Research map / Optimization / Optimizers
SGD momentum and step-size schedules
Studies momentum, batch size, and step-size schedules for stochastic gradient descent.
72 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Optimizers, keyword cluster “adaptive · optimizers · momentum”
State History Tried Baselines 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.
8 papers in 2023–24 and 21 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 3.3% to 7.2%.
Open questions the data points to
- Papers report Adam on Penn Treebank LSTM (test perplexity) anywhere from 57.83 to 66.67: comparisons against it depend on whose number you take.
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 · Barzilai-Borwein Step Size for Stochastic Gradient Descent (NeurIPS 2016 · 131 citations)
- 2017 · Stochastic Adaptive Quasi-Newton Methods for Minimizing Expected Values (ICML 2017 · 23 citations)
- 2018 · Don't Decay the Learning Rate, Increase the Batch Size (ICLR 2018 · 590 citations)
- 2019 · Quasi-hyperbolic momentum and Adam for deep learning (ICLR 2019 · 87 citations)
- 2020 · Accelerating SGD with momentum for over-parameterized learning (ICLR 2020 · 46 citations)
- 2021 · Multiplicative Noise and Heavy Tails in Stochastic Optimization (ICML 2021 · 30 citations)
- 2022 · On the SDEs and Scaling Rules for Adaptive Gradient Algorithms (NeurIPS 2022 · 5 citations)
- 2023 · Generalized Polyak Step Size for First Order Optimization with Momentum (ICML 2023 · 3 citations)
- 2024 · On the Convergence of Loss and Uncertainty-based Active Learning Algorithms (NeurIPS 2024 · 3 citations)
- 2025 · Enhancing Optimizer Stability: Momentum Adaptation of The NGN Step-size (NeurIPS 2025 · 0 citations)
- 2026 · Adaptive Momentum and Nonlinear Damping for Neural Network Training (ICML 2026 · 0 citations)
Earliest papers here
- Barzilai-Borwein Step Size for Stochastic Gradient Descent (NeurIPS 2016 · 131 citations)
- Learning Step Size Controllers for Robust Neural Network Training (AAAI 2016 · 74 citations)
- Starting Small - Learning with Adaptive Sample Sizes (ICML 2016 · 13 citations)
What has been tried
52 papers here report 461 measured changes (a component added, removed or swapped, compared with a baseline): helped 58%, no clear effect 18%, hurt 17%, 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 |
|---|---|---|---|---|
| Use larger SVAG noise-scale multiplier ℓ | CIFAR-10, batch size B=512 · test performance | No clear effect | The Marginal Value of Momentum for Small Learning Rate SGD (ICLR 2024 · 1 citation) | |
| use NGN-M version 1 instead of version 2 | Diabetes quadratic · convergence | Helped | Enhancing Optimizer Stability: Momentum Adaptation of The NGN Step-size (NeurIPS 2025 · 0 citations) | |
| use a nonzero gradient shift a instead of a=0 | quadratic problems with mini-batch noise · loss convergence | No clear effect | SGD with memory: fundamental properties and stochastic acceleration (ICLR 2025 · 0 citations) | |
| Update the learning rate every Φ>1 iterations (lazy update) | Convergence (experiments across tasks) · convergence | No clear effect | Gradient descent with generalized Newton’s method (ICLR 2025 · 0 citations) | |
| Increase AdamW beta1 above 0.9, including with a scheduler | 110M LLM training · performance | No clear effect | The AdEMAMix Optimizer: Better, Faster, Older (ICLR 2025 · 0 citations) | |
| Move the MomDecSPS correcting factor 1−β outside the minimum | Experiments reported in the paper · practical performance | Hurt | Stochastic Polyak Step-sizes and Momentum: Convergence Guarantees and Practical Performance (ICLR 2025 · 0 citations) | |
| Use increasing low-pass momentum instead of decreasing low-pass momentum | CIFAR-100 · Top-1 accuracy | 69.69\textsubscript{0.75} -> 77.12\textsubscript{0.07} | Helped | On the Performance Analysis of Momentum Method: A Frequency Domain Perspective (ICLR 2025 · 0 citations) |
| Use lower bound 0 instead of an informative lower bound | ImageNet32 · validation accuracy | No clear effect | MoMo: Momentum Models for Adaptive Learning Rates (ICML 2024 · 0 citations) |
Baseline numbers that disagree
The same baseline on the same benchmark and metric, reported more than 5% apart by different papers here. Training budgets, data splits and reimplementations differ, so state which number you compare with.
| Baseline | Benchmark | Metric | Reported | Papers |
|---|---|---|---|---|
| Adam | Penn Treebank LSTM | test perplexity | 57.83 – 66.67 | 2 papers, e.g. ICLR 2019 and ICML 2021 |
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
- CIFAR10 · 4 of 10 papers
- CIFAR100 · 4 of 10 papers
- ImageNet1k · 2 of 10 papers
Baselines
- Adam · 3 of 10 papers
- ALR-SMAG · 2 of 10 papers
- AdamW · 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 29 papers; from OpenAlex and the papers' affiliations).
- Meta · 2 papers
Use it
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Related approaches
Same keyword cluster
- Adam convergence and adaptive learning rates (78 papers)
- Memory-efficient LLM optimizers (79 papers)
- Second-order and structured preconditioning (70 papers)
Elsewhere in the topic
- Stochastic gradient MCMC (142 papers)
- Surrogate losses and robust solvers (119 papers)
- Differentiating through embedded optimization (117 papers)
- Constrained and non-backprop training (97 papers)
- Natural gradient and Fisher approximations (77 papers)
- Randomized gradient estimation (77 papers)
- Stein variational gradient descent (47 papers)
- Gradient-based meta-learning theory (40 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).