arXiv subjects

Haochen Wen

Publications and source records attributed to Haochen Wen.

3 recordsLinked to original sources

arXiv2026

Transferability of Learned States in Neural PDE Solvers

Assessing useful reuse in neural PDE solvers is challenging: final accuracy can reflect source learning and target-time computation. Our reuse contract separates solution accuracy, learning contribution, and numerical utility through paired state comparisons, matched target information and budgets, and cost accounting. A literature audit extracts 18 version-specific protocol records from 12 papers, documenting retained states, target-time resources, and reported controls. For a fixed linear system and residual tolerance, we construct two initial guesses with identical solution-error, energy-error, and residual norms, reaching the same solution with different conjugate-gradient (CG) iteration counts. Across 240 source-training trajectories, two linear PDE families, Fourier neural operators and convolutional networks, a fixed predictor's benefit reverses across correction algorithms. Among pairs with both relative prediction errors less than or equal to 5 percent on 64 in-distribution tasks (63 by 63 interior grids), reductions in all three norms accompany more CG iterations, at mean taskwise rates of 23.5 percent and 23.9 percent in two libraries. Work-based selection saves 2.50-3.33 CG iterations on held-out in-distribution tasks; matched adaptation demonstrates finite-budget pretraining value. Independent batches confirm a 0.73 percent complete online saving for one physics-trained Fourier neural operator against zero-initialized Poisson-preconditioned CG. Reuse requires matched state comparisons and downstream computational evidence.

cs.LG↗

arXiv2025

PersRM-R1: Enhance Personalized Reward Modeling with Reinforcement Learning

Reward models (RMs), which are central to existing post-training methods, aim to align LLM outputs with human values by providing feedback signals during fine-tuning. However, existing RMs struggle to capture nuanced, user-specific preferences, especially under limited data and across diverse domains. Thus, we introduce PersRM-R1, the first reasoning-based reward modeling framework specifically designed to identify and represent personal factors from only one or a few personal exemplars. To address challenges including limited data availability and the requirement for robust generalization, our approach combines synthetic data generation with a two-stage training pipeline consisting of supervised fine-tuning followed by reinforcement fine-tuning. Experimental results demonstrate that PersRM-R1 outperforms existing models of similar size and matches the performance of much larger models in both accuracy and generalizability, paving the way for more effective personalized LLMs.

cs.LG↗

arXiv2025

Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

cs.AI↗