Research map / Learning theory and algorithms / Sample complexity
Learning under log-concave distributions
Gives learning and sampling algorithms for log-concave and related distributions, including diffusion-model sampling.
80 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Sample complexity, keyword cluster “epsilon · log · tilde”
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.
26 papers in 2023–24 and 26 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 7.8% to 7.9%.
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
- 2017 · Sample and Computationally Efficient Learning Algorithms under S-Concave Distributions (NeurIPS 2017 · 8 citations)
- 2019 · Flexible Modeling of Diversity with Strongly Log-Concave Distributions (NeurIPS 2019 · 7 citations)
- 2020 · Robust One-Bit Recovery via ReLU Generative Networks: Near-Optimal Statistical Rate and Global Landscape Analysis (ICML 2020 · 14 citations)
- 2021 · List-Decodable Mean Estimation in Nearly-PCA Time (NeurIPS 2021 · 3 citations)
- 2022 · Sqrt(d) Dimension Dependence of Langevin Monte Carlo (ICLR 2022 · 4 citations)
- 2023 · On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions (NeurIPS 2023 · 19 citations)
- 2024 · Diffusion Posterior Sampling is Computationally Intractable (ICML 2024 · 2 citations)
- 2025 · A (1+?)-Approximation for Ultrametric Embedding in Subquadratic Time (AAAI 2025 · 0 citations)
- 2026 · Learning the Inverse Temperature of Ising Models under Hard Constraints using One Sample (ICLR 2026 · 1 citation)
Earliest papers here
- Sample and Computationally Efficient Learning Algorithms under S-Concave Distributions (NeurIPS 2017 · 8 citations)
- Flexible Modeling of Diversity with Strongly Log-Concave Distributions (NeurIPS 2019 · 7 citations)
- A Polynomial Time Algorithm for Log-Concave Maximum Likelihood via Locally Exponential Families (NeurIPS 2019 · 6 citations)
What has been tried
52 papers here report 227 measured changes (a component added, removed or swapped, compared with a baseline): helped 74%, no clear effect 3%, hurt 17%, 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 |
|---|---|---|---|---|
| Use the empirically selected multiplier c* instead of α when scaling approximate farthest-neighbor distances | five real-world datasets · approximation factor | Helped | A (1+?)-Approximation for Ultrametric Embedding in Subquadratic Time (AAAI 2025 · 0 citations) | |
| Require a linear map rather than a non-linear map | [?2;2~∞ norm · embedding dimension | \Omega(d) | Hurt | Beyond Worst-Case Dimensionality Reduction for Sparse Vectors (ICLR 2025 · 0 citations) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 52 papers; from OpenAlex and the papers' affiliations).
- University of California, San Diego · 10 papers
- University of Wisconsin - Madison · 8 papers
- Google · 3 papers
- Universität Köln · 3 papers
- Carnegie Mellon University · 2 papers
- TU Dortmund · 2 papers
- University of Chicago · 2 papers
- Purdue University · 2 papers
- IBM · 2 papers
- University of Texas, Austin · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Learning halfspaces under noise (84 papers)
- Private and query-efficient algorithms (70 papers)
- Coresets and sublinear estimation (35 papers)
Elsewhere in the topic
- Minimax estimation rates (109 papers)
- Sample complexity of learning distributions (101 papers)
- Optimal mean estimation and subsampling (95 papers)
- Density and property estimation (86 papers)
- Statistical-query lower bounds (85 papers)
- Computational thresholds in graphs and structure (84 papers)
- Robust and surrogate-loss learning bounds (83 papers)
- Sample complexity of ranking and selection (80 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).