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Deep neural networks have been widely applied as an effective approach to handle complex and practical problems. However, one of the most fundamental open problems is the lack of formal methods to analyze the safety of their behaviors. To address this challenge, we propose a parallelizable technique to compute exact reachable sets of a neural network to an input set. Our method currently focuses on feed-forward neural networks with ReLU activation functions. One of the primary challenges for polytope-based approaches is identifying the intersection between intermediate polytopes and hyperplanes from neurons. In this regard, we present a new approach to construct the polytopes with the face lattice, a complete combinatorial structure. The correctness and performance of our methodology are evaluated by verifying the safety of ACAS Xu networks and other benchmarks. Compared to state-of-the-art methods such as Reluplex, Marabou, and NNV, our approach exhibits a significantly higher efficiency. Additionally, our approach is capable of constructing the complete input set given an output set, so that any input that leads to safety violation can be tracked.
We propose a general framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. The anticommutation relation for fermions is usually implemented to a variational wave function by the Slater determinan
Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address this challen
We study strategy synthesis for partially observable Markov decision processes (POMDPs). The particular problem is to determine strategies that provably adhere to (probabilistic) temporal logic constraints. This problem is computationally intractable
Double-stranded DNA (dsDNA) has been established as an efficient medium for charge migration, bringing it to the forefront of the field of molecular electronics as well as biological research. The charge migration rate is controlled by the electronic
Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs, computes the lowe