Research map / Learning theory and algorithms / Combinatorial and search optimization
Constrained neural network optimization
Embeds linear or orthogonal constraints into network layers and analyzes constrained training and routing.
111 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Combinatorial and search optimization, keyword cluster “objective · multi · solutions”
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.
29 papers in 2023–24 and 24 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 8.4% to 6.6%.
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 · Derivative-Free Optimization via Classification (AAAI 2016 · 86 citations)
- 2017 · Hyperband: Bandit-Based Configuration Evaluation for Hyperparameter Optimization (ICLR 2017 · 79 citations)
- 2018 · A Constrained Deep Neural Network for Ordinal Regression (CVPR 2018 · 71 citations)
- 2019 · Neural Lyapunov Control (NeurIPS 2019 · 130 citations)
- 2020 · Augmenting Genetic Algorithms with Deep Neural Networks for Exploring the Chemical Space (ICLR 2020 · 111 citations)
- 2021 · DC3: A learning method for optimization with hard constraints (ICLR 2021 · 68 citations)
- 2022 · Do Current Multi-Task Optimization Methods in Deep Learning Even Help? (NeurIPS 2022 · 17 citations)
- 2023 · Constrained Efficient Global Optimization of Expensive Black-box Functions (ICML 2023 · 11 citations)
- 2024 · Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification (ICML 2024 · 10 citations)
- 2025 · A Hybrid Framework for Airfoil Optimization: Combining PINNs and Genetic Algorithm (Student Abstract) (AAAI 2025 · 1 citation)
- 2026 · Position: Adopt Constraints Over Fixed Penalties in Deep Learning (NeurIPS 2026 · 1 citation)
Earliest papers here
- Derivative-Free Optimization via Classification (AAAI 2016 · 86 citations)
- Identifying Sentiment Words Using an Optimization Model with L1 Regularization (AAAI 2016 · 8 citations)
- Hyperband: Bandit-Based Configuration Evaluation for Hyperparameter Optimization (ICLR 2017 · 79 citations)
What has been tried
87 papers here report 762 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 10%, hurt 18%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| increase ELM-PI hidden units to m=3200 or m=6400 | Synthetic n=4 nonlinear control · maximum testing error | 10^{-3}; 10^{-5} | Helped | Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification (ICML 2024 · 10 citations) |
| Add tanh pre-activation before each forward FFT | Mixed-precision FNO training · numerical stability | Helped | Guaranteed Approximation Bounds for Mixed-Precision Neural Operators (ICLR 2024 · 4 citations) | |
| Use the diagonal Jacobian approximation rather than the exact Jacobian | General nonlinear RNN evaluation · Newton iterations to convergence | approximately 2 times more Newton iterations | Hurt | Towards Scalable and Stable Parallelization of Nonlinear RNNs (NeurIPS 2024 · 2 citations) |
| remove all discrete bottlenecks | SALSA-CLRS BFS, size 1600 · graph-level accuracy | 100. -> 0.0 | Hurt | Discrete Neural Algorithmic Reasoning (ICML 2025 · 1 citation) |
| add task-network pre-training on the safe network output | Portfolio optimization · Optimality Gap | 3.14(6.36) -> 2.35(6.37) | Helped | Enforcing Hard Linear Constraints in Deep Learning Models with Decision Rules (NeurIPS 2025 · 1 citation) |
| use ASMCVaR with m=15 instead of m=10 | FF25EU · final cumulative wealth | 122.82 -> 123.13 | Helped | Autonomous Sparse Mean-CVaR Portfolio Optimization (ICML 2024 · 1 citation) |
| Using CP formulation instead of MILP (Gurobi) for no-bagging reconstruction | COMPAS, no bagging, max depth None · average reconstruction time (s) | 49.7 s (CP) vs 188.3 s (MILP) | Helped | Trained Random Forests Completely Reveal your Dataset (ICML 2024 · 1 citation) |
| Extend testing DVN depth from 40 to 300 | B2500(10) · GAP (%) | 0.362 -> 0.034 | Helped | Learning to Solve Quadratic Unconstrained Binary Optimization in a Classification Way (NeurIPS 2024 · 1 citation) |
| Increase the sparsity cap from m=10 to m=15 | FF25, T=60 · Sharpe ratio | 0.2481 -> 0.2481 | No clear effect | A Globally Optimal Portfolio for m-Sparse Sharpe Ratio Maximization (NeurIPS 2024 · 1 citation) |
| Add orthogonal scratchpad transformations | TSP · mean tour length | Helped | Rethinking Deep Thinking: Stable Learning of Algorithms using Lipschitz Constraints (NeurIPS 2024 · 1 citation) | |
| Set event loss weight $\lambda_2$ to 0.005 rather than the Neural ETC-PI reference 0.05 | Lorenz · Triggering times | {29} -> 114 | Hurt | Neural Event-Triggered Control with Optimal Scheduling (ICML 2025 · 0 citations) |
| Increase parametrization richness | COMPAS · maximum constraint violation | Helped | Near-Optimal Solutions of Constrained Learning Problems (ICLR 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 14 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- OSQP · 2 of 14 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 53 papers; from OpenAlex and the papers' affiliations).
- Massachusetts Institute of Technology · 4 papers
- University of Waterloo · 3 papers
- City University of Hong Kong · 3 papers
- California Institute of Technology · 2 papers
- Carnegie Mellon University · 2 papers
- University of Toronto · 2 papers
- Polytechnique Montreal · 2 papers
- Universität Stuttgart · 2 papers
- University of Pennsylvania · 2 papers
- University of Texas, Austin · 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
- Unsupervised neural combinatorial optimization (113 papers)
- Decision-focused optimization (97 papers)
- Multi-objective optimization (93 papers)
- Globally optimal geometric optimization (56 papers)
Elsewhere in the topic
- Logic and answer set programming theory (150 papers)
- Heuristic and local search algorithms (147 papers)
- Classical and HTN planning (145 papers)
- Structure and complexity of constraint reasoning (92 papers)
- Predict-then-optimize learning (89 papers)
- SAT and model counting solvers (89 papers)
- Heuristics for integer programming (60 papers)
- Differentiable and symbolic reasoning (56 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).