Research map / Optimization / Optimizers
Adam convergence and adaptive learning rates
Analyzes Adam-family convergence and adapts learning rates using hypergradients.
78 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · 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.
15 papers in 2023–24 and 30 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 6.2% to 10.3%.
Open questions the data points to
- Papers report Adam on ImageNet val (Top-1 accuracy) anywhere from 63.79 to 72.87: 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
- 2017 · The Marginal Value of Adaptive Gradient Methods in Machine Learning (NeurIPS 2017 · 546 citations)
- 2018 · On the Convergence of Adam and Beyond (ICLR 2018 · 1,616 citations)
- 2019 · Decoupled Weight Decay Regularization (ICLR 2019 · 9,419 citations)
- 2020 · On the Variance of the Adaptive Learning Rate and Beyond (ICLR 2020 · 602 citations)
- 2021 · AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights (ICLR 2021 · 93 citations)
- 2022 · Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum (ICML 2022 · 13 citations)
- 2023 · Noise Is Not the Main Factor Behind the Gap Between Sgd and Adam on Transformers, But Sign Descent Might Be (ICLR 2023 · 5 citations)
- 2024 · Why Transformers Need Adam: A Hessian Perspective (NeurIPS 2024 · 7 citations)
- 2025 · HVAdam: A Full-Dimension Adaptive Optimizer (AAAI 2025 · 0 citations)
- 2026 · Cautious Optimizers: Improving Training with One Line of Code (ICLR 2026 · 3 citations)
Earliest papers here
- The Marginal Value of Adaptive Gradient Methods in Machine Learning (NeurIPS 2017 · 546 citations)
- Neural Taylor Approximations: Convergence and Exploration in Rectifier Networks (ICML 2017 · 5 citations)
- On the Convergence of Adam and Beyond (ICLR 2018 · 1,616 citations)
What has been tried
57 papers here report 580 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 13%, hurt 16%, 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 |
|---|---|---|---|---|
| Reduce SQL num_v from 10 to 1 | BERT and ResNet18 initialization · JS^0 estimation | No clear effect | Why Transformers Need Adam: A Hessian Perspective (NeurIPS 2024 · 7 citations) | |
| Adapt the momentum schedule on perturbation rather than gradients | SST2 · accuracy | 90.6 -> 92.1 | Helped | ZO-AdaMU Optimizer: Adapting Perturbation by the Momentum and Uncertainty in Zeroth-Order Optimization (AAAI 2024 · 5 citations) |
| Vary Adam configuration from β₁=0.0, β₂=0.0 to β₁=0.9, β₂=0.999 | DistilGPT2-ELI5-Category · agreement with the predicted optimal-learning-rate curve | No clear effect | Surge Phenomenon in Optimal Learning Rate and Batch Size Scaling (NeurIPS 2024 · 4 citations) | |
| Set weight decay to 0.05 instead of 0.1 | ImageNet ViT · test accuracy | Helped | Prodigy: An Expeditiously Adaptive Parameter-Free Learner (ICML 2024 · 3 citations) | |
| Add decorrelation by excluding the current gradient from the second-moment estimate | Toy optimization, k = 50 · convergence | Helped | ADOPT: Modified Adam Can Converge with Any $\beta_2$ with the Optimal Rate (NeurIPS 2024 · 2 citations) | |
| Increase sliding window from m=10 to m=20 | GSM-8k, LLaMA-2 7B · accuracy | 34.72% -> 35.10% | Helped | MicroAdam: Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence (NeurIPS 2024 · 1 citation) |
| add hidden vector to Adam | Penn TreeBank valid · perplexity | 85.04 -> 84.54 | Helped | HVAdam: A Full-Dimension Adaptive Optimizer (AAAI 2025 · 0 citations) |
| Add the temporal-aware threshold using second-order gradient moments instead of BSO's fixed threshold | CIFAR-100 · accuracy | 72.57 -> 74.27; 72.34 -> 73.82; 72.15 -> 73.40 | Helped | BSO: Binary Spiking Online Optimization Algorithm (ICML 2025 · 0 citations) |
| Set β₂ to 0.9 or 0.99 | OpenWebText · performance | No clear effect | Understanding Adam Requires Better Rotation Dependent Assumptions (NeurIPS 2025 · 0 citations) | |
| Use AdamE with positive λ instead of SGD | Sparse linear regression with diagonal net · training points needed for ground-truth recovery | Helped | Adam Reduces a Unique Form of Sharpness: Theoretical Insights Near the Minimizer Manifold (NeurIPS 2025 · 0 citations) | |
| Use coupled L2 regularization instead of decoupled weight decay | Convex quadratic, high-noise asymptotic · expected loss | Hurt | Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise (ICLR 2025 · 0 citations) | |
| increase weight decay lambda | toy and training loss · convergence speed | Mixed | Lion Secretly Solves a Constrained Optimization: As Lyapunov Predicts (ICLR 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 | ImageNet val | Top-1 accuracy | 63.79 – 72.87 | 2 papers, e.g. NeurIPS 2020 and AAAI 2025 |
What reviewers will expect
Datasets and baselines named in the 17 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 · 7 of 17 papers
- CIFAR-100 · 5 of 17 papers
- ImageNet-1k · 3 of 17 papers
- MNIST · 3 of 17 papers
- ImageNet · 2 of 17 papers
- Penn TreeBank · 2 of 17 papers
- Fineweb · 2 of 17 papers
- Tiny ImageNet · 2 of 17 papers
Baselines
- SGD · 7 of 17 papers
- AdamW · 7 of 17 papers
- Adam · 5 of 17 papers
- RMSProp · 4 of 17 papers
- Signum · 2 of 17 papers
- SignSGD · 2 of 17 papers
- Muon · 2 of 17 papers
- SOAP · 2 of 17 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 45 papers; from OpenAlex and the papers' affiliations).
- University of British Columbia · 3 papers
- Samsung · 3 papers
- The Chinese University of Hong Kong · 3 papers
- Zhejiang University · 3 papers
- Wuhan University · 2 papers
- Tsinghua University · 2 papers
- University of Cambridge · 2 papers
- University of California, Los Angeles · 2 papers
- Amazon · 2 papers
- Technion - Israel Institute of Technology · 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
- Memory-efficient LLM optimizers (79 papers)
- SGD momentum and step-size schedules (72 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).