aiqbench analysis
This research introduces a scalable reachability analysis method for neural networks by deriving provable bounds on gradient and Hessian norms using Taylor expansions and activation function transformations. The approach significantly improves verification accuracy over existing baselines while preserving local network properties, offering rigorous guarantees for safety-critical AI applications.
Provable Bounds on the Hessian of Neural Networks: Derivative-Preserving Reachability Analysis
arXiv:2406.04476v2 Announce Type: replace Abstract: We propose a novel reachability analysis method tailored for neural networks with smooth activations. Our method relies on constructing an end-to-end first-order Taylor expansion of the network and bounding the remainder. To enable this, we develop a scalable algorithm for computing closed-form bounds on both the gradient norm and Hessian norm of the network. A key component is a loop transformation of the activation functions, which leverages their monotonicity to sharpen the bounds. This yields a local abstraction that preserves the network's value and gradient at the expansion point. For larger input domains, we integrate this local model into a branch-and-bound scheme, recursively refining the overapproximation. We validate our approach through extensive experiments and demonstrate scalability and accuracy improvements over state-of-the-art verification baselines.
Abstract:We propose a novel reachability analysis method tailored for neural networks with smooth activations. Our method relies on constructing an end-to-end first-order Taylor expansion of the network and bounding the remainder. To enable this, we develop a scalable algorithm for computing closed-form bounds on both the gradient norm and Hessian norm of the network. A key component is a loop transformation of the activation functions, which leverages their monotonicity to sharpen the bounds. This yields a local abstraction that preserves the network's value and gradient at the expansion point. For larger input domains, we integrate this local model into a branch-and-bound scheme, recursively refining the overapproximation. We validate our approach through extensive experiments and demonstrate scalability and accuracy improvements over state-of-the-art verification baselines.
Machine Learning (cs.LG); Systems and Control (eess.SY)
arXiv:2406.04476 [cs.LG]
(or arXiv:2406.04476v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2406.04476 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 219 words