# Implicit Hypothesis Testing and Divergence Preservation in Neural Network Representations

arXiv: https://arxiv.org/abs/2601.20477 · HTML: https://mlsanity.com/paper/2601.20477/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Caveats for information bottleneck in deterministic scenarios](https://mlsanity.com/paper/1808.07593/) (2018)
- [Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications](https://mlsanity.com/paper/1904.00176/) (2019)
- [Minimax Optimal Estimation of KL Divergence for Continuous Distributions](https://mlsanity.com/paper/2002.11599/) (2020)
- [The Yin-Yang dataset](https://mlsanity.com/paper/2102.08211/) (2021)
- [Evaluating Model Explanations without Ground Truth](https://mlsanity.com/paper/2505.10399/) (2025)
- [A Generalized Information Bottleneck Theory of Deep Learning](https://mlsanity.com/paper/2509.26327/) (2025)
- [Permutation-based Hypothesis Testing for Neural Networks](https://mlsanity.com/paper/2301.11354/) (2023)

## Abstract (arXiv)

We study the training dynamics of neural classifiers through the lens of binary hypothesis testing. We re-formalize classification as a collection of binary tests between class-conditional distributions induced by learned representations and show empirically that, along training trajectories, well-generalizing networks progressively approach Neyman-Pearson optimal decision rules, as measured by monotonic growth in the KL divergence retained by learned representations. We provide sufficient conditions for exact optimality, discuss its implications for training regularization, and define an informational plane, (so-called Evidence-Error plane) where convergence can be assessed methodically across network architecture.