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Source TargetCleanAdv. train
VanillaOne-hotThermometerVanillaOne-hotThermometer
EreaaVanilla Quantized One-hot2.0436.0224.583.4880.4457.69
39.2232.3925.6375.0275.9252.32
14.576.918.1139.0239.6018.02
11p1l ApvThermometer Vanilla (Madry)41.1214.3010.9861.8459.1632.93
=196.0=1
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ModelCleanFGSMPGD/LS-PGA
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Source TargetCleanAdv. train
VanillaOne-hotThermometerVanillaOne-hotThermometer
evaaVanilla (Madry)0.01179.711
Vanilla3.3860.1052.6045.4837.2149.91
Quantized70.5462.4655.3851.7445.3755.64
One-hot83.0056.2563.9454.5949.2157.28
11pl apaThermometer Vanilla (Madry)80.3366.2253.4557.0451.0360.90
85.601167.011
Vanilla85.6074.9973.7867.050.0971.03
Quantized84.5682.4382.2272.5272.2979.43
One-hot Thermometer86.01 88.2577.19 81.5977.70 80.8061.92 67.9660.02 67.4372.89 77.68
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Input: Image x, parameter ε
Output: ε-discretized mask around x
2mask ← (0)nxk
3low ← max{0,x - ε}
4high ← min{1,𝑥 +ε}
5for α←O to1by do
6mask ← mask+ fonehot (α * low + (1- α) * high) end
7return mask
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White-boxBlack-box
LevelsCleanPGD/LS-PGAVanilla, CleanVanilla, PGD
One-hot (4) One-hot (8) One-hot (16)99.09 99.10 99.1492.95 92.65 93.0898.23 98.49 98.3995.64 96.37
One-hot (32) One-hot (64)99.06 98.8993.51 93.6398.38 98.3596.26 95.78
Thermometer (4)95.74
99.1192.6298.2395.67
Thermometer (8)99.0893.4598.4495.93
Thermometer(16)99.0793.8898.2495.28
Thermometer (32)99.0294.1498.2495.49
Thermometer (64)99.0094.6298.33
95.71
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Source TargetCleanAdv. train
VanillaOne-hotThermometerVanillaOne-hotThermometer
Vanilla97.8897.8796.9993.0790.9796.46
One-hot98.2898.8398.0895.7395.9697.25
Thermometer98.4598.7098.0896.3595.7296.97
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ModelCleanFGSMPGD/LS-PGA
Vanilla99.0395.7091.36
One-hot99.0196.1493.77
Thermometer99.1396.1093.70
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ModelCleanFGSMPGD/LS-PGA
Vanilla87.1654.5034.71
One-hot92.1958.8758.96
Thermometer92.3266.6065.67
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TargetSourceCleanWhite-box PGD/LS-PGABlack-box
Vanilla, Clean-trainedVanilla, PGD-trained
evaaaVanilla One-hot74.3200.49.40
Thermometer73.2516.5555.7219.33
74.4416.5050.3318.49
Vanilla64.466.027.4611.77
AOne-hot66.5425.1163.0942.46
Thermometer68.4428.1463.2141.97
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White-boxBlack-box
LevelsCleanPGD/LS-PGAVanilla, CleanVanilla, PGD
Vanilla (Madry)87.350.0085.6067.00
One-hot (4)One-hot (8)One-hot (16)One-hot (32)One-hot (64)83.6785.6288.5488.5689.6359.5961.9867.8367.8265.6383.0384.9286.0185.6986.9472.0372.1061.9266.6465.77
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Source TargetCleanAdv. train
VanillaOne-hotThermometerVanillaOne-hotThermometer
Vanilla83.6282.0674.3152.8358.7365.24
One-hot88.1675.1175.4961.8959.1769.73
Thermometer87.5075.9174.8461.3958.5168.22
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TargetSourceWhite-boxBlack-box
CleanPGD/LS-PGAVanilla, Clean-trainedVanilla, PGD-trained
ereaVanilla97.906.9973.9442.04
One-hot97.5956.0275.7741.59
Thermometer97.8756.3778.0441.69
Vanilla94.7959.6381.2446.77
AOne-hot95.1287.3483.8443.40
Thermometer97.7494.7784.9748.67
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