Monge blunts Bayes: Hardness Results for Adversarial Training
Zac Cranko Aditya Krishna Menon Cheng Soon Ong Richard Nock Zhan Shi Christian Walder
Monge blunts Bayes: Hardness Results for Adversarial Training Zac - - PowerPoint PPT Presentation
Monge blunts Bayes: Hardness Results for Adversarial Training Zac Cranko Aditya Krishna Menon Richard Nock Cheng Soon Ong Zhan Shi Christian Walder Overview Hardness results on adversarial training. Key result applicable to a learner:
Zac Cranko Aditya Krishna Menon Cheng Soon Ong Richard Nock Zhan Shi Christian Walder
data shot
2 blunts — Cranko et al.
reveal generalisation improves on clean data as well
( in inf)
`(H, A, D) ≥ (1 − ") · `
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1- Classifiers 2- Adversaries 3- (differentiable) Loss 4- general adversarial loss
domain sign = class
domain
` : {−1, 1} × [0, 1] → R
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L(⇡)
.
= infc EY∼π`(Y, c)
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<latexit sha1_base64="L9+ZPceyhzbahWj3wpGT6nBa0c0=">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</latexit><latexit sha1_base64="L9+ZPceyhzbahWj3wpGT6nBa0c0=">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</latexit><latexit sha1_base64="L9+ZPceyhzbahWj3wpGT6nBa0c0=">ADlHicbVLbatRQFD2deKnjrVXwxZfgtOBDGZK+6INCsQwoiFRwemFmKCcnOzOHOTfPxTqEfIOv+mn+jTuZQZvUDQmLtdbOvmRnRnDnk+T3Vi+6dfvO3e17/fsPHj56vLP75NTpYBmMmRbanmfUgeAKxp57AefGApWZgLNseVzrZ9/AOq7VF78yMJN0rnjBGfVIjfemhu9d7gySYdJEfBOkGzAgmzi53O2tprlmQYLyTFDnJmli/Kyk1nMmoOpPgwND2ZLOYJQUQluVjbdVvE+MnlcaIuP8nHDXs8oqXRuJTN0SuoXrqvV5P+0SfDF61nJlQkeFsXKoKIvY7r0eOcW2BerBQZjn2GrMFtZR5XFC/36oTzNwCLA8gMCpaA5VzS82Cs+9YIJbaAr5ysKq/f93kQlbwebDtZS4HfwbUBzIDy3+qotZ7L+aKZFHjfjxe3kZn8tqnZV7gKu1dwxbSUVOXl1NMVel0wVY1D1VaN1Qas0M6hDEJ0ZJZ5IPCqeqzKj9WHcMFyk1/RXnR1Ub/tFXy6GAr6g7j+1bEGunleWwqsq36O5MwfFYofr+iDRgseadk/zJjg9HKbJMP18ODh6tznbfKcvCAvSUpekSPynpyQMWGEkx/kJ/kVPYveRMfRaG3tbW1ynpJWRJ/+AINYMx0=</latexit><latexit sha1_base64="L9+ZPceyhzbahWj3wpGT6nBa0c0=">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</latexit>`
ψ = `
<latexit sha1_base64="0y6L3Odxy4eIhTLGlhpNI0rSkzQ=">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</latexit><latexit sha1_base64="0y6L3Odxy4eIhTLGlhpNI0rSkzQ=">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</latexit><latexit sha1_base64="0y6L3Odxy4eIhTLGlhpNI0rSkzQ=">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</latexit><latexit sha1_base64="0y6L3Odxy4eIhTLGlhpNI0rSkzQ=">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</latexit>composite loss link ψ : [0, 1] → R
<latexit sha1_base64="eUXmsClgur7BYC+oFqx8qgUHjlQ=">ACx3icbVHLbtQwFPWEVxteU1h2YzGtxGI0SiokEKuKbmBXENWmkQj27nJWGPHkR+lIyuL/gZfwxb+gL/BSWfRtFzJ1tF93NoI7ixSfJ3FD14+Ojxk53d+Omz5y9ejvdenRnlNIM5U0LpC0oMCF7D3HIr4KLRQCQVcE7XJ138/BK04ar+bjcN5JUNS85Iza4luN3Bz7ru3gNReuzxvC2xR/xIpmOc40r1aWaK1+4EwSu6LUf2sPluNJMkt6w/dBugUTtLXT5d7IZ4ViTkJtmSDGLNKksbkn2nImoI0zZ6AhbE0qWARYEwkm9/1iLT4MngKXSodXW9x7b1d4Io3ZSBoyux3N3Vjn/F9s4Wz5Ife8bpyFmt0MKp3AVuGOK1xwDcyKTQCEaR52xWxFNGE2MBrHgzmuqTAegqOETE4yFeaNCvOrsIALJWG8BWg6/jwdpJxtOSV0MyfGAnyAflVDphedBhGKaya0qVKHB/Hh4W9/zFQa70rj3wdnRLE1m6dejyfGnrXA7aB+9QW9Rit6jY/QZnaI5Yugn+oV+oz/Rl0hFl9HVTWo02ta8RgOLrv8BLMrgUA=</latexit><latexit sha1_base64="eUXmsClgur7BYC+oFqx8qgUHjlQ=">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</latexit><latexit sha1_base64="eUXmsClgur7BYC+oFqx8qgUHjlQ=">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</latexit><latexit sha1_base64="eUXmsClgur7BYC+oFqx8qgUHjlQ=">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</latexit>`ψ(y, v)
.
