Linqi Song
Publications
PARM: Pipeline-Adapted Reward Model
Reward models (RMs) are central to aligning large language models (LLMs) with human preferences, powering RLHF and advanced decoding strategies. While most prior work focuses on single-step generation, real-world applications increasingly adopt multi-stage LLM pipelines, where effective reward guidance remains underexplored. We investigate this through code generation for combinatorial optimization, constructing a pipeline that integrates reward models into both formulation and solution stages. We identify a critical challenge: inconsistency between reward model predictions and actual pipeline execution outcomes. To address this, we propose the Pipeline-Adapted Reward Model (PARM), which leverages pipeline-specific data and direct preference optimization to align rewards with downstream feedback. We instantiate PARM as a two-stage pipeline (formulation -> code generation) and evaluate it on four public optimization benchmarks, measuring execution rate and solving accuracy against baselines and sampling methods. A supplementary cross-domain experiment on GSM8K assesses transferability. Results demonstrate that PARM consistently improves pipeline output quality and stability, providing new insights into reward modeling for multi-stage LLM reasoning.
Learning to Reason with Insight for Informal Theorem Proving
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. We propose $\mathtt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully exploit this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.