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This paper is concerned with the computation of the local Lipschitz constantof feedforward neural networks (FNNs) with activation functions being rectifiedlinear units (ReLUs). The local Lipschitz constant of an FNN for a target inputis a reasonable measure for its quantitative evaluation of the reliability. Byfollowing a standard procedure using multipliers that capture the behavior ofReLUs,we first reduce the upper bound computation problem of the localLipschitz constant into a semidefinite programming problem (SDP). Here we newlyintroduce copositive multipliers to capture the ReLU behavior accurately. Then,by considering the dual of the SDP for the upper bound computation, we secondderive a viable test to conclude the exactness of the computed upper bound.However, these SDPs are intractable for practical FNNs with hundreds of ReLUs.To address this issue, we further propose a method to construct a reduced ordermodel whose input-output property is identical to the original FNN over aneighborhood of the target input. We finally illustrate the effectiveness ofthe model reduction and exactness verification methods with numerical examplesof practical FNNs.

Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification