Research map / Learning theory and algorithms / Kernels and regression theory
Generalization theory of deep networks
Study generalization of ReLU, ResNet and deep architectures via width, depth and sparsity.
67 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Kernels and regression theory, keyword cluster “generalization bounds · pac · generalization error”
State History Tried Checklist 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.
19 papers in 2023–24 and 12 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 7.7% to 4.9%.
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 · Spectrally-normalized margin bounds for neural networks (NeurIPS 2017 · 164 citations)
- 2018 · Entropy and mutual information in models of deep neural networks (NeurIPS 2018 · 139 citations)
- 2019 · Random deep neural networks are biased towards simple functions (NeurIPS 2019 · 30 citations)
- 2020 · Truth or backpropaganda? An empirical investigation of deep learning theory (ICLR 2020 · 16 citations)
- 2021 · A Universal Law of Robustness via Isoperimetry (NeurIPS 2021 · 75 citations)
- 2022 · Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality (ICLR 2022 · 10 citations)
- 2023 · How Does Information Bottleneck Help Deep Learning? (ICML 2023 · 14 citations)
- 2024 · Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss (ICML 2024 · 3 citations)
- 2025 · Optimal Control Operator Perspective and a Neural Adaptive Spectral Method (AAAI 2025 · 2 citations)
- 2026 · Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers (ICLR 2026 · 0 citations)
Earliest papers here
- Spectrally-normalized margin bounds for neural networks (NeurIPS 2017 · 164 citations)
- Net-Trim: Convex Pruning of Deep Neural Networks with Performance Guarantee (NeurIPS 2017 · 27 citations)
- Entropy and mutual information in models of deep neural networks (NeurIPS 2018 · 139 citations)
What has been tried
49 papers here report 335 measured changes (a component added, removed or swapped, compared with a baseline): helped 57%, no clear effect 13%, hurt 20%, mixed 9%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| add adaptive basis parameters | Quadrotor · ID MAPE | 7.86 \times 10^{-6} -> 6.17 \times 10^{-6} | Helped | Optimal Control Operator Perspective and a Neural Adaptive Spectral Method (AAAI 2025 · 2 citations) |
| Increase the number of heads, up to d^2 heads | Synthetic random linear attention · performance | Helped | Learning Linear Attention in Polynomial Time (NeurIPS 2025 · 1 citation) | |
| Use positive magnitude at scale s=√n instead of s=10^-2 | Vision transformer and GNN experiments · granulated Kendall coefficient | Helped | Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms (NeurIPS 2024 · 1 citation) | |
| Use normalized Tanh shifted by 1.2 instead of 1.603 | MNIST (Dense) test · misclassification error | 2.088 -> 2.437 | Hurt | Subhomogeneous Deep Equilibrium Models (ICML 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 8 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 · 3 of 8 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 31 papers; from OpenAlex and the papers' affiliations).
- Massachusetts Institute of Technology · 3 papers
- Amazon · 3 papers
- University of Maryland, College Park · 2 papers
- New York University · 2 papers
- EPFL · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
Get alerts. Describe your idea in scime atlas and save it (free scime account): you get a weekly email when new preprints land close to it.
Related approaches
Same keyword cluster
- Statistical perspectives on generalization (99 papers)
- Information-theoretic generalization bounds (94 papers)
- Empirical generalization measures (61 papers)
- PAC-Bayes bounds (39 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).