Efficiently Learning One Hidden Layer ReLU Networks From Queries

Model extraction attacks have renewed interest in the classic problem of learning neural networks from queries. This work gives the first polynomial-time algorithm for learning one hidden layer neural networks provided black-box access to the network. Formally, we show that if F is an arbitrary one hidden layer neural network with ReLU activations, there is an algorithm with query complexity and running time that is polynomial in all parameters that outputs a network F achieving low square loss relative to F with respect to the Gaussian measure. While a number of works in the security literature have proposed and empirically demonstrated the effectiveness of certain algorithms for this problem, ours is the first with fully polynomial-time guarantees of efficiency for worst-case networks (in particular our algorithm succeeds in the overparameterized setting).