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The most scalable approaches to certifying neural network robustness dependon computing sound linear lower and upper bounds for the network's activationfunctions. Current approaches are limited in that the linear bounds must behandcrafted by an expert, and can be sub-optimal, especially when the network'sarchitecture composes operations using, for example, multiplication such as inLSTMs and the recently popular Swish activation. The dependence on an expertprevents the application of robustness certification to developments in thestate-of-the-art of activation functions, and furthermore the lack of tightnessguarantees may give a false sense of insecurity about a particular model. Tothe best of our knowledge, we are the first to consider the problem ofautomatically computing tight linear bounds for arbitrary n-dimensionalactivation functions. We propose LinSyn, the first approach that achieves tightbounds for any arbitrary activation function, while only leveraging themathematical definition of the activation function itself. Our approachleverages an efficient heuristic approach to synthesize bounds that are tightand usually sound, and then verifies the soundness (and adjusts the bounds ifnecessary) using the highly optimized branch-and-bound SMT solver, dReal. Eventhough our approach depends on an SMT solver, we show that the runtime isreasonable in practice, and, compared with state of the art, our approach oftenachieves 2-5X tighter final output bounds and more than quadruple certifiedrobustness.

LinSyn: Synthesizing Tight Linear Bounds for Arbitrary Neural Network Activation Functions