= `(y, −1(v))
<latexit sha1_base64="FQWi2BI0lPpPhRICTC9xur37Y=">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</latexit><latexit sha1_base64="FQWi2BI0lPpPhRICTC9xur37Y=">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</latexit><latexit sha1_base64="FQWi2BI0lPpPhRICTC9xur37Y=">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</latexit><latexit sha1_base64="FQWi2BI0lPpPhRICTC9xur37Y=">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</latexit>canonical loss
ψ
.
= −L0
<latexit sha1_base64="l6hu/y32eQZrbtosN/wuz7uocw=">AEgXicbVPbtQwEHXpAmW5tfDIi0VbcVFZfsCEkKqQJVA4qEIepGaZeU4k61b2zG+tF1Z+QG+hlf4E/6GSbqoTbaWEo3nLl7MiOF80nyd+HGYu/mrdtLd/p3791/8HB5dGeK4PlsMtLWdqDjDmQsOuF17CgbHAVCZhPzv5UOP7p2CdKPU3PzUwUmyiRSE486gaL6+txbTxEi3kVUyNE1VF0xwK+EFf0ZRn9tnaeHk1GSTNofPCcCasktnZGa8sbqd5yYMC7blkzh0OE+NHkVkvuISqnwYHhvETNoFDFDVT4EaxSaSi6jJaVFa/LSnjfaqRWTKuanKkKmYP3JdrFZehx0GX7wZRaFN8KD5RaAiSOpLWveG5sIC93KAuNWYK6UHzHLuMcO9vutOMFMLMDJBgTOZKugOLHMHAl+jgGoKi3gLwer+tXS5khZgE25GxO7guKDYUEF6YcuzNpyp2mlWypw25dG2cdM/zFPDGS+VYjqPqWdT1LpgqloOVRs1tjRgZekcwiBlB8bxoz5ozL9+YfFz1XfvBTkOI9JWJAxrROzKg6qKr6rOv7g3GCHqwtSlsXtLuGUWcE0h0vKXpdi7CW40wWdcTXs4dw7HvEm58wdvyTUl25FLjtGwlcxUWwcVfU9phl4tkGPxy/nouE8WlR1HUdf528urMDN/F82tu+TQgYu3rC7ZvPC3uZgmAyGXzZXt97PVnCJPCFPyXMyJK/JFvlIdsgu4eQn+UV+kz+9xd6LXtLbvKDeWJjZPCat03v7D6+Zkc8=</latexit><latexit sha1_base64="l6hu/y32eQZrbtosN/wuz7uocw=">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</latexit><latexit sha1_base64="l6hu/y32eQZrbtosN/wuz7uocw=">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</latexit><latexit sha1_base64="l6hu/y32eQZrbtosN/wuz7uocw=">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</latexit>blunt predictor
h
.
