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

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