Enhancing Linear Bound Tightness in Neural Network Verification via Sampling-Based Underestimation
Keywords: Formal Verification of Neural Networks; Probabilistic approaches; Linear Relaxation-Based Perturbation Analysis
Abstract: We present $\texttt{PT-LiRPA}$ (Probabilistically Tightened LiRPA), a novel approach that enhances existing linear relaxation-based perturbation analysis (LiRPA) methods for neural network verification. $\texttt{PT-LiRPA}$ combines LiRPA approaches with a sampling-based underestimation technique to compute probabilistically optimal intermediate bounds, resulting in tighter linear lower and upper bounds. Notably, we show that this approach preserves the soundness of verification results while significantly tightening the bounds for generic non-linear functions. Additionally, we introduce a new metric, $\Delta^*$, to quantify the tightness for LiRPA bounds and to bound the magnitude of the possible error in the sample-based overestimation, thus complementing the probabilistic bound of statistical results we use. Our empirical evaluation, conducted on several state-of-the-art benchmarks, including those from the International Verification of Neural Networks Competition, demonstrates that $\texttt{PT-LiRPA}$ achieves higher or comparable verified accuracy with lower verification times. The significantly tighter bounds and better efficiency allow us to verify instances where state-of-the-art methods could not provide a specific answer.
Supplementary Material: zip
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 10070
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