= ψ 1
2
= 0
<latexit sha1_base64="KdhJD46RQujLwUPIEn2mTEhbZlA=">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</latexit><latexit sha1_base64="KdhJD46RQujLwUPIEn2mTEhbZlA=">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</latexit><latexit sha1_base64="KdhJD46RQujLwUPIEn2mTEhbZlA=">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</latexit><latexit sha1_base64="KdhJD46RQujLwUPIEn2mTEhbZlA=">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</latexit>(often) corresponding loss:
`(H, A, D)
.
= min
h∈H E(X,Y)∼D
max
a∈A `(Y, h a(X))
( “hidden”)
ψ
<latexit sha1_base64="iWga5ZXxIOqjq9iJGKhQVoq+qk=">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</latexit><latexit sha1_base64="iWga5ZXxIOqjq9iJGKhQVoq+qk=">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</latexit><latexit sha1_base64="iWga5ZXxIOqjq9iJGKhQVoq+qk=">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</latexit><latexit sha1_base64="iWga5ZXxIOqjq9iJGKhQVoq+qk=">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</latexit>kδk δ∗
<latexit sha1_base64="N801/Fgd9SeWocT49UR5Je4XdcI=">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</latexit><latexit sha1_base64="N801/Fgd9SeWocT49UR5Je4XdcI=">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</latexit><latexit sha1_base64="N801/Fgd9SeWocT49UR5Je4XdcI=">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</latexit><latexit sha1_base64="N801/Fgd9SeWocT49UR5Je4XdcI=">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</latexit>particular case, Madry et al.’18: s.t.
x
a
→ x + δ
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4 blunts — Cranko et al.
`
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+
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.
= max
h∈H{ϕ(P, f, π, 2L(1)) − ϕ(N, f, 1 − π, −2L(0))}
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.
= (L0) ψ1 h a
<latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit>with and
ϕ(Q, f, u, v)
.
= Z
X
u · (f(x) + v)dQ(x)
<latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit>“+” ex. “-” ex.
Example: if and , then is Integral Probability Metric for class L(0) = L(1)
<latexit sha1_base64="pN93QRCEQ14U6yZNRgS9Hl3cXY=">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</latexit><latexit sha1_base64="pN93QRCEQ14U6yZNRgS9Hl3cXY=">AD3XicbZJLbxMxEMfdhkcJr5QeuViklVqpinZ7gUulClQJA5FIm2qJIq83tnEih+LHy2RtUduiCtHrnDl2/Bt8G4i2t1gyau/5ve3PTM7Sc6ZsVH0Z2OzdefuvftbD9oPHz1+8rSz/ezcKcp9KniSg8SYoAzCX3LIdBroGIhMNFMn9T8osr0IYp+dEuchgLMpUsY5TYEJp0dnZHNH70QE+xpWKD3YnW7Ui6qF10W8El20WmeT7c3fo1RJ0BayokxwzjK7dgTbRnlULRHzkBO6JxMYRikJALM2FfZF3gvRFKcKR2tLiK3j7hiTBmIZLgFMTOTJOVwf+xobPZq7FnMncWJF0+lDmOrcJlK3DKNFDLF0EQqlnIFdMZ0YTa0LB2u/aOy6caYH4IjhJeK8hPNclnjH4OD2ChNIRPClq2926bjEsyNnW63gwfuhP+DmSHwnHLtLqu40SUlyaKp7gqD9cPV/2rhUqXNpkpQvYSrqkSgsjUjyxZBK9xeVFqV9RprlUOmitjAgbOGziMRYg7Gaoqx8y/LxqGy4Cr/DJ/2WSDGzZostMbdtpkKWTwKXBjQ2ka+NKphe8VhT8umgVeQTGMx36UCN+N1ygLUw/FvyveieAIUx43Z3pdnB/14qgXfzjqnrxezfsWeo5eoH0Uo5foBL1FZ6iPKFqgH+gn+tWatL60vra+La2bG6szO6i2Wt/ArNqTxk=</latexit><latexit sha1_base64="pN93QRCEQ14U6yZNRgS9Hl3cXY=">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</latexit><latexit sha1_base64="pN93QRCEQ14U6yZNRgS9Hl3cXY=">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</latexit>π = 1/2
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∝
<latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">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</latexit><latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">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</latexit><latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">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</latexit><latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">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</latexit>Example: if and , then is Integral Probability Metric for class
