# Posterior concentrations of fully-connected Bayesian neural networks with general priors on the weights

arXiv: https://arxiv.org/abs/2403.14225 · HTML: https://mlsanity.com/paper/2403.14225/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 81 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 3 of 3)

- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Deep ReLU network approximation of functions on a manifold](https://mlsanity.com/paper/1908.00695/) (2019)
- [Bayesian Inference for Large Scale Image Classification](https://mlsanity.com/paper/1908.03491/) (2019)

## Built on by (most cited first, 7 of 7)

- [Posterior and variational inference for deep neural networks with heavy-tailed weights](https://mlsanity.com/paper/2406.03369/) (2024)
- [Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds](https://mlsanity.com/paper/2410.21702/) (2024)
- [Accommodate Knowledge Conflicts in Retrieval-augmented LLMs: Towards Robust Response Generation in the Wild](https://mlsanity.com/paper/2504.12982/) (2025)
- [Posterior Contraction for Sparse Neural Networks in Besov Spaces with Intrinsic Dimensionality](https://mlsanity.com/paper/2506.19144/) (2025)
- [Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling](https://mlsanity.com/paper/2608.25052/) (2026)
- [Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs](https://mlsanity.com/paper/2605.08672/) (2026)
- [A Composite Activation Function for Learning Stable Binary Representations](https://mlsanity.com/paper/2605.11558/) (2026)

## Abstract (arXiv)

Bayesian approaches for training deep neural networks (BNNs) have received significant interest and have been effectively utilized in a wide range of applications. There have been several studies on the properties of posterior concentrations of BNNs. However, most of these studies only demonstrate results in BNN models with sparse or heavy-tailed priors. Surprisingly, no theoretical results currently exist for BNNs using Gaussian priors, which are the most commonly used one. The lack of theory arises from the absence of approximation results of Deep Neural Networks (DNNs) that are non-sparse and have bounded parameters. In this paper, we present a new approximation theory for non-sparse DNNs with bounded parameters. Additionally, based on the approximation theory, we show that BNNs with non-sparse general priors can achieve near-minimax optimal posterior concentration rates to the true model.