# Generalization of Hamiltonian algorithms

arXiv: https://arxiv.org/abs/2405.14469 · HTML: https://mlsanity.com/paper/2405.14469/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 9 of 9)

- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors](https://mlsanity.com/paper/1712.09376/) (2017)
- [PAC-Bayes Analysis Beyond the Usual Bounds](https://mlsanity.com/paper/2006.13057/) (2020)
- [PAC-Bayes bounds for stable algorithms with instance-dependent priors](https://mlsanity.com/paper/1806.06827/) (2018)
- [Distribution-Dependent Analysis of Gibbs-ERM Principle](https://mlsanity.com/paper/1902.01846/) (2019)

## Built on by (most cited first, 2 of 2)

- [Generalization of Gibbs and Langevin Monte Carlo Algorithms in the Interpolation Regime](https://mlsanity.com/paper/2510.06028/) (2025)
- [Generalization of the Gibbs algorithm with high probability at low temperatures](https://mlsanity.com/paper/2502.11071/) (2025)

## Abstract (arXiv)

The paper proves generalization results for a class of stochastic learning algorithms. The method applies whenever the algorithm generates an absolutely continuous distribution relative to some a-priori measure and the Radon Nikodym derivative has subgaussian concentration. Applications are bounds for the Gibbs algorithm and randomizations of stable deterministic algorithms as well as PAC-Bayesian bounds with data-dependent priors.