Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Variational Bayesian deep learning
Parameterizes and analyzes variational posteriors for deep models, linking ensembles to Bayesian inference.
105 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Uncertainty and Gaussian processes, keyword cluster “bayesian inference · posterior · priors”
State History Benchmarks Tried Checklist Preprints Who Export
Where it stands
Few recent reports The tracked benchmarks have at most one report from 2025–26 that could beat the old record, too few to say whether they are still moving.
23 papers in 2023–24 and 21 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 8.5% to 6.8%.
No longer reported by papers here: CIFAR-10 (accuracy, last in 2024); Boston (Test RMSE, last in 2020); CIFAR-100 (accuracy, last in 2024); Concrete (Test RMSE, last in 2020); Kin8nm (Test RMSE, last in 2020).
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
- 2016 · Doubly Decomposing Nonparametric Tensor Regression (ICML 2016 · 19 citations)
- 2017 · Bayesian Compression for Deep Learning (NeurIPS 2017 · 335 citations)
- 2018 · Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam (ICML 2018 · 59 citations)
- 2019 · A Simple Baseline for Bayesian Uncertainty in Deep Learning (NeurIPS 2019 · 173 citations)
- 2020 · Bayesian Deep Learning and a Probabilistic Perspective of Generalization (NeurIPS 2020 · 177 citations)
- 2021 · Laplace Redux - Effortless Bayesian Deep Learning (NeurIPS 2021 · 27 citations)
- 2022 · A Variational Bayesian Method for Similarity Learning in Non-Rigid Image Registration (CVPR 2022 · 17 citations)
- 2023 · Learning Analytical Posterior Probability for Human Mesh Recovery (CVPR 2023 · 24 citations)
- 2024 · Variational Bayesian Last Layers (ICLR 2024 · 6 citations)
- 2025 · Deep Bayesian Filter for Bayes-Faithful Data Assimilation (ICML 2025 · 0 citations)
- 2026 · Gaussian Mean Field Variational Inference can Overestimate Predictive Variance (ICML 2026 · 0 citations)
Earliest papers here
- Doubly Decomposing Nonparametric Tensor Regression (ICML 2016 · 19 citations)
- Kernel Bayesian Inference with Posterior Regularization (NeurIPS 2016 · 7 citations)
- Analysis of Variational Bayesian Factorizations for Sparse and Low-Rank Estimation (ICML 2016 · 0 citations)
Benchmark records
The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.
CIFAR-10 · accuracy (higher is better)
5 papers, 2021–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2021 | 86.11 | Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning (ICML 2021 · 11 citations) |
| 2022 | 96.5 | Feature Space Particle Inference for Neural Network Ensembles (ICML 2022 · 0 citations) |
Boston · Test RMSE (lower is better)
4 papers, 2018–2020 · not reported since 2020
| Year | Best so far | Set by |
|---|---|---|
| 2018 | 2.742 | Noisy Natural Gradient as Variational Inference (ICML 2018 · 25 citations) |
| 2019 | 2.369 | Dropout as a Structured Shrinkage Prior (ICML 2019 · 23 citations) |
CIFAR-10 · NLL (lower is better)
4 papers, 2019–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 0.123 | A Simple Baseline for Bayesian Uncertainty in Deep Learning (NeurIPS 2019 · 173 citations) |
| 2022 | 0.107 | Feature Space Particle Inference for Neural Network Ensembles (ICML 2022 · 0 citations) |
CIFAR-100 · accuracy (higher is better)
4 papers, 2022–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2022 | 82.9 | Feature Space Particle Inference for Neural Network Ensembles (ICML 2022 · 0 citations) |
Concrete · Test RMSE (lower is better)
4 papers, 2018–2020 · not reported since 2020
| Year | Best so far | Set by |
|---|---|---|
| 2018 | 5.019 | Noisy Natural Gradient as Variational Inference (ICML 2018 · 25 citations) |
| 2019 | 3.935 | Dropout as a Structured Shrinkage Prior (ICML 2019 · 23 citations) |
Kin8nm · Test RMSE (lower is better)
4 papers, 2018–2020 · not reported since 2020
| Year | Best so far | Set by |
|---|---|---|
| 2018 | 0.076 | Noisy Natural Gradient as Variational Inference (ICML 2018 · 25 citations) |
What has been tried
