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Persistent Classification: Understanding Adversarial Attacks by Studying Decision Boundary Dynamics

Journal Article · · Statistical Analysis and Data Mining
DOI:https://doi.org/10.1002/sam.11716· OSTI ID:2504244
 [1];  [2];  [3];  [4];  [3];  [5];  [6]
  1. Univ. of Arizona, Tucson, AZ (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Univ. of Texas at San Antonio, TX (United States)
  3. Univ. of Arizona, Tucson, AZ (United States)
  4. Univ. of Texas, Arlington, TX (United States)
  5. Univ. of Texas at San Antonio, TX (United States)
  6. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations
There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, the high codimension in the ambient space of the data manifolds of interest, and that the structure of machine learning models may encourage classifiers to develop decision boundaries close to data points. This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary. Similarly to the smoothed classifier literature, we define a (natural or adversarial) data point to be (γ, σ)-stable if the probability of the same classification is at least γ for points sampled in a Gaussian neighborhood of the point with a given standard deviation σ. We focus on studying the differences between persistence metrics along interpolants of natural and adversarial points. We show that adversarial examples have significantly lower persistence than natural examples for large neural networks in the context of the MNIST and ImageNet datasets. We connect this lack of persistence with decision boundary geometry by measuring angles of interpolants with respect to decision boundaries. Finally, we connect this approach with robustness by developing a manifold alignment gradient metric and demonstrating the increase in robustness that can be achieved when training with the addition of this metric.
Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001
OSTI ID:
2504244
Alternate ID(s):
OSTI ID: 2530499
OSTI ID: 2530371
Report Number(s):
LA-UR--23-26395
Journal Information:
Statistical Analysis and Data Mining, Journal Name: Statistical Analysis and Data Mining Journal Issue: 1 Vol. 18; ISSN 1932-1864
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English

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conference June 2009
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Decision Boundary-aware Data Augmentation for Adversarial Training journal January 2022
Mr2DNM: A Novel Mutual Information-Based Dendritic Neuron Model journal August 2019

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY