Deterministic Gaussian Averaged Neural Networks

TL;DR

This paper introduces a deterministic approach to compute Gaussian averages of neural networks, enabling efficient certification of model robustness against adversarial attacks without stochastic sampling.

Contribution

A novel deterministic method for Gaussian averaging in neural networks that matches stochastic methods in robustness certification while requiring only one inference pass.

Findings

Achieves comparable certified accuracy to randomized smoothing

Requires only a single model evaluation during inference

Provides robustness certification for both regression and classification models

Abstract

We present a deterministic method to compute the Gaussian average of neural networks used in regression and classification. Our method is based on an equivalence between training with a particular regularized loss, and the expected values of Gaussian averages. We use this equivalence to certify models which perform well on clean data but are not robust to adversarial perturbations. In terms of certified accuracy and adversarial robustness, our method is comparable to known stochastic methods such as randomized smoothing, but requires only a single model evaluation during inference.