∝
<latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">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</latexit><latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">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</latexit><latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">AD0XicbZJLb9NAEMe3MY8SXi0cuaxIK3GoIruXckGqQJVA4lAEaRMlUbVej5NV9mH20RKtLCGuHLnCl+Db8G1YOxGtHVayNZrf3YeO2nBmbFx/GerE926fefu9r3u/QcPHz3e2X1yZpTFAZUcaWHKTHAmYSBZbDsNBARMrhPF28qfj5JWjDlPxklwVMBZlJljNKbHCN9iaFVoVexc7vbgf1wdvGsna6KH1Ob3Y7fyeZIo6AdJSTowZJ3Fhp5oyiHsjtxBgpCF2QG42BKIsBMfV1xifeDJ8O50uGTFtfemxGeCGOWIg1KQezctFnl/B8bO5u/nHomC2dB0lWi3HFsFa7axnTQC1fBoNQzUKtmM6JtSGIXW7jTyumGmAxQE4SnijIT/TpJgz+iUkwEJpCL8MtOzu3xQZl+Zs5nRzGD5MJ7wI5AfCcu0umriVFSXpopnuG4PN4Pr+TVclUqb3JSheglXVAlBZOYnliyD1rirGxXNmn17qC5MiZg4LyFaqD38nQVbVa/n3ZEowCruvL/ajNhtds2GYn1+ykzTLI4XPgxobWNPCVUgvfL0v/qmw3eAnlOJn6Sp8L9mgLGw6lP+ueCeCImx50t7pTePsJ/E/eTDYe/49Xrft9Ez9By9QAk6QsfoLTpFA0SRQD/QT/Qr+hgto6/Rt5W0s7WOeYoaJ/r+F8FwTN4=</latexit><latexit sha1_base64="2xeUZTcFDv7AbuSyq4+9ebYO5ug=">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</latexit>assumptions),
5 blunts — Cranko et al.
`
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+
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.
= max
h∈H{ϕ(P, f, π, 2L(1)) − ϕ(N, f, 1 − π, −2L(0))}
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.
= (L0) ψ1 h a
<latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit>with and
ϕ(Q, f, u, v)
.
= Z
X
u · (f(x) + v)dQ(x)
<latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit>“+” ex.
L(0) = L(1)
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< l a t e x i t s h a 1 _ b a s e 6 4 = " G W N N d R z z K b O G 4 p j p x x + / K T a P 3 B c = " > A A A D 9 3 i c b Z P L b t N A F I a n N Z c S L m 1 h y W Z E Wε
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< l a t e x i t s h a 1 _ b a s e 6 4 = " n d 2 c R i 3 n k t Q d J E / 3 D M J Z U G a c l S Q = " > A A A D 1 X i c b Z J L b 9 N A E M e 3 M Y 8 S X i c u V i k l T h U U d w L X J A q U K U i c S g S a V I l V r V e j 5 N V 9 u H uA
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Example: if and , then is Integral Probability Metric for class
∝
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6 blunts — Cranko et al.
`
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+
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.
= max
h∈H{ϕ(P, f, π, 2L(1)) − ϕ(N, f, 1 − π, −2L(0))}
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.
= (L0) ψ1 h a
<latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">AD/nicbZPNbtNAEMe3NR8lfKVw5LIirShSG8UVElyQKlAlkDgUibSp4hCt1+NklV2v2Y+WaGWJ5+ABuCEkThy5whvwNqydiNYOI9kez+/uzPjcZxzpk2v92dtPbhy9dr1jRutm7du37nb3rx3rKVFPpUcqkGMdHAWQZ9wyHQa6AiJjDSTx7WfKTM1CayeydmecwEmSsZRYnxo3H6yleIogRQ+4J29iMbq0WMcUaYojnLN3ru9sFi+T6tHC2OyNW53et1eZXjVCZdOBy3taLy5/j1KJLUCMkM50XoY9nIzckQZRjkUrchqyAmdkQkMvZsRAXrkqvIKvO0jCU6l8ldmcBW9vMIRofVcxF4piJnqJiuD/2NDa9JnI8ey3BrI6OKg1HJsJC57hROmgBo+9w6hivlcMZ0SRajxHW21aufYfKIAZrtgKeG1gtxEkXzK6Ed/ABZSgb8loLW9mWRtnHKJlbVm+F8d/zng3RXWG6Ykud1HIty01jyBFfl4friqn+1UKlSOtWFz6DcyqFIFniIkPmXqtXpS+Leo0VzIHxaXWHgPnDezHxsdt5qsq59C9KRqCU4+r/FJ32mSDCzZosMLdthk1dB6ro0vTQFfKJVw3aJwz4tmgWdQDMORi2LhOuEKZf63gOLfFq+FV/gpD5szveoc73fDXjd8u985eLGc9w30AD1EOyhET9EBeoWOUB9R9Bn9RL/Q7+BT8CX4GnxbSNfXlmvuo5oFP/4CPxhb4g=</latexit><latexit sha1_base64="yEn3Y1VioexjzPuKb/E3szQW1OM=">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</latexit>with and
ϕ(Q, f, u, v)
.
