Generating Accurate Pseudo-labels in Semi-Supervised Learning and Avoiding Overconfident Predictions via Hermite Polynomial Activations

TL;DR

This paper investigates Hermite polynomial activations as an alternative to ReLUs in deep networks, demonstrating notable benefits in semi-supervised learning, including improved pseudo-label accuracy and robustness, supported by theoretical analysis.

Contribution

It introduces Hermite polynomial activations for deep networks, showing their advantages in semi-supervised learning and providing theoretical insights into their robustness and mathematical properties.

Findings

Hermite activations improve pseudo-label accuracy in SSL.

Networks with Hermite activations are more robust to noise.

Hermite-based models offer runtime and financial savings.

Abstract

Rectified Linear Units (ReLUs) are among the most widely used activation function in a broad variety of tasks in vision. Recent theoretical results suggest that despite their excellent practical performance, in various cases, a substitution with basis expansions (e.g., polynomials) can yield significant benefits from both the optimization and generalization perspective. Unfortunately, the existing results remain limited to networks with a couple of layers, and the practical viability of these results is not yet known. Motivated by some of these results, we explore the use of Hermite polynomial expansions as a substitute for ReLUs in deep networks. While our experiments with supervised learning do not provide a clear verdict, we find that this strategy offers considerable benefits in semi-supervised learning (SSL) / transductive learning settings. We carefully develop this idea and show how the use of Hermite polynomials based activations can yield improvements in pseudo-label accuracies and sizable financial savings (due to concurrent runtime benefits). Further, we show via theoretical analysis, that the networks (with Hermite activations) offer robustness to noise and other attractive mathematical properties.