Attention-based neural architectures have become central to state-of-the-art methods in real-time nonlinear control. As these data-driven models continue to be integrated into increasingly safety-critical domains, ensuring statistically grounded and provably safe decision-making becomes essential. This paper introduces a novel reactive control framework for gap-based navigation using the Attentive Neural Process (AttNP) and a physics-informed extension, the PI-AttNP. Both models are evaluated in a simulated F1TENTH-style Ackermann steering racecar environment, chosen as a fast-paced proxy for safety-critical autonomous driving scenarios. The PI-AttNP augments the AttNP architecture with approximate model-based priors to inject physical inductive bias, enabling faster convergence and improved prediction accuracy suited for real-time control. To further ensure safety, we derive and implement a control barrier function (CBF)-based filtering mechanism that analytically enforces collision avoidance constraints. This CBF formulation is fully compatible with the learned AttNP controller and generalizes across a wide range of racing scenarios, providing a lightweight and certifiable safety layer. Our results demonstrate competitive closed-loop performance while ensuring real-time constraint satisfaction.