Research map / Learning theory and algorithms / Sample complexity
Learning halfspaces under noise
Develops efficient and label-optimal algorithms for halfspaces under noise and misspecification.
84 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · 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.
22 papers in 2023–24 and 22 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 6.6% to 6.7%.
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 · Quantum Perceptron Models (NeurIPS 2016 · 98 citations)
- 2017 · Revisiting Perceptron: Efficient and Label-Optimal Learning of Halfspaces (NeurIPS 2017 · 20 citations)
- 2018 · Query Complexity of Bayesian Private Learning (NeurIPS 2018 · 12 citations)
- 2019 · Sublinear quantum algorithms for training linear and kernel-based classifiers (ICML 2019 · 41 citations)
- 2020 · Task-Robust Model-Agnostic Meta-Learning (NeurIPS 2020 · 24 citations)
- 2021 · An Exponential Improvement on the Memorization Capacity of Deep Threshold Networks (NeurIPS 2021 · 9 citations)
- 2022 · Cryptographic Hardness of Learning Halfspaces with Massart Noise (NeurIPS 2022 · 5 citations)
- 2023 · Learning Distributions over Quantum Measurement Outcomes (ICML 2023 · 1 citation)
- 2024 · Testably Learning Polynomial Threshold Functions (NeurIPS 2024 · 2 citations)
- 2025 · Statistical Query Hardness of Multiclass Linear Classification with Random Classification Noise (ICML 2025 · 0 citations)
- 2026 · Learning Junta Distributions, Quantum Junta States, and QAC$^0$ Circuits (ICML 2026 · 1 citation)
Earliest papers here
- Quantum Perceptron Models (NeurIPS 2016 · 98 citations)
- Noise-Adaptive Margin-Based Active Learning and Lower Bounds under Tsybakov Noise Condition (AAAI 2016 · 11 citations)
- Revisiting Perceptron: Efficient and Label-Optimal Learning of Halfspaces (NeurIPS 2017 · 20 citations)
What has been tried
53 papers here report 228 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 9%, hurt 18%, mixed 7%. 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 improved 27-subsample splitting, two independent voting classifiers, and an ERM tie-breaker instead of the initial approach | Agnostic PAC learning · error upper bound | 15τ -> 2.1τ | Helped | On Agnostic PAC Learning in the Small Error Regime (NeurIPS 2025 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 44 papers; from OpenAlex and the papers' affiliations).
- University of Wisconsin - Madison · 12 papers
- University of California, San Diego · 8 papers
- University of Texas at Austin · 5 papers
- University of Texas, Austin · 3 papers
- Stevens Institute of Technology · 2 papers
- UT Austin · 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
- Learning under log-concave distributions (80 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).