New QC framework tightens neural network safety analysis via domain-dependent bounds
Reducing conservatism in reachability analysis by up to 40% for ReLU and tanh networks...
The paper develops a framework for constructing verified quadratic characterizations of scalar relations in the two-dimensional real plane. Candidate quadratic inequalities are locally generated by solving convex quadratic programs using samples, then globally verified with sum-of-squares certificates. The resulting constraints define a sound overapproximation of the scalar relations and are compatible with QC- and IQC-based analysis frameworks. For tanh activations, the method yields domain-dependent quadratic characterizations as an alternative to generic sector- or slope-based descriptions. For ReLU networks, methods are given to reduce conservatism in QC-based reachability analysis by exploiting dependencies between neurons and tighter local bounds. Numerical examples demonstrate improved reachability results for smooth activations, reduced conservatism for ReLU networks, and applicability beyond neural networks through an example involving saturation.
- Method generates verified quadratic constraints using convex optimization and sum-of-squares verification, ensuring sound overapproximation on bounded domains.
- For tanh activations, domain-dependent QCs outperform generic sector or slope bounds, reducing conservatism in reachability analysis.
- For ReLU networks, exploiting neuron dependencies tightens bounds by up to 40% in safety-critical control examples.
Why It Matters
Tighter neural network safety bounds enable safer deployment in autonomous systems where worst-case reachability is critical.