Research map / Optimization / Implicit bias and generalization
Implicit regularization of SGD
Analyzes implicit regularization from SGD in least squares, matrix factorization, and diagonal networks.
55 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · 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.
12 papers in 2023–24 and 15 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 5.1% to 5.7%.
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 · Generalization Properties and Implicit Regularization for Multiple Passes SGM (ICML 2016 · 45 citations)
- 2017 · Implicit Regularization in Matrix Factorization (NeurIPS 2017 · 135 citations)
- 2018 · Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval and Matrix Completion (ICML 2018 · 62 citations)
- 2019 · Learning-to-Learn Stochastic Gradient Descent with Biased Regularization (ICML 2019 · 40 citations)
- 2020 · The Implicit Regularization of Stochastic Gradient Flow for Least Squares (ICML 2020 · 34 citations)
- 2021 · On the Origin of Implicit Regularization in Stochastic Gradient Descent (ICLR 2021 · 39 citations)
- 2022 · Stochastic Training is Not Necessary for Generalization (ICLR 2022 · 6 citations)
- 2023 · (S)GD over Diagonal Linear Networks: Implicit bias, Large Stepsizes and Edge of Stability (NeurIPS 2023 · 2 citations)
- 2024 · Achieving Margin Maximization Exponentially Fast via Progressive Norm Rescaling (ICML 2024 · 0 citations)
- 2025 · Convergence Analysis of Federated Learning Methods Using Backward Error Analysis (AAAI 2025 · 2 citations)
- 2026 · Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration (ICML 2026 · 0 citations)
Earliest papers here
- Generalization Properties and Implicit Regularization for Multiple Passes SGM (ICML 2016 · 45 citations)
- Implicit Regularization in Matrix Factorization (NeurIPS 2017 · 135 citations)
- Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval and Matrix Completion (ICML 2018 · 62 citations)
What has been tried
43 papers here report 312 measured changes (a component added, removed or swapped, compared with a baseline): helped 62%, no clear effect 9%, hurt 22%, 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 |
|---|---|---|---|---|
| remove the dispersion term from FedAvg | MNIST and FEMNIST · test accuracy | Helped | Convergence Analysis of Federated Learning Methods Using Backward Error Analysis (AAAI 2025 · 2 citations) | |
| Use reg-SGD with the theoretically optimal schedules (p=1/3, q=2/3) instead of the more aggressive schedules (p=q=2/3) | X-ray tomography · convergence to the minimum-norm solution | Helped | Controlling the Flow: Stability and Convergence for Stochastic Gradient Descent with Decaying Regularization (NeurIPS 2025 · 2 citations) | |
| Use polynomially increasing rather than exponentially increasing progressive radii | Synthetic linearly separable datasets · margin gap | Mixed | Achieving Margin Maximization Exponentially Fast via Progressive Norm Rescaling (ICML 2024 · 0 citations) | |
| Increase initialization scale | Sparse linear regression · statistical error | Hurt | Implicit Regularization of Decentralized Gradient Descent for Sparse Regression (NeurIPS 2024 · 0 citations) | |
| Replace softmax attention with BaseConv and train end-to-end | Least squares, end-to-end · MSE | 100\times worse | Hurt | Towards Learning High-Precision Least Squares Algorithms with Sequence Models (ICLR 2025) |
What reviewers will expect
Datasets and baselines named in the 11 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 11 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 27 papers; from OpenAlex and the papers' affiliations).
- Peking University · 3 papers
- Seoul National University · 2 papers
- Princeton University · 2 papers
- Michigan State University · 2 papers
- New York University · 2 papers
- Meta · 2 papers
- Technische Universität München · 2 papers
- University of California, Berkeley · 2 papers
- Korea Advanced Institute of Science and Technology · 2 papers
Use it
Download BibTeX of 37 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 bias in linear networks (53 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).