No Unique Minimizer, No Problem: On the Consistency of Robust Neural Classifiers

2026-08-09

AI Summary

Neural network classifiers are highly susceptible to label noise and adversarial corruptions, yet existing robust methods lack statistical consistency guarantees under non-identifiable parameterizations. This work proposes a robust classification framework based on the S-divergence family that dispenses with the assumption of parameter identifiability, formulating training as a stochastic optimization problem over a non-identifiable parameter space. For the first time, it establishes convergence of the empirical S-divergence minimizer to the population-optimal equivalence class without requiring a unique minimizer, and verifies that this convergence condition holds for several mainstream architectures. Experiments on vision and language benchmarks demonstrate that S-divergence training achieves robustness on par with state-of-the-art methods while preserving accuracy on clean data.

Abstract

Neural network classifiers trained by cross-entropy minimization are highly sensitive to label noise and adversarial contamination. While robust alternatives offer bounded influence and resistance to corruption, their statistical foundations in the deep learning setting are insufficient due to a fundamental difficulty: neural parameterizations are non-identifiable, so the population loss minimizer is an equivalence class of parameters, not a unique point. We develop a consistency theory for robust neural classifiers based on the S-divergence family that requires no identifiability assumption. Casting training as stochastic optimization over a non-identifiable parameter space, we prove that empirical S-divergence minimizers converge to the population-optimal equivalence class under mild regularity conditions, and verify these conditions for three architecture choices. We further establish that limit points of the robust training algorithm are stationary points of the empirical objective. Experiments on vision and language benchmark datasets confirm that S-divergence training maintains clean-data accuracy while exhibiting performance competitive with existing robust methods.

Problem

• robust neural classifiers
• non-identifiability
• label noise
• adversarial contamination
• consistency

Innovation

• S-divergence
• non-identifiability
• robust classification
• consistency theory
• stochastic optimization