Gradient-Regularized Out-of-Distribution Detection

One of the challenges for neural networks in real-life applications is the overconfident errors these models make when the data is not from the original training distribution. Addressing this issue is known as Out-of-Distribution (OOD) detection. Many state-of-the-art OOD methods employ an auxiliary dataset as a surrogate for OOD data during training to achieve improved performance. However, these methods fail to fully exploit the local information embedded in the auxiliary dataset. In this work, we propose the idea of leveraging the information embedded in the gradient of the loss function during training to enable the network to not only learn a desired OOD score for each sample but also to exhibit similar behavior in a local neighborhood around each sample. We also develop a novel energy-based sampling method to allow the network to be exposed to more informative OOD samples during the training phase. This is especially important when the auxiliary dataset is large. We demonstrate the effectiveness of our method through extensive experiments on several OOD benchmarks, improving the existing state-of-the-art FPR95 by 4% on our ImageNet experiment. We further provide a theoretical analysis through the lens of certified robustness and Lipschitz analysis to showcase the theoretical foundation of our work. We will publicly release our code after the review process.

ReachLipBnB: A branch-and-bound method for reachability analysis of neural autonomous systems using Lipschitz bounds

We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain directions of interest offline using a convex program. We then use these bounds to obtain an instantaneous but conservative polyhedral approximation of the reachable set using Lipschitz continuity arguments. To reduce conservatism, we incorporate our bounding algorithm within a branching strategy to decrease the over-approximation error within an arbitrary accuracy. We then extend our method to reachability analysis of control systems with neural network controllers. Finally, to capture the shape of the reachable sets as accurately as possible, we use sample trajectories to inform the directions of the reachable set over-approximations using Principal Component Analysis (PCA). We evaluate the performance of the proposed method in several open-loop and closed-loop settings.