Research map / Learning theory and algorithms / Combinatorial and search optimization
Semidefinite relaxations for verification
Tightens neural network verification with SDP relaxations, bound propagation and branch-and-bound.
47 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2018–2026) · an approach in Combinatorial and search optimization, keyword cluster “integer · linear · mixed”
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.
12 papers in 2023–24 and 15 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 3.5% to 4.1%.
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
- 2018 · Towards Fast Computation of Certified Robustness for ReLU Networks (ICML 2018 · 149 citations)
- 2019 · Robustness Verification of Classification Deep Neural Networks via Linear Programming (CVPR 2019 · 42 citations)
- 2020 · The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification (NeurIPS 2020 · 42 citations)
- 2021 · Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Neural Network Robustness Verification (NeurIPS 2021 · 94 citations)
- 2022 · General Cutting Planes for Bound-Propagation-Based Neural Network Verification (NeurIPS 2022 · 33 citations)
- 2023 · Neural Lyapunov Control for Discrete-Time Systems (NeurIPS 2023 · 4 citations)
- 2024 · Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planes (NeurIPS 2024 · 8 citations)
- 2025 · Dynamic Algorithm Termination for Branch-and-Bound-based Neural Network Verification (AAAI 2025 · 3 citations)
- 2026 · Expressiveness of Multi-Neuron Convex Relaxations in Neural Network Certification (ICLR 2026 · 1 citation)
Earliest papers here
- Towards Fast Computation of Certified Robustness for ReLU Networks (ICML 2018 · 149 citations)
- Robustness Verification of Classification Deep Neural Networks via Linear Programming (CVPR 2019 · 42 citations)
- Robustness Verification of Tree-based Models (NeurIPS 2019 · 38 citations)
What has been tried
34 papers here report 326 measured changes (a component added, removed or swapped, compared with a baseline): helped 71%, no clear effect 9%, hurt 17%, mixed 3%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add multi-tree search to base BICCOS | CIFAR CNN-B-Adv · Ver.% | 52.0 -> 52.5 | Helped | Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planes (NeurIPS 2024 · 8 citations) |
| Disable the heuristic and attempt to stabilise all unstable nodes at every back-substitution step | cifar biasfield, bias fields ε=6 · 10−2 · runtime | 1708 -> 1843 | Hurt | Dynamic Back-Substitution in Bound-Propagation-Based Neural Network Verification (AAAI 2025 · 3 citations) |
| Use ECLipsE-Fast's closed-form scalar identity-matrix relaxation instead of LipSDP-Layer | 20 layers · computation time (sec) | 125.05 -> 0.0515 | Helped | ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networks (NeurIPS 2024 · 2 citations) |
| Use the previous formulation that enforces the Lyapunov derivative condition over the entire region | 2D quadrotor · verification success | Hurt | Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation (ICML 2024 · 1 citation) | |
| add reordering to relaxed clipping | lsnc · subproblems | 92,402,227 -> 66,412,652 | Helped | Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verification (NeurIPS 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 9 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 · 4 of 9 papers
- CIFAR-10 · 3 of 9 papers
Baselines
- αβ-CROWN · 2 of 9 papers
- VeriNet · 2 of 9 papers
- Oval · 2 of 9 papers
- alpha-CROWN · 2 of 9 papers
- GCP-CROWN · 2 of 9 papers
- BICCOS · 2 of 9 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 27 papers; from OpenAlex and the papers' affiliations).
- University of Illinois, Urbana Champaign · 7 papers
- Imperial College London · 3 papers
- RWTH Aachen University · 3 papers
- University of Illinois at Urbana-Champaign · 3 papers
- University of Glasgow · 2 papers
- University of California, San Diego · 2 papers
- Massachusetts Institute of Technology · 2 papers
- Google · 2 papers
- UIUC · 2 papers
Use it
Download BibTeX of 38 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Predict-then-optimize learning (89 papers)
- Heuristics for integer programming (60 papers)
- Learning branch-and-cut for MILP (54 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)
- Unsupervised neural combinatorial optimization (113 papers)
- Constrained neural network optimization (111 papers)
- Decision-focused optimization (97 papers)
- Multi-objective optimization (93 papers)
- Structure and complexity of constraint reasoning (92 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).