IAM

DAVIDSTUTZ

11thAUGUST2018

READING

Moustapha Cissé, Piotr Bojanowski, Edouard Grave, Yann Dauphin, Nicolas Usunier. Parseval Networks: Improving Robustness to Adversarial Examples. ICML 2017: 854-863.

Cisse et al. propose parseval networks, deep neural networks regularized to learn orthonormal weight matrices. Similar to the work by Hein et al. [1], the mean idea is to constrain the Lipschitz constant of the network – which essentially means constraining the Lipschitz constants of each layer independently. For weight matrices, this can be achieved by constraining the matrix-norm. However, this (depending on the norm used) is often intractable during gradient descent training. Therefore, Cisse et al. propose to use a per-layer regularizer of the form:

$R(W) = \|W^TW – I\|$

where $I$ is the identity matrix. During training, this regularizer is supposed to ensure that the learned weigth matrices are orthonormal – an efficient alternative to regular matrix manifold optimization techniques (see the paper).

  • [1] Matthias Hein, Maksym Andriushchenko: Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation. CoRR abs/1705.08475 (2017)
Also find this summary on ShortScience.org.

What is your opinion on the summarized work? Or do you know related work that is of interest? Let me know your thoughts in the comments below: