# An Information-Theoretic Approach to Generalization Theory

arXiv: https://arxiv.org/abs/2408.13275 · HTML: https://mlsanity.com/paper/2408.13275/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2024.

## Built on by (most cited first, 9 of 9)

- [Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization](https://mlsanity.com/paper/2410.02833/) (2024)
- [The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms](https://mlsanity.com/paper/2411.12030/) (2024)
- [Proofs for Folklore Theorems on the Radon-Nikodym Derivative](https://mlsanity.com/paper/2501.18374/) (2025)
- [Ensuring Reliability via Hyperparameter Selection: Review and Advances](https://mlsanity.com/paper/2502.04206/) (2025)
- [Scaling Laws are Redundancy Laws](https://mlsanity.com/paper/2509.20721/) (2025)
- [Refined PAC-Bayes Bounds for Offline Bandits](https://mlsanity.com/paper/2502.11953/) (2025)
- [Koopman-Based Generalization of Deep Reinforcement Learning With Application to Wireless Communications](https://mlsanity.com/paper/2503.02961/) (2025)
- [Generalization Analysis and Method for Domain Generalization for a Family of Recurrent Neural Networks](https://mlsanity.com/paper/2601.08122/) (2026)
- [Equivalence Between Nested Gibbs Measures and Log-Linear Combinations of Gibbs Measures](https://mlsanity.com/paper/2609.19988/) (2026)

## Abstract (arXiv)

We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and the training data. We consider two categories of generalization guarantees: 1) Guarantees in expectation: These bounds measure performance in the average case. Here, the dependence between the algorithm and the data is often captured by information measures. While these measures offer an intuitive interpretation, they overlook the geometry of the algorithm's hypothesis class. Here, we introduce bounds using the Wasserstein distance to incorporate geometry, and a structured, systematic method to derive bounds capturing the dependence between the algorithm and an individual datum, and between the algorithm and subsets of the training data. 2) PAC-Bayesian guarantees: These bounds measure the performance level with high probability. Here, the dependence between the algorithm and the data is often measured by the relative entropy. We establish connections between the Seeger--Langford and Catoni's bounds, revealing that the former is optimized by the Gibbs posterior. We introduce novel, tighter bounds for various types of loss functions. To achieve this, we introduce a new technique to optimize parameters in probabilistic statements. To study the limitations of these approaches, we present a counter-example where most of the information-theoretic bounds fail while traditional approaches do not. Finally, we explore the relationship between privacy and generalization. We show that algorithms with a bounded maximal leakage generalize. For discrete data, we derive new bounds for differentially private algorithms that guarantee generalization even with a constant privacy parameter, which is in contrast to previous bounds in the literature.