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

arXiv: https://arxiv.org/abs/1909.05479 · HTML: https://mlsanity.com/paper/1909.05479/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 13 of 13)

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- [Simpler Certified Radius Maximization by Propagating Covariances](https://mlsanity.com/paper/2104.05888/) (2021)
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- [Real World Large Scale Recommendation Systems Reproducibility and Smooth Activations](https://mlsanity.com/paper/2202.06499/) (2022)
- [Semi-supervised learning by selective training with pseudo labels via confidence estimation](https://mlsanity.com/paper/2103.08193/) (2021)
- [Polynomial, trigonometric, and tropical activations](https://mlsanity.com/paper/2502.01247/) (2025)

## Abstract (arXiv)

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.