Formal verification of neural networks is essential before their deployment in safety-critical applications. However, existing methods for formally verifying neural networks are not yet scalable enough to handle practical problems involving a large number of neurons. We address this challenge by introducing a fully automatic and sound reduction of neural networks using reachability analysis. The soundness ensures that the verification of the reduced network entails the verification of the original network. To the best of our knowledge, we present the first sound reduction approach that is applicable to neural networks with any type of element-wise activation function, such as ReLU, sigmoid, and tanh. The network reduction is computed on the fly while simultaneously verifying the original network and its specifications. All parameters are automatically tuned to minimize the network size without compromising verifiability. We further show the applicability of our approach to convolutional neural networks by explicitly exploiting similar neighboring pixels. Our evaluation shows that our approach can reduce the number of neurons to a fraction of the original number of neurons with minor outer-approximation and thus reduce the verification time to a similar degree.

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