Computation and Formal Verification of Neural Network Contraction Metrics
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it