Ensuring safety in autonomous systems with vision-based control remains a critical challenge due to the high dimensionality of image inputs and the fact that the relationship between true system state and its visual manifestation is unknown. Existing methods for learning-based control in such settings typically lack formal safety guarantees. To address this challenge, we introduce a novel semi-probabilistic verification framework that integrates reachability analysis with conditional generative networks and distribution-free tail bounds to enable efficient and scalable verification of vision-based neural network controllers. Next, we develop a gradient-based training approach that employs a novel safety loss function, safety-aware data-sampling strategy to efficiently select and store critical training examples, and curriculum learning, to efficiently synthesize safe controllers in the semi-probabilistic framework. Empirical evaluations in X-Plane 11 airplane landing simulation, CARLA-simulated autonomous lane following, F1Tenth vehicle lane following in a physical visually-rich miniature environment, and Airsim-simulated drone navigation and obstacle avoidance demonstrate the effectiveness of our method in achieving formal safety guarantees while maintaining strong nominal performance.

Knowledge distillation is a widely adopted technique for transferring capabilities from LLMs to smaller, more efficient student models.However, unauthorized use of knowledge distillation takes unfair advantage of the considerable effort and cost put into developing frontier models.We investigate methods for modifying teacher-generated reasoning traces to achieve two objectives that deter unauthorized distillation: (1) anti-distillation, or degrading the training usefulness of query responses, and (2) API watermarking, which embeds verifiable signatures in student models.We introduce several approaches for dynamically rewriting a teacher's reasoning outputs while preserving answer correctness and semantic coherence.Two of these leverage the rewriting capabilities of LLMs, while others use gradient-based techniques.Our experiments show that a simple instruction-based rewriting approach achieves a strong anti-distillation effect while maintaining or even improving teacher performance.Furthermore, we show that our rewriting approach also enables embedding watermarks that can be reliably detected with essentially no false alarms.Our code is available at https:// github.com/xhOwenMa/trace-rewriting.