No abstract

No abstract

No abstract

Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising alternative. However, even for reasonably-sized neural networks, these relaxations are not tractable, and so must be replaced by even weaker relaxations in practice. In this work, we propose a novel operator splitting method that can directly solve a convex relaxation of the problem to high accuracy, by splitting it into smaller sub-problems that often have analytical solutions. The method is modular, scales to very large problem instances, and compromises of operations that are amenable to fast parallelization with GPU acceleration. We demonstrate our method in bounding the worst-case performance of large convolutional networks in image classification and reinforcement learning settings, and in reachability analysis of neural network dynamical systems.

Motivated by problems such as molecular energy prediction, we derive an (improper) kernel between geometric inputs, that is able to capture the relevant rotational and translation invariances in geometric data. Since many physical simulations based upon geometric data produce derivatives of the output quantity with respect to the input positions, we derive an approach that incorporates derivative information into our kernel learning. We further show how to exploit the low rank structure of the resulting kernel matrices to speed up learning. Finally, we evaluated the method in the context of molecular energy prediction, showing good performance for modeling previously unseen molecular configurations. Integrating the approach into a Bayesian optimization, we show substantial improvement over the state of the art in molecular energy optimization.