20149 ] TJ /R74 5.9776 Tf 5.31016 3.80898 Td [ (2) -0.10619 ] TJ /R46 8.9664 Tf 4.15078 -3.80898 Td (\054) Tj -234.008 -10.959 Td [ (where) -352.986 (lar) 18.0116 (ge) -353.988 (discrepanc) 14.9974 (y) -353.011 (is) -353.999 (observ) 15.0028 (ed\056) -620.023 (\050c\051) -354.018 (The) -352.989 (discrepanc) 14.9974 (y) -354.013 (is) -353 (re\055) ] TJ T* [ (duced) -238.994 (by) -239 (consi) 0.99656 (dering) -238.981 (the) -239.011 (quantization) -239.022 (loss) ] TJ /R76 8.9664 Tf 154.297 0 Td [ (j) -0.501 ] TJ /R70 8.9664 Tf 2.56016 0 Td [ <0e> -0.89854 ] TJ /R76 8.9664 Tf 4.42578 0 Td [ (j) -0.501 ] TJ /R72 8.9664 Tf 5.11914 0 Td [ (\075) -0.39753 ] TJ /R76 8.9664 Tf 9.72773 0 Td [ (j) -0.501 ] TJ /R70 8.9664 Tf 2.55938 0 Td [ (b) -0.39753 ] TJ /R76 8.9664 Tf 5.61367 0 Td [ <00> -0.39753 ] TJ /R70 8.9664 Tf 8.83203 0 Td [ (h) -0.20149 ] TJ /R76 8.9664 Tf 5.31016 0 Td [ (j) -0.501 ] TJ /R46 8.9664 Tf 4.70117 0 Td (in) Tj /R70 8.9664 Tf 9.11602 0 Td [ (g) -0.09802 ] TJ /R74 5.9776 Tf 4.39492 -0.99609 Td [ (2) -0.10619 ] TJ /R46 8.9664 Tf 4.15078 0.99609 Td [ (\056) -305.982 (\050d\051) ] TJ -220.808 -10.959 Td [ (W) 80.0106 (e) -249.997 (minimize) -250.017 (the) -249.989 (discrepanc) 14.9974 (y) -249.978 (through) -249.984 (series) -250.011 (e) 15.0137 (xpansion) -249.984 (in) ] TJ /R70 8.9664 Tf 208.69 0 Td [ (g) -0.09802 ] TJ /R74 5.9776 Tf 4.39531 -0.99609 Td [ (3) -0.10619 ] TJ /R46 8.9664 Tf 4.15078 0.99609 Td (\056) Tj /R46 9.9626 Tf -217.236 -32.4789 Td [ (preserving) -326.987 (objecti) 24.9983 (v) 14.9828 (e) -325.99 (is) -326.992 (a) -327.009 (mix) 15.0024 (ed) -325.985 (inte) 14.9926 (ger) -327.009 (optimization) -326.985 (prob\055) ] TJ 11.9551 TL T* [ (lem) -387.999 (due) -388.989 (to) -388.001 (the) -388.987 (discrete) -388.004 (constraint) -387.984 (of) -388.994 (binary) -387.999 (codes) -388.004 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 522.968 272.283 Tm (2) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 527.949 272.283 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 532.662 272.283 Tm (20) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 542.624 272.283 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 308.862 260.328 Tm (21) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 318.825 260.328 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 322.87 260.328 Tm (27) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 332.832 260.328 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 336.867 260.328 Tm (51) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 346.829 260.328 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 350.874 260.328 Tm (52) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 360.837 260.328 Tm [ (\135\054) -297.009 (which) -288.996 (is) -288.018 (incompatible) -287.981 (to) -288.021 (the) -287.981 (gradient) -288.991 (based) ] TJ -51.9746 -11.9559 Td [ (training) -305.018 (of) -305.986 (neural) -305.003 (netw) 10.0081 (orks\056) -477.004 (The) -305.003 (k) 10.0032 (e) 15.0122 (y) -305.983 (challenge) -304.998 (of) -305.988 (hashing) ] TJ 11.9551 TL T* [ (learning) -385.017 (lies) -383.997 (on) -384.985 (the) -384.987 (discrete) -384.005 (constraint) -385.004 (optimization\056) -714.013 (Re\055) ] TJ T* [ (laxation) -415.982 (on) -416 (the) -416.002 (binary) -415.994 (code) -416.009 (transforms) -417 (the) -416 (discrete) -416 (opti\055) ] TJ T* [ (mization) -347.006 (problem) -347.993 (into) -347.016 (a) -347.986 (continuous) -346.996 (one) -346.996 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 479.053 212.507 Tm (32) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 489.016 212.507 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 493.449 212.507 Tm (42) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 503.411 212.507 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 