# A General Framework for the Practical Disintegration of PAC-Bayesian Bounds

arXiv: https://arxiv.org/abs/2102.08649 · HTML: https://mlsanity.com/paper/2102.08649/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 12 references that are in the map.
- First posted on arXiv 17 Feb 2021.

## Builds on (most cited first, 2 of 2)

- [Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networks](https://mlsanity.com/paper/2006.12228/) (2020)
- [PAC-Bayes and Domain Adaptation](https://mlsanity.com/paper/1707.05712/) (2017)

## Built on by (most cited first, 21 of 21)

- [Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound](https://mlsanity.com/paper/2106.12535/) (2021)
- [A PAC-Bayesian Link Between Generalisation and Flat Minima](https://mlsanity.com/paper/2402.08508/) (2024)
- [Data-dependent Generalization Bounds via Variable-Size Compressibility](https://mlsanity.com/paper/2303.05369/) (2023)
- [Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Sets](https://mlsanity.com/paper/2404.17442/) (2024)
- [Leveraging PAC-Bayes Theory and Gibbs Distributions for Generalization Bounds with Complexity Measures](https://mlsanity.com/paper/2402.13285/) (2024)
- [PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction](https://mlsanity.com/paper/2312.04658/) (2023)
- [From Mutual Information to Expected Dynamics: New Generalization Bounds for Heavy-Tailed SGD](https://mlsanity.com/paper/2312.00427/) (2023)
- [Generalization Bounds via Meta-Learned Model Representations: PAC-Bayes and Sample Compression Hypernetworks](https://mlsanity.com/paper/2410.13577/) (2024)
- [A Framework for Bounding Deterministic Risk with PAC-Bayes: Applications to Majority Votes](https://mlsanity.com/paper/2510.25569/) (2025)
- [Tighter Generalisation Bounds via Interpolation](https://mlsanity.com/paper/2402.05101/) (2024)
- [Non-vacuous Generalization Bounds for Deep Neural Networks without any modification to the trained models](https://mlsanity.com/paper/2503.07325/) (2025)
- [Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data](https://mlsanity.com/paper/2509.00924/) (2025)
- [Kernel Interpolation as a Bayes Point Machine](https://mlsanity.com/paper/2110.04274/) (2021)
- [Practicality of generalization guarantees for unsupervised domain adaptation with neural networks](https://mlsanity.com/paper/2303.08720/) (2023)
- [Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Bounds](https://mlsanity.com/paper/2411.06276/) (2024)
- [Some theoretical improvements on the tightness of PAC-Bayes risk certificates for neural networks](https://mlsanity.com/paper/2510.07935/) (2025)
- [PAC-Bayesian Bounds on Constrained f-Entropic Risk Measures](https://mlsanity.com/paper/2510.11169/) (2025)
- [Smoothness-Based Derandomization of PAC-Bayes Bounds](https://mlsanity.com/paper/2606.19105/) (2026)
- [Generalization of the Gibbs algorithm with high probability at low temperatures](https://mlsanity.com/paper/2502.11071/) (2025)
- [PAC-Bayesian Generalization Guarantees for Fairness on Stochastic and Deterministic Classifiers](https://mlsanity.com/paper/2602.11722/) (2026)
- [On the disintegration of the stochastic majority vote: From PAC-Bayesian bounds to a self-bounding algorithm](https://mlsanity.com/paper/2609.16803/) (2026)

## Abstract (arXiv)

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic models such as neural networks. As an alternative to this step, we introduce new PAC-Bayesian generalization bounds that have the originality to provide disintegrated bounds, i.e., they give guarantees over one single hypothesis instead of the usual averaged analysis. Our bounds are easily optimizable and can be used to design learning algorithms. We illustrate this behavior on neural networks, and we show a significant practical improvement over the state-of-the-art framework.