Research map / Learning theory and algorithms / Combinatorial and search optimization
Differentiable and symbolic reasoning
Learns circuit-SAT, symbolic regression and neurosymbolic programs through differentiable approaches.
56 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Combinatorial and search optimization, keyword cluster “logic · sat · boolean”
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.
14 papers in 2023–24 and 18 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 4.0% to 5.0%.
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 · Making Neural Programming Architectures Generalize via Recursion (ICLR 2017 · 96 citations)
- 2018 · A Unified View of Piecewise Linear Neural Network Verification (NeurIPS 2018 · 133 citations)
- 2019 · Neural Logic Machines (ICLR 2019 · 45 citations)
- 2020 · AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity (NeurIPS 2020 · 85 citations)
- 2021 · Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients (ICLR 2021 · 49 citations)
- 2022 · Tractable Explanations for d-DNNF Classifiers (AAAI 2022 · 28 citations)
- 2023 · Training Fully Connected Neural Networks is $\exists\mathbb{R}$-Complete (NeurIPS 2023 · 6 citations)
- 2024 · Neural Closure Certificates (AAAI 2024 · 7 citations)
- 2025 · Dimension Reduction for Symbolic Regression (AAAI 2025 · 2 citations)
- 2026 · CAffNet: Hard Constraint-Affine Neural Networks (ICML 2026 · 0 citations)
Earliest papers here
- Making Neural Programming Architectures Generalize via Recursion (ICLR 2017 · 96 citations)
- A Unified View of Piecewise Linear Neural Network Verification (NeurIPS 2018 · 133 citations)
- Interpreting Neural Network Judgments via Minimal, Stable, and Symbolic Corrections (NeurIPS 2018 · 36 citations)
What has been tried
40 papers here report 360 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 9%, hurt 17%, 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 two hidden layers rather than one in coefficient embedding | Shape position, Q and F7, n=2 · accuracy (%) | 66.8 -> 67.2; 54.1 -> 54.3 | Helped | Learning to compute Gröbner bases (NeurIPS 2024 · 4 citations) |
| use the default (8, 5) hidden-layer configuration rather than (3, 2) | 194 hardware verification tasks · completed tasks | 25% -> 93% | Helped | Neural Model Checking (NeurIPS 2024 · 3 citations) |
| Increase beam size from 1 to 5 | Feynman · reduction rate | 0.489 -> 0.491 | No clear effect | Dimension Reduction for Symbolic Regression (AAAI 2025 · 2 citations) |
| Add SMT filtering of counterexample regions to approximation-based verification | VCAS level flight, DNC · safety verification | Helped | Provably Safe Neural Network Controllers via Differential Dynamic Logic (NeurIPS 2024 · 2 citations) | |
| set λc to 1 or 10 instead of 100 | Spacecraft Rendezvous · certification success rate | 3/3 -> 0/3 | Hurt | SEEV: Synthesis with Efficient Exact Verification for ReLU Neural Barrier Functions (NeurIPS 2024 · 2 citations) |
| Add hidden-neuron activation amplification in gamma2 | 2-SAT analysis test set, hidden layer · epsilon (prefix replaceability) | 0.249 -> 0.0128 | Helped | Validating Mechanistic Interpretations: An Axiomatic Approach (ICML 2025 · 1 citation) |
| polynomial zonotope without splitting or relaxation | MNISTFC image · verification result | 0.16s | Hurt | Exponent Relaxation of Polynomial Zonotopes and Its Applications in Formal Neural Network Verification (AAAI 2024 · 1 citation) |
| add optimal-solution supervision from small instances | MVC, larger graphs (trained on 16 nodes) · model-to-algorithm weight ratio | 0.995 ± 0.004 -> 0.943 ± 0.004 (16 nodes); 0.994 ± 0.011 -> 0.957 ± 0.002 (1024 nodes) | Helped | Primal-Dual Neural Algorithmic Reasoning (ICML 2025 · 0 citations) |
| increase sketch decomposition from dims 16 to dims 8, 2 | sum16 · accuracy | 83.52 -> 83.88 | Helped | CTSketch: Compositional Tensor Sketching for Scalable Neurosymbolic Learning (NeurIPS 2025 · 0 citations) |
| Replace MLP neurons with simple-neuron fits | Modular addition · test accuracy | 100% | No clear effect | Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks (NeurIPS 2025 · 0 citations) |
| Add alignment training before prediction training | MDLformer training-strategy ablation · RMSE | Helped | Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length (ICLR 2025 · 0 citations) | |
| increase the maximum internal irrep degree | Positivity verification equivariance tests · equivariance error | Hurt | Learning Polynomial Problems with $SL(2, \mathbb{R})$-Equivariance (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.
Datasets
- MNIST · 2 of 14 papers
Baselines
- DSR · 2 of 14 papers
- Operon · 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 32 papers; from OpenAlex and the papers' affiliations).
- Amazon · 3 papers
- Carnegie Mellon University · 2 papers
- Karlsruher Institut für Technologie · 2 papers
- Google DeepMind · 2 papers
- University of Birmingham · 2 papers
- University of London · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Logic and answer set programming theory (150 papers)
- Structure and complexity of constraint reasoning (92 papers)
- SAT and model counting solvers (89 papers)
Elsewhere in the topic
- Heuristic and local search algorithms (147 papers)
- Classical and HTN planning (145 papers)
- Unsupervised neural combinatorial optimization (113 papers)
- Constrained neural network optimization (111 papers)
- Decision-focused optimization (97 papers)
- Multi-objective optimization (93 papers)
- Predict-then-optimize learning (89 papers)
- Heuristics for integer programming (60 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).