507.845 212.507 Tm (46) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 517.807 212.507 Tm [ (\135\056) -602.997 (The) ] TJ -208.945 -11.9551 Td [ (discrepanc) 14.9852 (y) -275.008 (introduced) -274.986 (by) -275.003 (relaxation) -274.993 (leads) -275.003 (to) -275.003 (the) -275.003 (de) 25.0154 (viation) ] TJ 11.9547 TL T* [ (from) -191.017 (the) -190 (optimal) -190.988 (binary) -191.012 (codes) -191.017 (and) -190.003 (the) -191.017 (optimal) -190.988 (hashing) -190.998 (func\055) ] TJ 11.9563 TL T* [ (tions\056) -716.005 (The) -384.99 (coupling) -385 (of) -384.992 (the) -386.004 (solution) -384.985 (to) -384.985 (binary) -385.019 (codes) -386.004 (with) ] TJ 11.9551 TL T* [ (the) -295.982 (optimization) -294.99 (o) 14.9828 (v) 14.9828 (er) -295.997 (hashing) -296 (functions) -295.014 (aggra) 19.9967 (v) 24.9811 (ates) -295.985 (the) -295.98 (op\055) ] TJ T* [ (timization) -267.004 (of) -267.992 (the) -267.007 (discrete) -267.004 (constraint) -266.985 (problem\056) -361.989 (Although) -267.99 (the) ] TJ T* [ (quantization) -196.004 (error) -196.016 (is) -195.014 (tak) 10.0057 (en) -196.007 (into) -195.982 (consideration) -196.011 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 489.803 140.776 Tm (10) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 499.766 140.776 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 502.645 140.776 Tm (11) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 512.607 140.776 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 515.496 140.776 Tm (25) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 525.459 140.776 Tm [ (\135) -196.011 (and) ] TJ -216.597 -11.9551 Td [ (direct) -332.016 (solutions) -330.989 (on) -332.013 (binary) -330.989 (codes) -332.013 (are) -331.013 (proposed) -331.999 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 500.762 128.821 Tm (28) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 510.725 128.821 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 515.048 128.821 Tm (30) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 525.011 128.821 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 529.345 128.821 Tm (36) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R46 9.9626 Tf 1 0 0 1 539.307 128.821 Tm (\135\054) Tj -230.445 -11.9551 Td [ (the) -295.982 (hashing) -296 (functions) -295.997 (are) -294.98 (still) -295.995 (learned) -295.99 (with) -296.005 (a) -295.995 (separated) -295.985 (op\055) ] TJ 11.9559 TL T* [ (timization) -487.007 (o) 14.9828 (v) 14.9828 (er) -486.985 (continuous) -487.992 (outputs) -487.017 (and) -487.012 (a) -486.982 (post\055step) -488.002 (sign) ] TJ 11.9551 TL T* [ (thresholding\056) -620.982 (This) -353.997 (may) -354.007 (deteriorate) -352.99 (the) -354.01 (quality) -353.985 (of) -354.019 (hashing) ] TJ T* [ (functions) -250.005 (and) -249.993 (f) 9.99588 (ail) -249.988 (to) -249.985 (generate) -250.002 (optimal) -249.997 (binary) -249.983 (codes\056) ] TJ -13.741 -29.8879 Td (1) Tj ET Q Q Q q q 1 1 1 rg /a0 gs 48.406 786.422 515.188 -52.699 re f q /s5 gs /x6 Do Q q /s7 gs /x8 Do Q q /s9 gs /x10 Do Q q /s11 gs /x12 Do Q Q Q Q q 1 0 0 1 0 0 cm BT /F1 12 Tf 14.4 TL ET 1 1 1 rg n 270 47 72 14 re f* 0.5 0.5 0.5 rg BT /F2 9 Tf 10.8 TL ET BT 1 0 0 1 297 50 Tm (6838) Tj T* ET Q endstream endobj 15 0 obj << /Filter /FlateDecode /Resources << /ExtGState << /a0 << /CA 1 /ca 1 >> >> /XObject << /x18 16 0 R >> >> /Length 28 /Group << /Type /Group /S 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Jc "82w8VSnGW;" endstream endobj 17 0 obj << /ExtGState << /a0 << /CA 1 /ca 1 >> >> >> endobj 18 0 obj << /Filter /FlateDecode /BitsPerComponent 8 /Height 428 /Length 6081 /ColorSpace /DeviceCMYK /DecodeParms << /Columns 571 /Colors 4 /Predictor 15 >> /Width 571 /Subtype /Image >> stream x{u}'HҴX#Z/2뭂r)#WÀ 2( *pDZP*f%0 US@/van|z2pgyͤ `> @/ hb ( &v