Summary of Adversarial Flows: a Gradient Flow Characterization Of Adversarial Attacks, by Lukas Weigand et al.
Adversarial flows: A gradient flow characterization of adversarial attacks
by Lukas Weigand, Tim Roith, Martin Burger
First submitted to arxiv on: 8 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Analysis of PDEs (math.AP)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A novel approach to understanding adversarial attacks on neuronal networks is presented, where the popular fast gradient sign method and its iterative variant are interpreted as explicit Euler discretizations of a differential inclusion. The paper demonstrates convergence of this discretization to the associated gradient flow, leveraging the concept of p-curves of maximal slope in the case p=infinity. Additionally, it shows that curves in the Wasserstein space can be characterized by a representing measure on the space of curves in the underlying Banach space, which fulfill the differential inclusion. The theory is applied to the finite-dimensional setting, demonstrating convergence of normalized gradient descent methods and characterizing the inner optimization task of adversarial training objectives via ∞-curves of maximum slope on an optimal transport space. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper takes a unique approach to understanding how to perform attacks on neural networks. It shows that a popular method for doing this is actually equivalent to a type of mathematical equation called a differential inclusion. The authors also prove that certain types of curves can be used to represent the paths taken by these attacks, and they apply their theory to understand how different methods for training neural networks work. |
Keywords
» Artificial intelligence » Gradient descent » Optimization