90 papers here report 867 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 9%, hurt 21%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add a D-VBLL post-training layer to a trained DNN | CIFAR-10 · accuracy | 95.8 ± 0.19 -> 96.4 ± 0.01 | No clear effect | Variational Bayesian Last Layers (ICLR 2024 · 6 citations) |
| Initialize permutation candidates using SLR instead of random initialization | Abalone (K=8) · convergence speed | Helped | Shuffled Deep Regression (AAAI 2024 · 1 citation) | |
| Use linearized Hessian or linearized empirical Fisher instead of Monte Carlo approximations | MNIST · NLPD | Helped | Bayesian Online Natural Gradient (BONG) (NeurIPS 2024 · 1 citation) | |
| Use different dictionaries rather than the db4 dictionary | MNIST · nMSE | No clear effect | Sparse Bayesian Generative Modeling for Compressive Sensing (NeurIPS 2024 · 1 citation) | |
| Use squared rather than linear confidence to set observation covariance | LaSOT airplane test videos · IoU | Helped | Deep Bayesian Filter for Bayes-Faithful Data Assimilation (ICML 2025 · 0 citations) | |
| Use multiple particles (FHBI 4p) instead of single particle SAM | VTAB-1K Natural datasets · Top-1 accuracy (CIFAR100) | 74.8 vs 72.7 | Helped | Improving Generalization with Flat Hilbert Bayesian Inference (ICML 2025 · 0 citations) |
| Jointly optimize a learned embedding instead of fixing the embedding to identity | Curved-manifold benchmarks, especially tail adjustments and anisotropic distortions · power | Helped | CoLT: The conditional localization test for assessing the accuracy of neural posterior estimates (NeurIPS 2025 · 0 citations) | |
| increase the mixture size to N=20 | 2D Gaussian-mixture target · KL | Helped | Variational Inference with Mixtures of Isotropic Gaussians (NeurIPS 2025 · 0 citations) | |
| Use full VIKING ELBO optimization rather than post-hoc tuning of variational parameters only | Fashion MNIST · accuracy | Helped | VIKING: Deep variational inference with stochastic projections (NeurIPS 2025 · 0 citations) | |
| Condition primarily on previous base noise instead of previous latents | Funnel · negative ELBO | 0.01 -> 0.38 | Hurt | Model-Informed Flows for Bayesian Inference (NeurIPS 2025 · 0 citations) |
| Remove MILE's proposed numerical-stability adjustments and use naive MCLMC | Airfoil · NaN chains (%) | 0% -> 86% | Hurt | Microcanonical Langevin Ensembles: Advancing the Sampling of Bayesian Neural Networks (ICLR 2025 · 0 citations) |
| Replace moment-matching with local linearisation | MNIST · accuracy | 0.949 -> 0.976 | Helped | Streamlining Prediction in Bayesian Deep Learning (ICLR 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 19 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MNIST · 5 of 19 papers
- Fashion-MNIST · 3 of 19 papers
- CIFAR-10 · 3 of 19 papers
- CIFAR-100 · 3 of 19 papers
- Ionosphere · 2 of 19 papers
Baselines
- AdamW · 2 of 19 papers
- SGLD · 2 of 19 papers
- SVGD · 2 of 19 papers
- MAP · 2 of 19 papers
- IVON · 2 of 19 papers
- SWAG · 2 of 19 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 44 papers; from OpenAlex and the papers' affiliations).
- Technical University of Denmark · 4 papers
- Google · 2 papers
- Google DeepMind · 2 papers
- Eberhard-Karls-Universität Tübingen · 2 papers
- University of Warwick · 2 papers
- University of Massachusetts at Amherst · 2 papers
- University of Cambridge · 2 papers
- University of Maryland, College Park · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Nonparametric and PAC-Bayes Bayesian learning (130 papers)
- Simulation-based inference (118 papers)
- Approximate inference in Bayesian neural networks (93 papers)
- Bayesian view of meta-learning (63 papers)
Elsewhere in the topic
- Priors and functional variational uncertainty (112 papers)
- Sparse variational Gaussian processes (92 papers)
- PAC-Bayes and decoupled GP learning (83 papers)
- Epistemic versus aleatoric decomposition (75 papers)
- Single-model predictive uncertainty (74 papers)
- Bayesian decision-making under uncertainty (57 papers)
- Infinite-width networks as Gaussian processes (49 papers)
- Regression uncertainty quantification (43 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).