= Z
X
u · (f(x) + v)dQ(x)
<latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit><latexit sha1_base64="ZqaZKvj2E2tnsDZGZTQtTFOX1SY=">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</latexit>“+” ex.
L(0) = L(1)
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min
h∈H E(X,Y)∼D
max
a∈A `(Y, h a(X))
Adversarial mean embedding of on (Adversarial) MMD between and
mmd[P, N|a]
.
= kµa,P µa,NkH
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H
<latexit sha1_base64="nd2cRi3nktQdJE/3DMJZUGaclSQ=">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</latexit><latexit sha1_base64="nd2cRi3nktQdJE/3DMJZUGaclSQ=">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</latexit><latexit sha1_base64="nd2cRi3nktQdJE/3DMJZUGaclSQ=">AD1XicbZJLb9NAEMe3MY8SXi0cuViklThUdwLXJAqUKUicSgSaVIlVrVej5NV9uHuoyVa7Q1x5cgVvgLfhm/D2olo7bDSWqP5/Wfn4clKRrUZDP5sdaI7d+/d37Qfjo8ZOnO7vPzrS0isCQSCbVOMaGBUwNQwGJcKM8YjLF+4qPrkBpKsVnsywh5XgmaEJNsGV7k05NnOCmTvxexc7vUF/UJ940jWRg+tz+nFbuf3NJfEchCGMKz1JBmUJnVYGUoY+O7UaigxWeAZTIpMAedurpqH+8HTx4XUoUrTFx7b0c4zLVe8iwoqyJ1m1XO/7GJNcWb1FRWgOCrBIVlsVGxtUI4pwqIYtg4GJoqHWmMyxwsSEQXW7jTy2nCmAxQHYMKRGQ26mcDmn5EtIEHOpIHxyUK7f1ukbVbQmVXNYbgwnfBXoDjglhmq5HUTZ7x6NJMsj+v24mZwPb+Gq1IpXWgfqhdwTSTnWORuavAyaLUtfWVb36SlkiUoJrUOGBhrYZKp4LcidFWtl/voW4LzgOv6CnfeZuMbNm6z4xt23GY5FHAZuDahNQVspVTc9b13b327wSvwkyR104y7XrJBadh28P+e+MCDImx50t7pTePsJ8M+smnw97Ru/W+b6MX6CV6hRL0Gh2hE3SKhoigS/QD/US/olHko6/Rt5W0s7WOeY4aJ/r+F2IDTnw=</latexit>κ
<latexit sha1_base64="TVSqQIu59y0ZKr2w6HlqK2MT8c=">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</latexit><latexit sha1_base64="TVSqQIu59y0ZKr2w6HlqK2MT8c=">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</latexit><latexit sha1_base64="TVSqQIu59y0ZKr2w6HlqK2MT8c=">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</latexit><latexit sha1_base64="TVSqQIu59y0ZKr2w6HlqK2MT8c=">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</latexit>µa,Q
.
