Golyadkin Confronts Perceptual Distance and Curvatures: Coping with Ambiguity

George Kamberov

Keywords: Doppelgangers, perceptual distance, perceptually indistinguishable, robustness, conceptual accuracy, testing accuracy, conceptual coherence, perceptual curvature

TL;DR: Robustness may not be possible and may not be needed -- coherence is sufficient.

Abstract:

The adversarial vulnerability of classifiers reveals a core divergence: ML systems make distinctions without difference; biological systems tolerate difference without distinction-- and survive because of it.

Adversarial vulnerability is analyzed through decision boundaries and distance-based perturbation models. However, the distances used do not match true perceptual distances and the overall approach fails to account for the misalignments with perceptual topology and geometry. We discuss contexts in which the perceptual distance is computable. In particular, we discuss image recognition contexts in which the perceptual distance between any two inputs is finite. The finiteness underpins an inherent, and informally accepted by the ML community, vulnerability of classifiers defined on such images, rendering all labels susceptible to adversarial attacks.

This demonstrates why some valiant attempts to achieve robustness may be doomed. And yet, biological systems function and thrive despite or may be even because of the ever-present ambiguity. Systems function not because they are robust but because they are sufficiently conceptually coherent. The notions of coherency, conceptual coherency, coherency failure rate, and the conceptual margin of a labeled data set are defined and discussed in this paper.

We define latent adversarial vulnerability, showing that vulnerability arises not only from adversarial perturbations but also through conceptual drift along perceptual Sorites, and introduce perceptual curvature which can be used to identify latent adversarial vulnerability regions.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 949