Yiliu Sun

Zongji Yu, Wenshui Luo, Yiliu Sun et al.

Post-training has significantly enhanced the reasoning capability of Large Reasoning Models (LRMs), especially with Reinforcement Learning (RL) like Group Relative Policy Optimization (GRPO). However, GRPO-style RL methods in multi-domain settings often fail to achieve consistent improvements across all domains due to inherent interference in policy optimization. Prior studies on multi-domain RL primarily focus on alleviating cross-domain interference, while often neglecting the pivotal role of knowledge sharing, which we argue is the key to transforming cross-domain interactions from harmful competition into beneficial transfer. To address this limitation, we propose Multi-domain Contrastive Policy Optimization (MCPO), which analyzes the structural relationships among rollouts and promotes cross-domain knowledge sharing and in-domain knowledge consolidation in a contrastive manner. Specifically, for a given prompt, MCPO identifies transferable reasoning trajectories from other domains as positive examples, while treating incorrect rollouts as negative ones. It then encourages consistent representations for positive pairs and pushes negative pairs apart, thereby facilitating knowledge transfer and reducing interference. Moreover, MCPO aligns intra-domain correct rollouts to build a consolidated representation space. In this way, MCPO contrastively learns a harmonious representation space that can accommodate diverse multi-domain knowledge. Empirical results show that MCPO improves the reasoning capabilities of LRMs across multiple domains and even outperforms single-domain training in some cases. Code is available at https://github.com/Maricalce/MCPO.

Peiji Li, Linyang Li, Handa Sun et al.

Large language models have demonstrated strong reasoning capabilities in complex tasks through tool integration, which is typically framed as a Markov Decision Process and optimized with trajectory-level RL algorithms such as GRPO. However, a common class of reasoning tasks, iterative optimization, presents distinct challenges: the agent interacts with the same underlying environment state across turns, and the value of a trajectory is determined by the best turn-level reward rather than cumulative returns. Existing GRPO-based methods cannot perform fine-grained, turn-level optimization in such settings, while black-box optimization methods discard prior knowledge and reasoning capabilities. To address this gap, we propose Turn-Level GRPO (TL-GRPO), a lightweight RL algorithm that performs turn-level group sampling for fine-grained optimization. We evaluate TL-GRPO on analog circuit sizing (ACS), a challenging scientific optimization task requiring multiple simulations and domain expertise. Results show that TL-GRPO outperforms standard GRPO and Bayesian optimization methods across various specifications. Furthermore, our 30B model trained with TL-GRPO achieves state-of-the-art performance on ACS tasks under same simulation budget, demonstrating both strong generalization and practical utility.

Yiliu Sun, Zicheng Zhao, Yang Wei et al.

Reinforcement Learning with Verifiable Rewards (RLVR) significantly enhances the reasoning capability of Large Language Models (LLMs). Current RLVR approaches typically conduct training across all generated tokens, but neglect to explore which tokens (e.g., prefix tokens) actually contribute to reasoning. This uniform training strategy spends substantial effort on optimizing low-return tokens, which in turn impedes the potential improvement from high-return tokens and reduces overall training effectiveness. To address this issue, we propose a novel RLVR approach called Progressive Prefix-token Policy Optimization (PPPO), which highlights the significance of the prefix segment of generated outputs. Specifically, inspired by the well-established human thinking theory of Path Dependence, where early-stage thoughts substantially constrain subsequent thinking trajectory, we identify an analogous phenomenon in LLM reasoning termed Beginning Lock-in Effect (BLE). PPPO leverages this finding by focusing its optimization objective on the prefix reasoning process of LLMs. This targeted optimization strategy can positively influence subsequent reasoning processes, and ultimately improve final results. To improve the learning effectiveness of LLMs on how to start reasoning with high quality, PPPO introduces two training strategies: (a) Progressive Prefix Retention, which shapes a progressive learning process by increasing the proportion of retained prefix tokens during training; (b) Continuation Accumulated Reward, which mitigates reward bias by sampling multiple continuations for one prefix token sequence, and accumulating their scores as the reward signal. Extensive experimental results on various reasoning tasks demonstrate that our proposed PPPO outperforms representative RLVR methods, with the accuracy improvements of 18.02% on only 26.17% training tokens.