= Z
X
κ(a(x), .)dQ(x)
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< l a t e x i t s h a 1 _ b a s e 6 4 = " V u j G Z 9 L d L l O 7 W r f p R Ks.t.mmd[P, N|a] ≤ 8"`
<latexit sha1_base64="VqfgwZN9UH/l4WZPo57tX24BSN8=">AEJXicbZPNahRBEMc7WT/i+pXo0UvjEhAJy04u5iIEJaAgEsEkG3bW0NTs2nSH5Pq7iRLO8/j3TfwAbyJ4MmjV30DezaLyUxsmKGo37+6q6qrs1IK6waDHwuLnWvXb9xcutW9fefuvfvLKw92rfHIYcbaXCYMQtSaNhxwkYlghMZRL2sqOXNd87AbTC6PduWsJYsYkWheDMRdfB8ijNYCJ0gGPNENn0adVNHZw5y4NSeTXaXnv7kY0pTSUc0w2anjCE0gpNE1LNCWgNZ+SLlA3k1B5d2OljuDfqD2aJXjWRu9Mh8bR+sLH5Oc8O9Au24ZNaOkHpxoGhE1xCTM1bKBk/YhMYRVMzBXYcZl2o6Gr05LQwGD/t6Mx7OSIwZe1UZVGpmDu0bVY7/8dG3hUb4yB06R1ofn5Q4SV1htYtpblA4E5Oo8E4ipgr5YcMGXex8d1u4xfThDgaA08Z7JRUJgKw8FP4sHUGUQ4i8H1N3VyLrs0JMPDabEWJ34i1Dsa8dALNaRNnqt40MzKns/JoM3jWv4arVqEtbBWz13DKjVIs3m3q2DRqrS+r2vZVk14MRMQgZQvzDKPf61hVPa7hTdUS7Ec8y68I+202vGDNtu6YFtlkMBx5FbF0tDkOdKVKFfVeF51S7wBKpRMg5pkIvuUJFfD1Q/dvitYqKOVJe6avGrvr/WTQT96t9zZfzOd9iTwij8kTkpBnZJO8Itkh3Dyhfwiv8mfzqfO1863zvdz6eLCPOYhazOz7/1KG+</latexit><latexit sha1_base64="VqfgwZN9UH/l4WZPo57tX24BSN8=">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</latexit><latexit sha1_base64="VqfgwZN9UH/l4WZPo57tX24BSN8=">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</latexit><latexit sha1_base64="VqfgwZN9UH/l4WZPo57tX24BSN8=">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</latexit>(more in paper / poster)
N
<latexit sha1_base64="CiPwV5ltRlafin1tx86CiSAYts=">ADy3icbZJLb9NAEMe3MY9iXi0cuViklThUkd1LuSBVoEogASqCtKmSqFqvx84q+zD7aAmLjxy5wvfg2/BtWDsRrR1Wms0v/sPDxpyag2cfxnoxfcuHnr9uad8O69+w8ebm0/OtHSKgJDIplUoxRrYFTA0FDYFQqwDxlcJrOX9X89AKUplJ8MosSphwXguaUYONdH3fe75xv9eNB3Jxo3UhWRh+tzvH5du/3JPEchCGMKz1OIlLM3VYGUoYVOHEaigxmeMCxt4UmIOeuqbWKtr1nizKpfJXmKjxXo9wmGu94KlXcmxmustq5/Y2Jr8+dRUVoDgiwT5ZFRkZ141FGFRDFt7ARFfa0RmWGFi/HjCsJXHloUCmO+BJZi1GnKFwuWMki8+QcSlAv/JQIlw97pI2zSnhVXtYTg/Hf8vIN/jlhmq5GUbp7x+NJUsi5r2onZwM7+Wq1YpnevKVy/gkjOscjcxOCF12pbVrVtqzYtlSxBMam1x8BYB5NUeb8Vvqt6qdzbqiM487ipL3dnXTa6YqMuO7piR12WQ6fPdfGt6aALZWKu0FVuRdVt8ELqMbJ1E1S7vrJGqV+x6H698Qb7hV+y5PuTq8bJ/uDJB4kH/b7hy9X+76JnqCn6BlK0AE6RK/RMRoigr0A/1Ev4J3gQ6+Bt+W0t7GKuYxap3g+1+lgUnw</latexit><latexit sha1_base64="CiPwV5ltRlafin1tx86CiSAYts=">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</latexit><latexit sha1_base64="CiPwV5ltRlafin1tx86CiSAYts=">ADy3icbZJLb9NAEMe3MY9iXi0cuViklThUkd1LuSBVoEogASqCtKmSqFqvx84q+zD7aAmLjxy5wvfg2/BtWDsRrR1Wms0v/sPDxpyag2cfxnoxfcuHnr9uad8O69+w8ebm0/OtHSKgJDIplUoxRrYFTA0FDYFQqwDxlcJrOX9X89AKUplJ8MosSphwXguaUYONdH3fe75xv9eNB3Jxo3UhWRh+tzvH5du/3JPEchCGMKz1OIlLM3VYGUoYVOHEaigxmeMCxt4UmIOeuqbWKtr1nizKpfJXmKjxXo9wmGu94KlXcmxmustq5/Y2Jr8+dRUVoDgiwT5ZFRkZ141FGFRDFt7ARFfa0RmWGFi/HjCsJXHloUCmO+BJZi1GnKFwuWMki8+QcSlAv/JQIlw97pI2zSnhVXtYTg/Hf8vIN/jlhmq5GUbp7x+NJUsi5r2onZwM7+Wq1YpnevKVy/gkjOscjcxOCF12pbVrVtqzYtlSxBMam1x8BYB5NUeb8Vvqt6qdzbqiM487ipL3dnXTa6YqMuO7piR12WQ6fPdfGt6aALZWKu0FVuRdVt8ELqMbJ1E1S7vrJGqV+x6H698Qb7hV+y5PuTq8bJ/uDJB4kH/b7hy9X+76JnqCn6BlK0AE6RK/RMRoigr0A/1Ev4J3gQ6+Bt+W0t7GKuYxap3g+1+lgUnw</latexit><latexit sha1_base64="CiPwV5ltRlafin1tx86CiSAYts=">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</latexit>(if and )
