Robustness Verifcation in Neural Networks

Adrian Wurm

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arXiv · 2403.13441

Robustness Verifcation in Neural Networks

Adrian Wurm

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Abstract

In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in form of Linear Programming instances, one question is whether there do exist valid inputs such that the network computes a valid output? And does this property hold for all valid inputs? Do two given networks compute the same function? Is there a smaller network computing the same function? The complexity of these questions have been investigated recently from a practical point of view and approximated by heuristic algorithms. We complement these achievements by giving a theoretical framework that enables us to interchange security and efficiency questions in neural networks and analyze their computational complexities. We show that the problems are conquerable in a semi-linear setting, meaning that for piecewise linear activation functions and when the sum- or maximum metric is used, most of them are in P or in NP at most.

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Adrian Wurm. 2024-03-20. Robustness Verifcation in Neural Networks. https://arxiv.org/abs/2403.13441

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