Nuo Chen

Qifan Zhang, Xiaobin Hong, Jianheng Tang et al.

Large Language Models (LLMs) have demonstrated strong reasoning abilities, making them suitable for complex tasks such as graph computation. Traditional reasoning steps paradigm for graph problems is hindered by unverifiable steps, limited long-term reasoning, and poor generalization to graph variations. To overcome these limitations, we introduce GCoder, a code-based LLM designed to enhance problem-solving in generalized graph computation problems. Our method involves constructing an extensive training dataset, GraphWild, featuring diverse graph formats and algorithms. We employ a multi-stage training process, including Supervised Fine-Tuning (SFT) and Reinforcement Learning from Compiler Feedback (RLCF), to refine model capabilities. For unseen tasks, a hybrid retrieval technique is used to augment performance. Experiments demonstrate that GCoder outperforms GPT-4o, with an average accuracy improvement of 16.42% across various graph computational problems. Furthermore, GCoder efficiently manages large-scale graphs with millions of nodes and diverse input formats, overcoming the limitations of previous models focused on the reasoning steps paradigm. This advancement paves the way for more intuitive and effective graph problem-solving using LLMs. Code and data are available at here: https://github.com/Bklight999/WWW25-GCoder/tree/master.

Yuyao Wang, Bowen Liu, Jianheng Tang et al.

Reasoning Large Language Models (RLLMs) have recently achieved remarkable progress on complex reasoning tasks, largely enabled by their long chain-of-thought (Long CoT) capabilities. However, developing these Long CoT behaviors relies heavily on post-training with high-quality datasets, which are typically costly and human-curated (e.g., mathematics and code), leaving scalable alternatives unexplored. In this work, we introduce NP-hard (NPH) graph problems as a novel synthetic training corpus, as they inherently require deep reasoning, extensive exploration, and reflective strategies, which are core characteristics of Long CoT reasoning. Building on this insight, we develop a two-stage post-training framework: (i) Long CoT Supervised Fine-Tuning (SFT) on rejection-sampled NPH graph instances, which substantially enhances reasoning depth, and (ii) Reinforcement Learning (RL) with a fine-grained reward design, which sharpens reasoning efficiency. Our flagship model, Graph-R1-7B, demonstrates strong generalization across mathematics, coding, STEM, and logic, and surpasses QwQ-32B on NPH graph problems in both accuracy and reasoning efficiency. These results position NPH graph problems as an effective and scalable resource for advancing Long CoT reasoning in LLMs, opening a new frontier for LLM post-training. Our implementation is available at https://github.com/Graph-Reasoner/Graph-R1, with models and datasets hosted in our Hugging Face collection HKUST-DSAIL/Graph-R1.

Nuo Chen, Zhiyuan Hu, Qingyun Zou et al.

Large Language Models (LLMs) are increasingly adopted as evaluators, offering a scalable alternative to human annotation. However, existing supervised fine-tuning (SFT) approaches often fall short in domains that demand complex reasoning. Judgment is inherently reasoning-intensive: beyond surface-level scoring, it requires verifying evidence, identifying errors, and justifying decisions. Through the analysis of evaluation tasks, we find a negative correlation between SFT performance gains and the proportion of reasoning-demanding samples, revealing the limits of SFT in such scenarios. To address this, we introduce JudgeLRM, a family of judgment-oriented LLMs, trained using reinforcement learning (RL) with judge-wise, outcome-driven rewards to activate reasoning capabilities. JudgeLRM consistently outperform SFT-tuned baselines in the same size, as well as other RL and SFT variants, and even surpass state-of-the-art reasoning models: notably, JudgeLRM-3B/4B exceeds GPT-4, while JudgeLRM-7B/8B/14B outperforms DeepSeek-R1 by over 2% in F1 score, with particularly strong gains on reasoning-heavy tasks. Our findings underscore the value of RL in unlocking reasoning-aligned LLM judges.

Miao Peng, Nuo Chen, Zongrui Suo et al.

Despite significant advancements in Large Language Models (LLMs), developing advanced reasoning capabilities in LLMs remains a key challenge. Process Reward Models (PRMs) have demonstrated exceptional promise in enhancing reasoning by providing step-wise feedback, particularly in the context of mathematical reasoning. However, their application to broader reasoning domains remains understudied, largely due to the high costs associated with manually creating step-level supervision. In this work, we explore the potential of PRMs in graph reasoning problems - a domain that demands sophisticated multi-step reasoning and offers opportunities for automated step-level data generation using established graph algorithms. We introduce GraphSILO, the largest dataset for graph reasoning problems with fine-grained step-wise labels, built using automated Task-oriented Trajectories and Monte Carlo Tree Search (MCTS) to generate detailed reasoning steps with step-wise labels. Building upon this dataset, we train GraphPRM, the first PRM designed for graph reasoning problems, and evaluate its effectiveness in two key settings: inference-time scaling and reinforcement learning via Direct Preference Optimization (DPO). Experimental results show that GraphPRM significantly improves LLM performance across 13 graph reasoning tasks, delivering a 9% gain for Qwen2.5-7B and demonstrating transferability to new graph reasoning datasets and new reasoning domains like mathematical problem-solving. Notably, GraphPRM enhances LLM performance on GSM8K and Math500, underscoring the cross-domain applicability of graph-based reasoning rewards. Our findings highlight the potential of PRMs in advancing reasoning across diverse domains, paving the way for more versatile and effective LLMs.

Qifan Zhang, Nuo Chen, Zehua Li et al.

Large Language Models (LLMs) have made remarkable strides in reasoning tasks, yet their performance often falters on novel and complex problems. Domain-specific continued pretraining (CPT) methods, such as those tailored for mathematical reasoning, have shown promise but lack transferability to broader reasoning tasks. In this work, we pioneer the use of Graph Problem Reasoning (GPR) to enhance the general reasoning capabilities of LLMs. GPR tasks, spanning pathfinding, network analysis, numerical computation, and topological reasoning, require sophisticated logical and relational reasoning, making them ideal for teaching diverse reasoning patterns. To achieve this, we introduce GraphPile, the first large-scale corpus specifically designed for CPT using GPR data. Spanning 10.9 billion tokens across 23 graph tasks, the dataset includes chain-of-thought, program-of-thought, trace of execution, and real-world graph data. Using GraphPile, we train GraphMind on popular base models Llama 3 and 3.1, as well as Gemma 2, achieving up to 4.9 percent higher accuracy in mathematical reasoning and up to 21.2 percent improvement in non-mathematical reasoning tasks such as logical and commonsense reasoning. By being the first to harness GPR for enhancing reasoning patterns and introducing the first dataset of its kind, our work bridges the gap between domain-specific pretraining and universal reasoning capabilities, advancing the adaptability and robustness of LLMs.