8 blunts — Cranko et al.
C(a, P, N)
.
= inf
µ2Π(P,N)
Z c(a(x), a(x0))dµ(x, x0)
<latexit sha1_base64="9l3BXncsrektu9uVgWBNRveYIiY=">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</latexit><latexit sha1_base64="9l3BXncsrektu9uVgWBNRveYIiY=">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</latexit><latexit sha1_base64="9l3BXncsrektu9uVgWBNRveYIiY=">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</latexit><latexit sha1_base64="9l3BXncsrektu9uVgWBNRveYIiY=">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</latexit>(Adversarial) OT plan between and
P
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c : X × X → R
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δ
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H
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Simple way to defeat strategies learning/tuning the loss — important case because common losses fit in (log, square, Matsushita, etc.)
RKHS example — suppose there exists a weakly contractive adversary in a feature map of the RKHS: Then ,composing just adversaries yields -Monge efficiency
9 blunts — Cranko et al.
(complete statements in paper / poster)
H
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1 /δ)
<latexit sha1_base64="bouXruMB/P4KnGwIVAgXJb8NOfo=">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</latexit><latexit sha1_base64="bouXruMB/P4KnGwIVAgXJb8NOfo=">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</latexit><latexit sha1_base64="bouXruMB/P4KnGwIVAgXJb8NOfo=">AD8XicbZPLbtNAFIanCZcSbiks2YxIK4JUpXE3sEGqQJVAYhEk0qSKQzQeHzujzHjMXFqikR+B2CH2LKDLTwIb8M4iWjtMpKto/P9Z87Fx1HOmTb9/p+tRvPa9Rs3t2+1bt+5e+9+e+fBiZWURhSyaUaR0QDZxkMDTMcxrkCIiIOo2jxquSjM1Cayey9WeYwFSTNWMIoMd41az/Z7QYHIRjyFIc0lgaHXKa4O5oFH8LBnB2EMXAPd2ftTr/Xx181Qg2RgdtzmC20/gRxpJaAZmhnGg9Cfq5mTqiDKMcilZoNeSELkgKE29mRICeulVHBd7znhgnUvknM3jlvRzhiNB6KSKvFMTMdZ2Vzv+xiTXJ86ljW4NZHSdKLEcG4nL8eCYKaCGL71BqGK+VkznRBFq/BbrUoem6cKYLEPlhJeaciliuRzRj/5BFhIBf4Vg8pae5dF2kYJS62qDsP56fgvBsm+sNwJc+rOBLlpZHkMV61h6vBq/lVXKVK6UQXvoMzqkUgmSxCw1Zeq2eVHatqjSXMkcFJdaewyc1zCNlPfbzHdVrp57W9QEpx6v6kvcaZ2NL9i4zo4v2HGdxZDAR8+18a0p4GulEq5XFO5FUW/wDIpJMHVhJFwnuEKZ/xOg+HfFG+EVfsuD+k5fNU4Oe0G/F7w7By93Oz7NnqEHqMuCtAzdIReowEaIo+o5/oF/rd1M0vza/Nb2tpY2sT8xBVTvP7XzyjVy4=</latexit><latexit sha1_base64="bouXruMB/P4KnGwIVAgXJb8NOfo=">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</latexit>10 blunts — Cranko et al.
