# Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2602.22925 · HTML: https://mlsanity.com/paper/2602.22925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss](https://mlsanity.com/paper/2002.04486/) (2020)
- [Understanding neural networks with reproducing kernel Banach spaces](https://mlsanity.com/paper/2109.09710/) (2021)
- [Infinite-width limit of deep linear neural networks](https://mlsanity.com/paper/2211.16980/) (2022)
- [Adaptive kernel predictors from feature-learning infinite limits of neural networks](https://mlsanity.com/paper/2502.07998/) (2025)
- [Sparse Representer Theorems for Learning in Reproducing Kernel Banach Spaces](https://mlsanity.com/paper/2305.12584/) (2023)
- [PAC-Bayes-Chernoff bounds for unbounded losses](https://mlsanity.com/paper/2401.01148/) (2024)
- [A Two-Scale Complexity Measure for Deep Learning Models](https://mlsanity.com/paper/2401.09184/) (2024)

## Abstract (arXiv)

We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate functions-on predictors, providing an emerging notion of complexity and feature learning directly at the functional level. We show that the posterior output rate function is obtained by a joint optimization over predictors and internal kernels, in contrast with fixed-kernel (NNGP) theory. Numerical experiments demonstrate that the resulting predictions accurately describe finite-width behavior for moderately sized networks, capturing non-Gaussian tails, posterior deformation, and data-dependent kernel selection effects.