Computation and Formal Verification of Neural Network Contraction Metrics
Bibliographic record
Abstract
A contraction metric defines a differential Lyapunov-like function that robustly captures the convergence between trajectories. In this letter, we investigate the use of neural networks for computing verifiable contraction metrics. We first prove the existence of a smooth neural network contraction metric within the domain of attraction of an exponentially stable equilibrium point. We then focus on the computation of a neural network contraction metric over a compact invariant set within the domain of attraction certified by a physics-informed neural network Lyapunov function. We consider both partial differential inequality (PDI) and equation (PDE) losses for computation. We show that sufficiently accurate neural approximate solutions to the PDI and PDE are guaranteed to be a contraction metric under mild technical assumptions. We rigorously verify the computed neural network contraction metric using a satisfiability modulo theories solver. Through numerical examples, we demonstrate that the proposed approach outperforms traditional semidefinite programming methods for finding sum-of-squares polynomial contraction metrics.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".