vs
H
<latexit sha1_base64="nd2cRi3nktQdJE/3DMJZUGaclSQ=">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</latexit><latexit sha1_base64="nd2cRi3nktQdJE/3DMJZUGaclSQ=">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</latexit><latexit sha1_base64="nd2cRi3nktQdJE/3DMJZUGaclSQ=">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</latexit>general transformation:
min Wasserstein-OT s.t.
a(x)
.
= (1 − λ) · x + λ · x0
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sha1_base64="d60dcGcSxsFJycSC9e2exAGrVk=">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</latexit>11 blunts — Cranko et al.
neighbour in other class cluster / class centroid sample centroid, etc.
(more in paper / poster)
d(a(x), x) ≤ α, ∀x
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blunts — Cranko et al.
12
W 2
2
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1D normal classes classes 1 & 3
λ
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<latexit sha1_base64="bGJ6Qq0RU8L06ye6Zv8uwf9O9l8=">AD3nicbZJLb9NAEMe3NY8SXilw42KRVuJQRXYvcEGqQJVA4lAk0qSKo7Bej5NVdr1mHy1htVduiCtHrnDk2/BtWDsRrR1Wms0v/sPDxpyajSUfRnazu4dv3GzZ1bndt37t673919cKqEkQGRDAhRylWwGgBA01g1EpAfOUwTBdvKr48BykoqJ4r5clTDieFTSnBGvmnYf7SW5xMQmJVz7OxwGru9abcX9aP6hJtGvDZ6aH1Oprvbv5NMEMOh0IRhpcZxVOqJxVJTwsB1EqOgxGSBZzD2ZoE5qImty3fhvdkYS6kv4UOa+/VCIu5UkueiXHeq7arHL+j42Nzp9PLC1Ko6Egq0S5YaEWYTWLMKMSiGZLb2Aiqa81JHPsx6H9xDqdRh5TziTA4gAMwazRkJ1JXM4p+eQThFxI8J8MZNHZvypSJs3pzMjmMKyfjv89kB9wzSV4qKJU149mgqWhXV7YTO4nl/DVamkypXz1RdwQTnuMhsovHSa5UpXWUb16SlFCVIJpTyGBhrYZJK7zeF76raM/vWtQRnHtf15faszUaXbNRmx5fsuM0yOGj50r71iSwlVJy23fOvnDtBs/BjeOJTVJue/EGpX7twf174g3Cr/lcXunN43Tw34c9eN3h72jl+t930GP0RP0FMXoGTpCr9EJGiCPqMf6Cf6FXwIvgRfg28r6fbWOuYhapzg+1+VoFGu</latexit><latexit sha1_base64="bGJ6Qq0RU8L06ye6Zv8uwf9O9l8=">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</latexit><latexit sha1_base64="bGJ6Qq0RU8L06ye6Zv8uwf9O9l8=">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</latexit><latexit sha1_base64="bGJ6Qq0RU8L06ye6Zv8uwf9O9l8=">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</latexit>d = k.k1
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13
W 2
2
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1D normal classes classes 1 & 3
λ
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train test
c = clean a = adversarial
worst trains on c ! best trains on (weak) a (even tested on c) !
d = k.k1
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(between class marginals)
generalisation on clean data
14
(H, `)
<latexit sha1_base64="Uc2RyaizLp4OTk7hYFl1F3j+yZk=">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</latexit><latexit sha1_base64="Uc2RyaizLp4OTk7hYFl1F3j+yZk=">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</latexit><latexit sha1_base64="Uc2RyaizLp4OTk7hYFl1F3j+yZk=">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</latexit><latexit sha1_base64="Uc2RyaizLp4OTk7hYFl1F3j+yZk=">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</latexit>data shot
blunts — Cranko et al.
(get your data shot at poster # 191)