The Dimpled Manifold Model of Adversarial Examples in Machine Learning (Research Paper Explained)

#adversarialexamples #dimpledmanifold #security

Adversarial Examples have long been a fascinating topic for many Machine Learning researchers. How can a tiny perturbation cause the neural network to change its output by so much? While many explanations have been proposed over the years, they all appear to fall short. This paper attempts to comprehensively explain the existence of adversarial examples by proposing a view of the classification landscape, which they call the Dimpled Manifold Model, which says that any classifier will adjust its decision boundary to align with the low-dimensional data manifold, and only slightly bend around the data. This potentially explains many phenomena around adversarial examples. Warning: In this video, I disagree. Remember that I'm not an authority, but simply give my own opinions.

OUTLINE:

0:00 - Intro & Overview

7:30 - The old mental image of Adversarial Examples

11:25 - The new Dimpled Manifold Hypothesis

22:55 - The Stretchy Feature Model

29:05 - Why do DNNs create Dimpled Manifolds?

38:30 - What can be explained with the new model?

1:00:40 - Experimental evidence for the Dimpled Manifold Model

1:10:25 - Is Goodfellow's claim debunked?

1:13:00 - Conclusion & Comments

Paper: https://arxiv.org/abs/2106.10151

My replication code: https://gist.github.com/yk/de8d987c4e...

Goodfellow's Talk: https://youtu.be/CIfsB_EYsVI?t=4280

Abstract:

The extreme fragility of deep neural networks when presented with tiny perturbations in their inputs was independently discovered by several research groups in 2013, but in spite of enormous effort these adversarial examples remained a baffling phenomenon with no clear explanation. In this paper we introduce a new conceptual framework (which we call the Dimpled Manifold Model) which provides a simple explanation for why adversarial examples exist, why their perturbations have such tiny norms, why these perturbations look like random noise, and why a network which was adversarially trained with incorrectly labeled images can still correctly classify test images. In the last part of the paper we describe the results of numerous experiments which strongly support this new model, and in particular our assertion that adversarial perturbations are roughly perpendicular to the low dimensional manifold which contains all the training examples.

Abstract: Adi Shamir, Odelia Melamed, Oriel BenShmuel

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