arXiv:2603.28590v2 Announce Type: replace Abstract: Large language models (LLMs) can generate chains of thought (CoTs) that are not always causally responsible for their final outputs. When such a mismatch occurs, the CoT no longer faithfully reflects the actual reasons (i.e., decision-critical factors) driving the model's behavior, leading to the reduced CoT monitorability problem. However, a comprehensive and fully open-source benchmark for thoroughly evaluating CoT monitorability remains lacking. To address this gap, we propose MonitorBench, a systematic benchmark for evaluating CoT monitorability in LLMs. MonitorBench provides: (1) a diverse set of 1,514 test instances with carefully designed decision-critical factors across 19 tasks spanning 7 categories to characterize \textit{when} CoTs can be used to monitor the factors driving LLM behavior; and (2) two stress-test settings to quantify \textit{the extent to which} CoT monitorability can be degraded. Extensive experiments across multiple popular LLMs with varying capabilities show that CoT monitorability is higher when the decision-critical factors shape the intermediate reasoning process without merely influencing the final answer. More capable LLMs tend to exhibit lower monitorability. And all evaluated LLMs can intentionally reduce monitorability under stress-tests, with monitorability dropping by up to 30\% in some tasks that do not require structural reasoning over the decision-critical factors. Overall, MonitorBench provides a basis for further research on evaluating future LLMs, studying advanced stress-test monitorability techniques, and developing new monitoring approaches. The code is available at https://github.com/ASTRAL-Group/MonitorBench.

arXiv:2601.06810v2 Announce Type: replace-cross Abstract: The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often unstable, computationally expensive, and difficult to scale. Here we introduce WFR Flow Matching (WFR-FM), a simulation-free training algorithm that unifies flow matching with dynamic unbalanced OT. Unlike classical flow matching which regresses only a transport vector field, WFR-FM simultaneously regresses a vector field for displacement and a scalar growth rate function for birth-death dynamics, yielding continuous flows under the WFR geometry. Theoretically, we show that minimizing the WFR-FM loss exactly recovers WFR geodesics. Empirically, WFR-FM yields more accurate and robust trajectory inference in single-cell biology, reconstructing consistent dynamics with proliferation and apoptosis, estimating time-varying growth fields, and applying to generative dynamics under imbalanced data. It outperforms state-of-the-art baselines in efficiency, stability, and reconstruction accuracy. Overall, WFR-FM establishes a unified and efficient paradigm for learning dynamical systems from unbalanced snapshots, where not only states but also mass evolve over time. The Python code is available at https://github.com/QiangweiPeng/WFR-FM.