arXiv:2411.18235v3 Announce Type: replace-cross Abstract: We study the problem of learning verifiably Lyapunov-stable neural controllers that provably satisfy the Lyapunov asymptotic stability condition within a region-of-attraction (ROA). Unlike previous works that adopted counterexample-guided training without considering the computation of verification in training, we introduce Certified Training with Branch-and-Bound (CT-BaB), a new certified training framework that optimizes certified bounds, thereby reducing the discrepancy between training and test-time verification that also computes certified bounds. To achieve a relatively global guarantee on an entire input region-of-interest, we propose a training-time BaB technique that maintains a dynamic training dataset and adaptively splits hard input subregions into smaller ones, to tighten certified bounds and ease the training. Meanwhile, subregions created by the training-time BaB also inform test-time verification, for a more efficient training-aware verification. We demonstrate that CT-BaB yields verification-friendly models that can be more efficiently verified at test time while achieving stronger verifiable guarantees with larger ROA. On the largest output-feedback 2D Quadrotor system experimented, CT-BaB reduces verification time by over 11X relative to the previous state-of-the-art baseline using Counterexample Guided Inductive Synthesis (CEGIS), while achieving 164X larger ROA. Code is available at https://github.com/shizhouxing/CT-BaB.

arXiv:2603.02235v1 Announce Type: cross Abstract: Neural network verification tools currently support only a narrow class of specifications, typically expressed as low-level constraints over raw inputs and outputs. This limitation significantly hinders their adoption and practical applicability across diverse application domains where correctness requirements are naturally expressed at a higher semantic level. This challenge is rooted in the inherent nature of deep neural networks, which learn internal representations that lack an explicit mapping to human-understandable features. To address this, we bridge this gap by introducing a novel component to the verification pipeline, making existing verification tools applicable to a broader range of domains and specification styles. Our framework enables users to formulate specifications in natural language, which are then automatically analyzed and translated into formal verification queries compatible with state-of-the-art neural network verifiers. We evaluate our approach on both structured and unstructured datasets, demonstrating that it successfully verifies complex semantic specifications that were previously inaccessible. Our results show that this translation process maintains high fidelity to user intent while incurring low computational overhead, thereby substantially extending the applicability of formal DNN verification to real-world, high-level requirements.