Research map / Learning theory and algorithms / Kernels and regression theory
PAC-Bayes bounds
Derive PAC-Bayesian generalization bounds with data-dependent priors and for meta-learning.
39 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2018–2026) · an approach in Kernels and regression theory, keyword cluster “generalization bounds · pac · generalization error”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
6 papers in 2023–24 and 7 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 2.4% to 2.8%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2018 · A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks (ICLR 2018 · 296 citations)
- 2019 · Fast-rate PAC-Bayes Generalization Bounds via Shifted Rademacher Processes (NeurIPS 2019 · 13 citations)
- 2020 · PAC-Bayesian Bound for the Conditional Value at Risk (NeurIPS 2020 · 11 citations)
- 2021 · Bridging the Gap Between Practice and PAC-Bayes Theory in Few-Shot Meta-Learning (NeurIPS 2021 · 11 citations)
- 2022 · PAC-Bayes Information Bottleneck (ICLR 2022 · 11 citations)
- 2023 · PAC-Bayesian Generalization Bounds for Adversarial Generative Models (ICML 2023 · 3 citations)
- 2024 · A Unified Recipe for Deriving (Time-Uniform) PAC-Bayes Bounds (NeurIPS 2024 · 6 citations)
- 2025 · PAC-Bayes Analysis for Recalibration in Classification (ICML 2025 · 0 citations)
- 2026 · Symmetries in PAC-Bayesian Learning (ICML 2026 · 0 citations)
Earliest papers here
- A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks (ICLR 2018 · 296 citations)
- Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory (ICML 2018 · 95 citations)
- PAC-Bayes bounds for stable algorithms with instance-dependent priors (NeurIPS 2018 · 14 citations)
What has been tried
27 papers here report 203 measured changes (a component added, removed or swapped, compared with a baseline): helped 58%, no clear effect 14%, hurt 23%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add the Brier score to the Brier + classification objective | MNIST · ECE | .0037 ± .0004 -> .0035 ± .0004 | Helped | PAC-Bayes Analysis for Recalibration in Classification (ICML 2025 · 0 citations) |
| Increase EASE γ from 50 to 5000 | ML 20M test · RH | 128.66 -> 118.91 | Helped | PAC-Bayes Bounds for Multivariate Linear Regression and Linear Autoencoders (NeurIPS 2025 · 0 citations) |
| increase κmax to 10 | Anaerobic digestion (LF training set) · final PAC-Bayes bound | 0.147 ± 0.022 | Hurt | Learning via Surrogate PAC-Bayes (NeurIPS 2024 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 13 papers; from OpenAlex and the papers' affiliations).
- University of Oxford · 2 papers
- University College London · 2 papers
Use it
Download BibTeX of 31 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Statistical perspectives on generalization (99 papers)
- Information-theoretic generalization bounds (94 papers)
- Generalization theory of deep networks (67 papers)
- Empirical generalization measures (61 papers)
Elsewhere in the topic
- RKHS kernel methods (127 papers)
- Neural tangent kernel analysis (109 papers)
- Kernel regression under shift (89 papers)
- High-dimensional asymptotic generalization (82 papers)
- High-dimensional linear regression theory (61 papers)
- Kernel ridge regression analysis (57 papers)
- Double descent and overfitting (53 papers)
- Random feature approximation (36 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).