# Bayesian Neural Networks: A Min-Max Game Framework

arXiv: https://arxiv.org/abs/2311.11126 · HTML: https://mlsanity.com/paper/2311.11126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 18 Nov 2023.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Improving the Robustness of Deep Neural Networks via Stability Training](https://mlsanity.com/paper/1604.04326/) (2016)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [Deep Learning for Hyperspectral Image Classification: An Overview](https://mlsanity.com/paper/1910.12861/) (2019)
- [Training Robust Deep Neural Networks via Adversarial Noise Propagation](https://mlsanity.com/paper/1909.09034/) (2019)
- [Robustness of Bayesian Neural Networks to Gradient-Based Attacks](https://mlsanity.com/paper/2002.04359/) (2020)
- [Analyzing the Noise Robustness of Deep Neural Networks](https://mlsanity.com/paper/2001.09395/) (2020)
- [PAC-Bayes Information Bottleneck](https://mlsanity.com/paper/2109.14509/) (2021)
- [Towards Proving the Adversarial Robustness of Deep Neural Networks](https://mlsanity.com/paper/1709.02802/) (2017)
- [Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction](https://mlsanity.com/paper/2111.06636/) (2021)
- [Minimax-Bayes Reinforcement Learning](https://mlsanity.com/paper/2302.10831/) (2023)
- [Closed-Loop Transcription via Convolutional Sparse Coding](https://mlsanity.com/paper/2302.09347/) (2023)

## Abstract (arXiv)

In deep learning, Bayesian neural networks (BNN) provide the role of robustness analysis, and the minimax method is used to be a conservative choice in the traditional Bayesian field. In this paper, we study a conservative BNN with the minimax method and formulate a two-player game between a deterministic neural network f and a sampling stochastic neural network f + r*xi. From this perspective, we understand the closed-loop neural networks with the minimax loss and reveal their connection to the BNN. We test the models on simple data sets, study their robustness under noise perturbation, and report some issues for searching r.