Yuqian Fu
Publications
Is Mathematical Problem-Solving Expertise in Large Language Models Associated with Assessment Performance?
Large Language Models (LLMs) are increasingly used in math education not only as problem solvers but also as assessors of learners' reasoning. However, it remains unclear whether stronger math problem-solving ability is associated with stronger step-level assessment performance. This study examines that relationship using the GSM8K and MATH subsets of PROCESSBENCH, a human-annotated benchmark for identifying the earliest erroneous step in mathematical reasoning. We evaluate two LLM-based math tutor agent settings, instantiated with GPT-4 and GPT-5, in two independent tasks on the same math problems: solving the original problem and assessing a benchmark-provided solution by predicting the earliest erroneous step. Results show a consistent within-model pattern: assessment accuracy is substantially higher on math problem items the same model solved correctly than on items it solved incorrectly, with statistically significant associations across both models and datasets. At the same time, assessment remains more difficult than direct problem solving, especially on error-present solutions. These findings suggest that math problem-solving expertise supports stronger assessment performance, but reliable step-level diagnosis also requires additional capabilities such as step tracking, monitoring, and precise error localization. The results have implications for the design and evaluation of AI-supported Adaptive Instructional Systems (AISs) for formative assessment in math education.
Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes
On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.
MOSAIC: A Unified Platform for Cross-Paradigm Comparison and Evaluation of Homogeneous and Heterogeneous Multi-Agent RL, LLM, VLM, and Human Decision-Makers
Reinforcement learning (RL), large language models (LLMs), and vision-language models (VLMs) have been widely studied in isolation. However, existing infrastructure lacks the ability to deploy agents from different decision-making paradigms within the same environment, making it difficult to study them in hybrid multi-agent settings or to compare their behaviour fairly under identical conditions. We present MOSAIC, an open-source platform that bridges this gap by incorporating a diverse set of existing reinforcement learning environments and enabling heterogeneous agents (RL policies, LLMs, VLMs, and human players) to operate within them in ad-hoc team settings with reproducible results. MOSAIC introduces three contributions. (i) An IPC-based worker protocol that wraps both native and third-party frameworks as isolated subprocess workers, each executing its native training and inference logic unmodified, communicating through a versioned inter-process protocol. (ii) An operator abstraction that forms an agent-level interface by mapping workers to agents: each operator, regardless of whether it is backed by an RL policy, an LLM, or a human, conforms to a minimal unified interface. (iii) A deterministic cross-paradigm evaluation framework offering two complementary modes: a manual mode that advances up to N concurrent operators in lock-step under shared seeds for fine-grained visual inspection of behavioural differences, and a script mode that drives automated, long-running evaluation through declarative Python scripts, for reproducible experiments. We release MOSAIC as an open, visual-first platform to facilitate reproducible cross-paradigm research across the RL, LLM, and human-in-the-loop communities.
VisNec: Measuring and Leveraging Visual Necessity for Multimodal Instruction Tuning
The effectiveness of multimodal instruction tuning depends not only on dataset scale, but critically on whether training samples genuinely require visual reasoning. However, existing instruction datasets often contain a substantial portion of visually redundant samples (solvable from text alone), as well as multimodally misaligned supervision that can degrade learning. To address this, we propose VisNec (Visual Necessity Score), a principled data selection framework that measures the marginal contribution of visual input during instruction tuning. By comparing predictive loss with and without visual context, VisNec identifies whether a training instance is vision-critical, redundant, or misaligned. To preserve task diversity, we combine VisNec with semantic clustering and select high-necessity samples within each cluster. Across 10 downstream benchmarks, training on only 15% of the LLaVA-665K dataset selected by VisNec achieves 100.2% of full-data performance. On the smaller Vision-Flan-186K dataset, our selection not only further reduces data size but also surpasses full-data training by 15.8%. These results demonstrate that measuring and leveraging visual necessity provides an effective solution for both efficient and robust multimodal instruction tuning. Codes and selected subsets will be released upon acceptance.