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Yufan Wang

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Published work

3 published item(s)

preprint2026arXiv

LLMs Know When They Know, but Do Not Act on It: A Metacognitive Harness for Test-time Scaling

Large language models (LLMs) often expose useful signals of self-monitoring: before solving a problem, they can estimate whether they are likely to succeed, and after solving it, they can judge whether their answer is likely to be correct. However, these signals are typically measured or elicited in isolation, rather than used to control inference. In this work, we ask whether LLMs possess latent metacognitive ability that can be turned into effective test-time control. Inspired by the Nelson--Narens theory from cognitive psychology, we propose a metacognitive harness that separates monitoring from reasoning. For each problem, the model first reports a pre-solve feeling-of-knowing (FOK) signal; after each solve attempt, it reports a post-solve judgment-of-learning (JOL) signal. Rather than treating these signals as passive confidence estimates, the harness turns them into an explicit control interface for reasoning: it decides when to trust the current solution, when to retry with compact metacognitive feedback, and when to pass multiple attempts to a final aggregator. Across text, code, and multimodal reasoning benchmarks, our harness substantially improves a fixed Claude Sonnet-4.6 base model without parameter updates or benchmark-specific fine-tuning. On the evaluated public benchmark snapshots, it raises pooled accuracy from 48.3 to 56.9 and exceeds the strongest listed leaderboard entries on the three primary evaluation settings: HLE-Verified, LiveCodeBench v6, and R-Bench-V. These results suggest that strong LLMs may already possess useful metacognitive ability, but require an explicit control harness to act on it during reasoning.

preprint2023arXiv

A principled distributional approach to trajectory similarity measurement

Existing measures and representations for trajectories have two longstanding fundamental shortcomings, i.e., they are computationally expensive and they can not guarantee the `uniqueness' property of a distance function: dist(X,Y) = 0 if and only if X=Y, where $X$ and $Y$ are two trajectories. This paper proposes a simple yet powerful way to represent trajectories and measure the similarity between two trajectories using a distributional kernel to address these shortcomings. It is a principled approach based on kernel mean embedding which has a strong theoretical underpinning. It has three distinctive features in comparison with existing approaches. (1) A distributional kernel is used for the very first time for trajectory representation and similarity measurement. (2) It does not rely on point-to-point distances which are used in most existing distances for trajectories. (3) It requires no learning, unlike existing learning and deep learning approaches. We show the generality of this new approach in three applications: (a) trajectory anomaly detection, (b) anomalous sub-trajectory detection, and (c) trajectory pattern mining. We identify that the distributional kernel has (i) a unique data-dependent property and the above uniqueness property which are the key factors that lead to its superior task-specific performance; and (ii) runtime orders of magnitude faster than existing distance measures.

preprint2021arXiv

Defects, modular differential equations, and free field realization of N = 4 VOAs

For all 4d $\mathcal{N} = 4$ SYM theories with simple gauge groups $G$, we show that the residues of the integrands in the $\mathcal{N} = 4$ Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the vacuum characters of rank$G$ copies of $bc βγ$ systems that provide the free field realization of associated $\mathcal{N} = 4$ VOAs. This result predicts that these residues, as module characters, are additional solutions to the flavored modular differential equations satisfied by the original Schur index. The prediction is verified in the $G = SU(2)$ case, where an additional logarithmic solution is constructed.