Yiliu Sun, Yanfang Zhang, Zicheng Zhao et al.

Nowadays, Large Language Models (LLMs) have been gradually employed to solve complex tasks. To face the challenge, task decomposition has become an effective way, which proposes to divide a complex task into multiple simpler subtasks and then solve them separately so that the difficulty of the original task can be reduced. However, the performance of existing task decomposition methods can be suboptimal when the task contains overly complex logic and constraints. In this situation, the solution generated by LLMs may deviate from the original purpose of the task, or contain redundant or even erroneous content. Therefore, inspired by the fact that humans possess two thinking systems including fast thinking and slow thinking, this paper introduces a new task decomposition method termed ``Fast-Slow-Thinking'' (FST), which stimulates LLMs to solve tasks through the cooperation of Fast Thinking (FT) and Slow Thinking (ST) steps. Here FT focuses more on the general and concise aspect of the task, and ST focuses more on the details of the task. In FT, LLMs are prompted to remove the constraints of the original task, therefore simplifying it to a general and concise one. In ST, we recall the constraints removed in FT, so that LLMs can improve the answer generated in FT to meet the requirements of the original task. Therefore, our FST method enables LLMs to consider a complex problem via a human-like cognition process from coarse to fine, the effectiveness of which has been well demonstrated by the experiments on three types of tasks.

Yanfang Zhang, Yiliu Sun, Yibing Zhan et al.

Recently, increasing attention has been focused on improving the ability of Large Language Models (LLMs) to perform complex reasoning. Advanced methods, such as Chain-of-Thought (CoT) and its variants, are found to enhance their reasoning skills by designing suitable prompts or breaking down complex problems into more manageable sub-problems. However, little concentration has been put on exploring the reasoning process, \textit{i.e.}, we discovered that most methods resort to Direct Reasoning (DR) and disregard Indirect Reasoning (IR). This can make LLMs difficult to solve IR tasks, which are often encountered in the real world. To address this issue, we propose a Direct-Indirect Reasoning (DIR) method, which considers DR and IR as multiple parallel reasoning paths that are merged to derive the final answer. We stimulate LLMs to implement IR by crafting prompt templates incorporating the principles of contrapositive and contradiction. These templates trigger LLMs to assume the negation of the conclusion as true, combine it with the premises to deduce a conclusion, and utilize the logical equivalence of the contrapositive to enhance their comprehension of the rules used in the reasoning process. Our DIR method is simple yet effective and can be straightforwardly integrated with existing variants of CoT methods. Experimental results on four datasets related to logical reasoning and mathematic proof demonstrate that our DIR method, when combined with various baseline methods, significantly outperforms all the original methods.

Yiliu Sun, Zicheng Zhao, Sheng Wan et al.

Nowadays, single Large Language Model (LLM) struggles with critical issues such as hallucination and inadequate reasoning abilities. To mitigate these issues, Multi-Agent Debate (MAD) has emerged as an effective strategy, where LLM agents engage in in-depth debates with others on tasks. However, existing MAD methods face two major issues: (a) too lengthy input contexts, which causes LLM agents to get lost in plenty of input information and experiences performance drop; and (b) the overconfidence dilemma, where self-assured LLM agents dominate the debate, leading to low debating effectiveness. To address these limitations, we propose a novel MAD method called "CortexDebate". Inspired by the human brain's tendency to establish a sparse and dynamically optimized network among cortical areas governed by white matter, CortexDebate constructs a sparse debating graph among LLM agents, where each LLM agent only debates with the ones that are helpful to it. To optimize the graph, we propose a module named McKinsey-based Debate Matter (MDM), which acts as an artificial analog to white matter. By integrating the McKinsey Trust Formula, a well-established measure of trustworthiness from sociology, MDM enables credible evaluations that guide graph optimization. The effectiveness of our CortexDebate has been well demonstrated by extensive experimental results across eight datasets from four task types.