Research map / Optimization / Optimizers
Constrained and non-backprop training
Trains networks with orthogonality constraints, growth steps, or alternating minimization instead of plain backpropagation.
97 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Optimizers, keyword cluster “differentiable · functions · loss”
State History Benchmarks Tried Baselines Checklist Preprints Who Export
Where it stands
Quiet None of the tracked benchmarks has a report from 2025–26.
16 papers in 2023–24 and 15 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 6.6% to 5.2%.
Open questions the data points to
- Papers report Unrolled–GAN on CIFAR-10 (FID) anywhere from 17.51 to 21.04: comparisons against it depend on whose number you take.
No longer reported by papers here: CIFAR-10 (accuracy, last in 2022); CIFAR-10 (FID, last in 2022).
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 · Training Neural Networks Without Gradients: A Scalable ADMM Approach (ICML 2016 · 140 citations)
- 2017 · GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium (NeurIPS 2017 · 4,380 citations)
- 2018 · Which Training Methods for GANs do actually Converge? (ICML 2018 · 814 citations)
- 2019 · Deep Leakage from Gradients (NeurIPS 2019 · 1,528 citations)
- 2020 · Estimating Training Data Influence by Tracing Gradient Descent (NeurIPS 2020 · 119 citations)
- 2021 · Deep Gradient Projection Networks for Pan-sharpening (CVPR 2021 · 233 citations)
- 2022 · Deep Generalized Unfolding Networks for Image Restoration (CVPR 2022 · 287 citations)
- 2023 · Plateau-Reduced Differentiable Path Tracing (CVPR 2023 · 17 citations)
- 2024 · EG-NAS: Neural Architecture Search with Fast Evolutionary Exploration (AAAI 2024 · 19 citations)
- 2025 · Towards Stable and Storage-efficient Dataset Distillation: Matching Convexified Trajectory (CVPR 2025 · 4 citations)
- 2026 · Mitigating Gradient Pathology in PINNs through Aligned Constraint (ICML 2026 · 0 citations)
Earliest papers here
- Training Neural Networks Without Gradients: A Scalable ADMM Approach (ICML 2016 · 140 citations)
- Noisy Activation Functions (ICML 2016 · 81 citations)
- GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium (NeurIPS 2017 · 4,380 citations)
Benchmark records
The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.
CIFAR-10 · accuracy (higher is better)
4 papers, 2021–2022 · not reported since 2022
| Year | Best so far | Set by |
|---|---|---|
| 2021 | 95 | On Training Implicit Models (NeurIPS 2021 · 12 citations) |
| 2022 | 96.51 | Feedback Gradient Descent: Efficient and Stable Optimization with Orthogonality for DNNs (AAAI 2022 · 3 citations) |
CIFAR-10 · FID (lower is better)
4 papers, 2017–2022 · not reported since 2022
| Year | Best so far | Set by |
|---|---|---|
| 2017 | 24.8 | GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium (NeurIPS 2017 · 4,380 citations) |
| 2021 | 12.19 | Taming GANs with Lookahead-Minmax (ICLR 2021 · 4 citations) |
| 2022 | 10.17 | Recursive Reasoning in Minimax Games: A Level $k$ Gradient Play Method (NeurIPS 2022 · 1 citation) |
What has been tried
84 papers here report 817 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 10%, hurt 20%, 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 |
|---|---|---|---|---|
| Use the compound fitness function with both performance loss L1 and similarity term L2 instead of either term alone | CIFAR-10 search phase · valid accuracy | Helped | EG-NAS: Neural Architecture Search with Fast Evolutionary Exploration (AAAI 2024 · 19 citations) | |
| Add probabilistic hard margin | UBC PhotoTour · FPR@95 (%) | about 0.18 | Helped | SDGMNet: Statistic-Based Dynamic Gradient Modulation for Local Descriptor Learning (AAAI 2024 · 6 citations) |
| add continuous sampling | CIFAR-10, ipc=10 · accuracy | 54.8±0.2 -> 56.2±0.3; 60.6±0.2 -> 61.3±0.5; 61.5±0.3 -> 61.8±0.6; 62.3±0.3 -> 62.8±0.3; 62.1±0.4 -> 62.8±0.2 | Helped | Towards Stable and Storage-efficient Dataset Distillation: Matching Convexified Trajectory (CVPR 2025 · 4 citations) |
| remove ensembling and use a single network | OpenML CC-18 small · normalized AUC | 0.780±0.037 -> 0.716±0.026 | Hurt | MotherNet: Fast Training and Inference via Hyper-Network Transformers (ICLR 2025 · 1 citation) |
| Train using 8-frame batch optimization rather than 15-frame streaming sequences | TartanAir validation split evaluated in streaming setting · ATE | No clear effect | From Variance to Veracity: Unbundling and Mitigating Gradient Variance in Differentiable Bundle Adjustment Layers (CVPR 2024 · 1 citation) | |
| Add constant-norm input encoding | Scale-Space HN on OASIS and Bayesian NN on OxfordFlowers-102 · accuracy / Dice | Helped | Magnitude Invariant Parametrizations Improve Hypernetwork Learning (ICLR 2024 · 1 citation) | |
| use Mamba instead of LSTM as the slow-net | CIFAR-10, ResNet-44 · test accuracy (%) | 92.07 ± 0.066 -> 92.63 ± 0.052 | Helped | Fast and Slow Gradient Approximation for Binary Neural Network Optimization (AAAI 2025 · 0 citations) |
| add full balance before training | MNIST test · accuracy | 90.1% -> 91.2% | Helped | Improving Deep Learning Speed and Performance Through Synaptic Neural Balance (AAAI 2025 · 0 citations) |
| Use ResNet instead of ICNN for DLT approximation | Multidimensional conjugate approximation · approximation error | Helped | Deep Legendre Transform (NeurIPS 2025 · 0 citations) | |
| add periodic projection every 10 iterations | Random target quaternion states · quaternion weight structure | Helped | Asymptotically Stable Quaternion-valued Hopfield-structured Neural Network with Periodic Projection-based Supervised Learning Rules (NeurIPS 2025 · 0 citations) | |
| Increase the mixing coefficient γ from 0 to 0.1 | CIFAR10/CIFAR100 ResNet training · test accuracy | Helped | Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functions (NeurIPS 2025 · 0 citations) | |
| Set Highway-BP iterations to k=0 | CIFAR10 · accuracy | 85% | Helped | Accelerated training through iterative gradient propagation along the residual path (ICLR 2025 · 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 |
|---|---|---|---|---|
| Unrolled–GAN | CIFAR-10 | FID | 17.51 – 21.04 | 2 papers, e.g. NeurIPS 2022 and ICLR 2021 |
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 · 4 of 11 papers
- CIFAR-100 · 3 of 11 papers
- MNIST · 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 31 papers; from OpenAlex and the papers' affiliations).
- Harbin 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
- Differentiating through embedded optimization (117 papers)
- Surrogate losses and robust solvers (119 papers)
- Randomized gradient estimation (77 papers)
- Multi-objective gradient methods (28 papers)
Elsewhere in the topic
- Stochastic gradient MCMC (142 papers)
- Memory-efficient LLM optimizers (79 papers)
- Adam convergence and adaptive learning rates (78 papers)
- Natural gradient and Fisher approximations (77 papers)
- SGD momentum and step-size schedules (72 papers)
- Second-order and structured preconditioning (70 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).