# A Probabilistic Representation of DNNs: Bridging Mutual Information and Generalization

arXiv: https://arxiv.org/abs/2106.10262 · HTML: https://mlsanity.com/paper/2106.10262/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Reasoning About Generalization via Conditional Mutual Information](https://mlsanity.com/paper/2001.09122/) (2020)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates](https://mlsanity.com/paper/1911.02151/) (2019)
- [How much does your data exploration overfit? Controlling bias via information usage](https://mlsanity.com/paper/1511.05219/) (2015)
- [Sharpened Generalization Bounds based on Conditional Mutual Information and an Application to Noisy, Iterative Algorithms](https://mlsanity.com/paper/2004.12983/) (2020)
- [Generalization Error Bounds for Noisy, Iterative Algorithms](https://mlsanity.com/paper/1801.04295/) (2018)
- [Chaining Mutual Information and Tightening Generalization Bounds](https://mlsanity.com/paper/1806.03803/) (2018)
- [An Information-Theoretic View for Deep Learning](https://mlsanity.com/paper/1804.09060/) (2018)
- [A Probabilistic Representation of Deep Learning for Improving The Information Theoretic Interpretability](https://mlsanity.com/paper/2010.14054/) (2020)

## Built on by (most cited first, 1 of 1)

- [Towards Generalizable Graph Contrastive Learning: An Information Theory Perspective](https://mlsanity.com/paper/2211.10929/) (2022)

## Abstract (arXiv)

Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.