seminar Elvis Dohmatob - December 10th, 2pm, Inria, F107

[Julien Mairal]

Dear all,

Elvis Dohmatob from Criteo Research is going to give a seminar at Inria on December 10th, at 2pm, room F107.

Feel free to pass the information to anyone interested.

Best,

Julien

Title: Limitations of adversarial robustness: strong No Free Lunch Theorem

 Manuscript: https://arxiv.org/abs/1810.04065

 Abstract:

 This manuscript presents some new results on adversarial robustness in machine

  learning, a very important yet largely open problem. We show that if conditioned on

  a class label the data distribution satisfies the Talagrand $W_2$ transportation-cost

  inequality (for example, this condition is satisfied if the conditional distribution has

  density which is log-concave; or the feature space is a compact homogeneous

  Riemannian manifold like a sphere, torus, or in fact any compact Lie group; etc.),

  any (non-perfect) classifier can be adversarially fooled with high probability once the

  perturbations are slightly greater than the natural noise level in the problem. We call

  this result The Strong "No Free Lunch'' Theorem as some recent impossibility results

  on the subject (Tsipras et al. 2018, Fawzi et al. 2018, Gilmer et al. 2018, etc.) can be

  immediately recovered as very particular cases. Our theoretical bounds are

  demonstrated on both simulated and real data (MNIST). We also briefly sketch how

  these bounds readily extend to distributional robustness. Finally, we conclude the

  manuscript with some speculation on possible future research directions.