Research map / Optimization / Implicit bias and generalization
Implicit bias in linear networks
Characterizes the max-margin-like solutions gradient flow selects in linear and separable classification settings.
53 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2018–2026) · an approach in Implicit bias and generalization, keyword cluster “implicit bias · regularization · bias gradient”
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.
14 papers in 2023–24 and 18 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 6.0% to 6.9%.
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
- 2018 · Characterizing Implicit Bias in Terms of Optimization Geometry (ICML 2018 · 168 citations)
- 2019 · The Implicit Bias of AdaGrad on Separable Data (NeurIPS 2019 · 5 citations)
- 2020 · Implicit Bias of Gradient Descent based Adversarial Training on Separable Data (ICLR 2020 · 21 citations)
- 2021 · A unifying view on implicit bias in training linear neural networks (ICLR 2021 · 27 citations)
- 2022 · Implicit Bias of Gradient Descent on Reparametrized Models: On Equivalence to Mirror Descent (NeurIPS 2022 · 2 citations)
- 2023 · Implicit Bias in Leaky ReLU Networks Trained on High-Dimensional Data (ICLR 2023 · 5 citations)
- 2024 · Beyond Implicit Bias: The Insignificance of SGD Noise in Online Learning (ICML 2024 · 1 citation)
- 2025 · Effects of Momentum in Implicit Bias of Gradient Flow for Diagonal Linear Networks (AAAI 2025 · 0 citations)
- 2026 · The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks (ICML 2026 · 0 citations)
Earliest papers here
- Characterizing Implicit Bias in Terms of Optimization Geometry (ICML 2018 · 168 citations)
- Implicit Bias of Gradient Descent on Linear Convolutional Networks (NeurIPS 2018 · 35 citations)
- The Implicit Bias of Gradient Descent on Separable Data (ICLR 2018 · 15 citations)
What has been tried
33 papers here report 218 measured changes (a component added, removed or swapped, compared with a baseline): helped 56%, no clear effect 11%, hurt 21%, mixed 11%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Increase batch size from 32 to 512 during training | CIFAR-5m online · loss trajectory alignment | Helped | Beyond Implicit Bias: The Insignificance of SGD Noise in Online Learning (ICML 2024 · 1 citation) | |
| Decrease the dataset scaling ε | Sparse regression with unbiased initialization · squared parameter distance to ground truth | Helped | Effects of Momentum in Implicit Bias of Gradient Flow for Diagonal Linear Networks (AAAI 2025 · 0 citations) | |
| vary the unscaled potential among x^2, |x|^3 + x^2, and x^4 + x^2 | common data set · implicit bias | No clear effect | Implicit Bias of Mirror Flow for Shallow Neural Networks in Univariate Regression (ICLR 2025 · 0 citations) | |
| Increase the number of training samples (n=1000, 10000, 50000) | Synthetic multi-cluster dataset · feature averaging | No clear effect | Feature Averaging: An Implicit Bias of Gradient Descent Leading to Non-Robustness in Neural Networks (ICLR 2025 · 0 citations) | |
| Incrementally increase sampling ratio and interval | Kodak (8 representative images) · Time (s) | 345.22 -> 211.04 | Helped | Nonparametric Teaching of Implicit Neural Representations (ICML 2024 · 0 citations) |
| Replace the identity cost matrix with a diagonal Q having only q1 positive | Unseen initial states · extrapolation | zero Q-optimality and cost measures | Helped | Implicit Bias of Policy Gradient in Linear Quadratic Control: Extrapolation to Unseen Initial States (ICML 2024 · 0 citations) |
| Increase network width | MNIST and CIFAR10, low-sample binary classification · test accuracy | Helped | Bias of Stochastic Gradient Descent or the Architecture: Disentangling the Effects of Overparameterization of Neural Networks (ICML 2024 · 0 citations) | |
| Increase co-correlation from 0.25 to 0.83 by altering weight initialization | MNIST test set · accuracy | 0.93 to 0.68 | Hurt | The Implicit Bias of Gradient Descent toward Collaboration between Layers: A Dynamic Analysis of Multilayer Perceptions (NeurIPS 2024 · 0 citations) |
| Increase environment heterogeneity | Matrix sensing simulation · Signal recovery proportion | Helped | The Implicit Bias of Heterogeneity towards Invariance: A Study of Multi-Environment Matrix Sensing (NeurIPS 2024 · 0 citations) | |
| Add stability constant ε = 10^{-8} to Adam | Synthetic separable data (logistic loss) · normalized ℓ∞-margin | No clear effect | The Implicit Bias of Adam on Separable Data (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 10 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 · 2 of 10 papers
- MNIST · 2 of 10 papers
Baselines
- gradient descent · 2 of 10 papers
- gradient flow · 2 of 10 papers
- signGD · 2 of 10 papers
- Adam · 2 of 10 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 32 papers; from OpenAlex and the papers' affiliations).
- University of Southampton · 2 papers
- University of California, Berkeley · 2 papers
- The University of Hong Kong · 2 papers
- Princeton 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
- Explicit and implicit regularization interplay (63 papers)
- Implicit regularization of SGD (55 papers)
Elsewhere in the topic
- Shallow ReLU network convergence (132 papers)
- Edge-of-stability dynamics (116 papers)
- Neural tangent kernel analysis (114 papers)
- SGD noise and flat minima (112 papers)
- Stability-based generalization analysis (88 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)
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).