An Exact Poly-Time Membership-Queries Algorithm for Extraction a three-Layer ReLU Network

We consider the natural problem of learning a ReLU network from queries, which was recently remotivated by model extraction attacks. In this work, we present a polynomial-time algorithm that can learn a depth-two ReLU network from queries under mild general position assumptions. We also present a polynomial-time algorithm that, under mild general position assumptions, can learn a rich class of depth-three ReLU networks from queries. For instance, it can learn most networks where the number of first layer neurons is smaller than the dimension and the number of second layer neurons. These two results substantially improve state-of-the-art: Until our work, polynomial-time algorithms were only shown to learn from queries depth-two networks under the assumption that either the underlying distribution is Gaussian (Chen et al. (2021)) or that the weights matrix rows are linearly independent (Milli et al. (2019)). For depth three or more, there were no known poly-time results. With the growth of neural-network-based applications, many commercial companies offer machine learning services, allowing public use of trained networks as a black-box. Those networks allow the user to query the model and, in some cases, return the exact output of the network to allow the users to reason about the model's output.