Yili Shen
Publications
SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation
Large language models often default to step-by-step computation even when efficient numerical shortcuts are available. This raises a basic question: do they exhibit number sense in a human-like behavioral sense, i.e., the ability to recognize numerical structure, apply shortcuts when appropriate, and avoid them when they are not? We introduce SenseMath, a controlled benchmark for evaluating structure-sensitive numerical reasoning in LLMs. SenseMath contains 4,800 items spanning eight shortcut categories and four digit scales, with matched strong-shortcut, weak-shortcut, and control variants. It supports three evaluation settings of increasing cognitive demand: Shortcut Use (whether models can apply shortcuts on shortcut-amenable problems); Applicability Judgment (whether they can recognize when a shortcut is appropriate or misleading); and Problem Generation (whether they can generate new problem items that correctly admit a given type of shortcut). Our evaluation across five LLMs, ranging from GPT-4o-mini to Llama-3.1-8B, shows a consistent pattern: when explicitly prompted, models readily adopt shortcut strategies and achieve substantial accuracy gains on shortcut-amenable items (up to 15%), yet under standard chain-of-thought prompting they spontaneously employ such strategies in fewer than 40% of cases, even when they demonstrably possess the requisite capability. Moreover, this competence is confined to the Use level; models systematically over-generalise shortcuts to problems where they do not apply, and fail to generate valid shortcut-bearing problems from scratch. Together, these results suggest that current LLMs exhibit procedural shortcut fluency without the structural understanding of when and why shortcuts work that underlies human number sense.
Driving Reaction Trajectories via Latent Flow Matching
Recent advances in reaction prediction have achieved near-saturated accuracy on standard benchmarks (e.g., USPTO), yet most state-of-the-art models formulate the task as a one-shot mapping from reactants to products, offering limited insight into the underlying reaction process. Procedural alternatives introduce stepwise generation but often rely on mechanism-specific supervision, discrete symbolic edits, and computationally expensive inference. In this work, we propose LatentRxnFlow, a new reaction prediction paradigm that models reactions as continuous latent trajectories anchored at the thermodynamic product state. Built on Conditional Flow Matching, our approach learns time-dependent latent dynamics directly from standard reactant-product pairs, without requiring mechanistic annotations or curated intermediate labels. While LatentRxnFlow achieves state-of-the-art performance on USPTO benchmarks, more importantly, the continuous formulation exposes the full generative trajectory, enabling trajectory-level diagnostics that are difficult to realize with discrete or one-shot models. We show that latent trajectory analysis allows us to localize and characterize failure modes and to mitigate certain errors via gated inference. Furthermore, geometric properties of the learned trajectories provide an intrinsic signal of epistemic uncertainty, helping prioritize reliably predictable reaction outcomes and flag ambiguous cases for additional validation. Overall, LatentRxnFlow combines strong predictive accuracy with improved transparency, diagnosability, and uncertainty awareness, moving reaction prediction toward more trustworthy deployment in high-throughput discovery workflows.