Research map / Learning theory and algorithms / Sample complexity
Robust and surrogate-loss learning bounds
Establishes upper and lower bounds for robust learning, surrogate losses and neural network hardness.
83 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Sample complexity, keyword cluster “al · bounds · et”
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.
25 papers in 2023–24 and 14 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 7.5% to 4.3%.
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 · Active Learning from Imperfect Labelers (NeurIPS 2016 · 34 citations)
- 2017 · Analytical Guarantees on Numerical Precision of Deep Neural Networks (ICML 2017 · 62 citations)
- 2018 · Lipschitz regularity of deep neural networks: analysis and efficient estimation (NeurIPS 2018 · 135 citations)
- 2019 · Certainty Equivalence is Efficient for Linear Quadratic Control (NeurIPS 2019 · 88 citations)
- 2020 · Universally Quantized Neural Compression (NeurIPS 2020 · 47 citations)
- 2021 · Towards a Unified Information-Theoretic Framework for Generalization (NeurIPS 2021 · 9 citations)
- 2022 · Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limit (NeurIPS 2022 · 11 citations)
- 2023 · Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities (ICLR 2023 · 3 citations)
- 2024 · Watermarks in the Sand: Impossibility of Strong Watermarking for Language Models (ICML 2024 · 9 citations)
- 2025 · The Cost of Robustness: Tighter Bounds on Parameter Complexity for Robust Memorization in ReLU Nets (NeurIPS 2025 · 0 citations)
- 2026 · Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety (ICML 2026 · 0 citations)
Earliest papers here
- Active Learning from Imperfect Labelers (NeurIPS 2016 · 34 citations)
- Analytical Guarantees on Numerical Precision of Deep Neural Networks (ICML 2017 · 62 citations)
- Noise-Tolerant Interactive Learning Using Pairwise Comparisons (NeurIPS 2017 · 16 citations)
What has been tried
58 papers here report 383 measured changes (a component added, removed or swapped, compared with a baseline): helped 66%, no clear effect 7%, hurt 20%, 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 |
|---|---|---|---|---|
| Add GenQ queries to document-embedding indexing | MARCO Lite test · Rec@1 | 7.09 -> 9.24 | Helped | Bottleneck-Minimal Indexing for Generative Document Retrieval (ICML 2024 · 1 citation) |
| Vary p from 0 to 1×10⁵ in ME-𝒜 | CIFAR-10 TRADES · robust accuracy | 63.17 -> 63.86; 63.41 | No clear effect | Uniformly Stable Algorithms for Adversarial Training and Beyond (ICML 2024 · 0 citations) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 39 papers; from OpenAlex and the papers' affiliations).
- Google · 6 papers
- Carnegie Mellon University · 3 papers
- Princeton University · 3 papers
- Pennsylvania State University · 2 papers
- Massachusetts Institute of Technology · 2 papers
- University of Wisconsin - Madison · 2 papers
- Harvard University · 2 papers
- University of Pennsylvania · 2 papers
- Korea Advanced Institute of Science and Technology · 2 papers
- Purdue University · 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
- Statistical-query lower bounds (85 papers)
- Computational thresholds in graphs and structure (84 papers)
- Generalization and limits under data constraints (72 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)
- Learning halfspaces under noise (84 papers)
- Sample complexity of ranking and selection (80 papers)
- Learning under log-concave distributions (80 papers)
- PAC learnability theory (79 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).