Research map / Optimization / Implicit bias and generalization
Shallow ReLU network convergence
Proves gradient descent convergence and generalization for shallow and deep ReLU or linear networks.
132 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Implicit bias and generalization, keyword cluster “relu · width · kernel”
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.
28 papers in 2023–24 and 23 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 11.9% to 8.8%.
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 · Learning Local Image Descriptors With Deep Siamese and Triplet Convolutional Networks by Minimising Global Loss Functions (CVPR 2016 · 173 citations)
- 2017 · Convergence Analysis of Two-layer Neural Networks with ReLU Activation (NeurIPS 2017 · 270 citations)
- 2018 · Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data (NeurIPS 2018 · 273 citations)
- 2019 · A Convergence Theory for Deep Learning via Over-Parameterization (ICML 2019 · 688 citations)
- 2020 · Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks (CVPR 2020 · 380 citations)
- 2021 · How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks? (ICLR 2021 · 23 citations)
- 2022 · High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation (NeurIPS 2022 · 10 citations)
- 2023 · Git Re-Basin: Merging Models modulo Permutation Symmetries (ICLR 2023 · 33 citations)
- 2024 · The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents (ICML 2024 · 2 citations)
- 2025 · Loss Landscape of Shallow ReLU-like Neural Networks: Stationary Points, Saddle Escape, and Network Embedding (ICLR 2025 · 1 citation)
- 2026 · Sharp description of local minima in the loss landscape of high-dimensional two-layer ReLU neural networks (ICML 2026 · 0 citations)
Earliest papers here
- Learning Local Image Descriptors With Deep Siamese and Triplet Convolutional Networks by Minimising Global Loss Functions (CVPR 2016 · 173 citations)
- Convergence Analysis of Two-layer Neural Networks with ReLU Activation (NeurIPS 2017 · 270 citations)
- The Loss Surface of Deep and Wide Neural Networks (ICML 2017 · 168 citations)
What has been tried
103 papers here report 631 measured changes (a component added, removed or swapped, compared with a baseline): helped 65%, no clear effect 12%, 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 |
|---|---|---|---|---|
| Add the objective gradient on activation variables η | Randomized neural networks · optimized objective value F(x*) | Helped | Activation-Descent Regularization for Input Optimization of ReLU Networks (ICML 2024 · 1 citation) | |
| smooth the loss while retaining a standard contrast with k^*_2=2 | Noisy ICA model · samples for spike recovery | d^3 | No clear effect | Feature learning from non-Gaussian inputs: the case of Independent Component Analysis in high dimensions (ICML 2025 · 0 citations) |
| replace ReLU activation with GeLU | Linear teacher, n=500 · interpolation | Hurt | Simplicity Bias and Optimization Threshold in Two-Layer ReLU Networks (ICML 2025 · 0 citations) | |
| Increase the number of random hyperplanes | MNIST classification, non-private SGD · test accuracy | Helped | Convex Approximation of Two-Layer ReLU Networks for Hidden State Differential Privacy (NeurIPS 2025 · 0 citations) | |
| remove singular value bounding (SVB) at initialization | Synthetic LeakyReLU training · training loss | stagnates around 10^{-3} | Hurt | Block Coordinate Descent for Neural Networks Provably Finds Global Minima (NeurIPS 2025 · 0 citations) |
| add a first-layer bias term | Iris test (γ = 0.01) · weighted average F1 score | 0.987 -> 1.000 | Helped | Convex Formulations for Training Two-Layer ReLU Neural Networks (ICLR 2025 · 0 citations) |
| Set b_L=64.0 instead of μP's b_L=1.0 | FashionMNIST test, batch size 1024 · accuracy | 83.21 -> 75.37 | Hurt | On the Parameterization of Second-Order Optimization Effective towards the Infinite Width (ICLR 2024 · 0 citations) |
| Add IMN to GmP | ImageNet32, batch size 1024 · top-1 validation accuracy (%) | 41.29±0.08 -> 42.70±0.15 | Helped | Neural Characteristic Activation Analysis and Geometric Parameterization for ReLU Networks (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 18 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- CIFAR-10 · 3 of 18 papers
- FashionMNIST · 3 of 18 papers
- MNIST · 2 of 18 papers
Baselines
- gradient descent · 2 of 18 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 51 papers; from OpenAlex and the papers' affiliations).
- Stanford University · 6 papers
- University of California, Los Angeles · 4 papers
- Inria · 3 papers
- Mila · 2 papers
- Concordia University · 2 papers
- Meta · 2 papers
- University of Illinois, Urbana Champaign · 2 papers
- University of California, San Diego · 2 papers
- Technion - Israel Institute of Technology · 2 papers
- The University of Hong Kong · 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
- Neural tangent kernel analysis (114 papers)
- Gradient flow and mean-field dynamics (77 papers)
- Low-rank and single-index recovery (70 papers)
- In-context learning as gradient descent (41 papers)
Elsewhere in the topic
- Edge-of-stability dynamics (116 papers)
- SGD noise and flat minima (112 papers)
- Stability-based generalization analysis (88 papers)
- Explicit and implicit regularization interplay (63 papers)
- Implicit regularization of SGD (55 papers)
- Implicit bias in linear networks (53 papers)
- Sharpness-aware minimization theory (37 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).