# A unified framework for information-theoretic generalization bounds

arXiv: https://arxiv.org/abs/2305.11042 · HTML: https://mlsanity.com/paper/2305.11042/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 18 May 2023.

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

- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Reasoning About Generalization via Conditional Mutual Information](https://mlsanity.com/paper/2001.09122/) (2020)
- [Tightening Mutual Information Based Bounds on Generalization Error](https://mlsanity.com/paper/1901.04609/) (2019)
- [Sharpened Generalization Bounds based on Conditional Mutual Information and an Application to Noisy, Iterative Algorithms](https://mlsanity.com/paper/2004.12983/) (2020)
- [Chaining Mutual Information and Tightening Generalization Bounds](https://mlsanity.com/paper/1806.03803/) (2018)
- [Information-theoretic generalization bounds for black-box learning algorithms](https://mlsanity.com/paper/2110.01584/) (2021)
- [Generalization Error Bounds Via R'enyi-, f-Divergences and Maximal Leakage](https://mlsanity.com/paper/1912.01439/) (2019)
- [Generalization Bounds via Information Density and Conditional Information Density](https://mlsanity.com/paper/2005.08044/) (2020)
- [Tighter expected generalization error bounds via Wasserstein distance](https://mlsanity.com/paper/2101.09315/) (2021)
- [Individually Conditional Individual Mutual Information Bound on Generalization Error](https://mlsanity.com/paper/2012.09922/) (2020)
- [Towards a Unified Information-Theoretic Framework for Generalization](https://mlsanity.com/paper/2111.05275/) (2021)
- [Generalization Bounds using Lower Tail Exponents in Stochastic Optimizers](https://mlsanity.com/paper/2108.00781/) (2021)
- [Generalization Bounds via Convex Analysis](https://mlsanity.com/paper/2202.04985/) (2022)
- [Chained Generalisation Bounds](https://mlsanity.com/paper/2203.00977/) (2022)

## Built on by (most cited first, 6 of 6)

- [Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure](https://mlsanity.com/paper/2312.12236/) (2023)
- [Better-than-KL PAC-Bayes Bounds](https://mlsanity.com/paper/2402.09201/) (2024)
- [An Information-Theoretic Analysis of OOD Generalization in Meta-Reinforcement Learning](https://mlsanity.com/paper/2510.23448/) (2025)
- [Tighter Information-Theoretic Generalization Bounds via a Novel Class of Change of Measure Inequalities](https://mlsanity.com/paper/2602.07999/) (2026)
- [Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewards](https://mlsanity.com/paper/2604.10727/) (2026)
- [Sample Complexity of Stochastic Optimization with Integer Variables](https://mlsanity.com/paper/2605.07239/) (2026)

## Abstract (arXiv)

This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation lemma based on a change of measure and a relaxation of Young's inequality in Lpsip Orlicz spaces. Using the decorrelation lemma in combination with other techniques, such as symmetrization, couplings, and chaining in the space of probability measures, we obtain new upper bounds on the generalization error, both in expectation and in high probability, and recover as special cases many of the existing generalization bounds, including the ones based on mutual information, conditional mutual information, stochastic chaining, and PAC-Bayes inequalities. In addition, the Fernique-Talagrand upper bound on the expected supremum of a subgaussian process emerges as a special case.