Quadratic Characterizations for Reachability Analysis of Neural Networks
Read the original on arXiv Machine Learning →The paper introduces a framework for constructing verified quadratic characterizations of scalar relations in two-dimensional space, using convex quadratic programs and sum-of-squares certificates to generate locally valid inequalities that are globally verified. These constraints provide sound overapproximations compatible with existing QC and IQC analysis tools, and can be embedded in semidefinite programs for reachability and safety analysis of feedforward neural networks. The method improves reachability results for smooth activations like tanh, reduces conservatism for ReLU networks by exploiting neuron dependencies, and extends beyond neural networks to other nonlinear systems such as saturation.
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