Beyond Input Understanding: Diagnosing Multilingual Mathematical Reasoning with Directed Acyclic Trace Graphs

Large reasoning models (LRMs) achieve strong mathematical reasoning performance in English, but remain much less reliable in many low- and medium-resource languages. This gap is often explained as a failure to understand non-English problem statements. We show that this view is incomplete: even when the problem is given in English, controlling the model's reasoning language can substantially reduce accuracy, suggesting that language also affects reasoning execution itself. To study this effect, we introduce DATG, a Directed Acyclic Trace Graph framework that maps reasoning traces to language-independent mathematical anchors and dependencies. This allows us to align target-language traces with reference DAGs and measure whether they cover required mathematical nodes, respect dependency edges, and avoid harmful mathematical actions. Experiments on the Qwen3 series across 12 languages show that non-English reasoning often suffers from reduced anchor coverage and weaker dependency fidelity, especially in low-resource languages. Motivated by this diagnosis, we propose Loop-Retry and Formula-Retry, two simple test-time controls targeting DATG-exposed failure modes, and show that they consistently improve target-language reasoning performance in low-resource languages.

Integrating Higher-Order Dynamics and Roadway-Compliance into Constrained ILQR-based Trajectory Planning for Autonomous Vehicles

This paper addresses the advancements in on-road trajectory planning for Autonomous Passenger Vehicles (APV). Trajectory planning aims to produce a globally optimal route for APVs, considering various factors such as vehicle dynamics, constraints, and detected obstacles. Traditional techniques involve a combination of sampling methods followed by optimization algorithms, where the former ensures global awareness and the latter refines for local optima. Notably, the Constrained Iterative Linear Quadratic Regulator (CILQR) optimization algorithm has recently emerged, adapted for APV systems, emphasizing improved safety and comfort. However, existing implementations utilizing the vehicle bicycle kinematic model may not guarantee controllable trajectories. We augment this model by incorporating higher-order terms, including the first and second-order derivatives of curvature and longitudinal jerk. This inclusion facilitates a richer representation in our cost and constraint design. We also address roadway compliance, emphasizing adherence to lane boundaries and directions, which past work often overlooked. Lastly, we adopt a relaxed logarithmic barrier function to address the CILQR's dependency on feasible initial trajectories. The proposed methodology is then validated through simulation and real-world experiment driving scenes in real time.