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In this paper, we propose R$^3$: Learning Reasoning through Reverse Curriculum Reinforcement Learning (RL), a novel method that employs only outcome supervision to achieve the benefits of process supervision for large language models. The…

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal…

Computation and Language · Computer Science 2023-09-06 Peiyi Wang , Lei Li , Liang Chen , Feifan Song , Binghuai Lin , Yunbo Cao , Tianyu Liu , Zhifang Sui

Reinforcement learning with verifiable rewards (RLVR) has shown promise in enhancing the reasoning performance of large language models (LLMs) by increasing test-time compute. However, even after extensive RLVR training, such models still…

Artificial Intelligence · Computer Science 2026-03-10 Pinzheng Wang , Shuli Xu , Juntao Li , Yu Luo , Dong Li , Jianye Hao , Min Zhang

Long-horizon tasks requiring multi-step reasoning and dynamic re-planning remain challenging for large language models (LLMs). Sequential prompting methods are prone to context drift, loss of goal information, and recurrent failure cycles,…

Artificial Intelligence · Computer Science 2025-10-30 Zhenyu Zhang , Tianyi Chen , Weiran Xu , Alex Pentland , Jiaxin Pei

Existing large language models (LLMs) face challenges of following complex instructions, especially when multiple constraints are present and organized in paralleling, chaining, and branching structures. One intuitive solution, namely…

Computer Vision and Pattern Recognition · Computer Science 2025-10-01 Yulei Qin , Gang Li , Zongyi Li , Zihan Xu , Yuchen Shi , Zhekai Lin , Xiao Cui , Ke Li , Xing Sun

Reinforcement Learning (RL) has emerged as a transformative approach for aligning and enhancing Large Language Models (LLMs), addressing critical challenges in instruction following, ethical alignment, and reasoning capabilities. This…

Artificial Intelligence · Computer Science 2025-07-08 Saksham Sahai Srivastava , Vaneet Aggarwal

Large Reasoning Models (LRMs) have achieved remarkable success on reasoning-intensive tasks such as mathematics and programming. However, their enhanced reasoning capabilities do not necessarily translate to improved safety performance-and…

Computation and Language · Computer Science 2026-04-21 Zhexin Zhang , Xian Qi Loye , Victor Shea-Jay Huang , Junxiao Yang , Qi Zhu , Shiyao Cui , Fei Mi , Lifeng Shang , Yingkang Wang , Hongning Wang , Minlie Huang

Large Reasoning Models (LRMs) have significantly improved problem-solving through explicit Chain-of-Thought (CoT) reasoning. However, this capability creates a Safety-Helpfulness Paradox: the reasoning process itself can be misused to…

Artificial Intelligence · Computer Science 2026-01-27 Xin Gao , Shaohan Yu , Zerui Chen , Yueming Lyu , Weichen Yu , Guanghao Li , Jiyao Liu , Jianxiong Gao , Jian Liang , Ziwei Liu , Chenyang Si

Reverse thinking plays a crucial role in human reasoning. Humans can reason not only from a problem to a solution but also in reverse, i.e., start from the solution and reason towards the problem. This often enhances overall reasoning…

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular…

Artificial Intelligence · Computer Science 2026-01-12 Zenghao Duan , Liang Pang , Zihao Wei , Wenbin Duan , Yuxin Tian , Shicheng Xu , Jingcheng Deng , Zhiyi Yin , Xueqi Cheng

Reinforcement learning (RL) has increasingly become a pivotal technique in the post-training of large language models (LLMs). The effective exploration of the output space is essential for the success of RL. We observe that for complex…

Machine Learning · Computer Science 2025-07-08 Shihan Dou , Muling Wu , Jingwen Xu , Rui Zheng , Tao Gui , Qi Zhang , Xuanjing Huang

Large Reasoning Models (LRMs) have recently shown impressive performance on complex reasoning tasks, often by engaging in self-reflective behaviors such as self-critique and backtracking. However, not all reflections are beneficial-many are…

Artificial Intelligence · Computer Science 2026-01-21 Hanbin Wang , Jingwei Song , Jinpeng Li , Qi Zhu , Fei Mi , Ganqu Cui , Yasheng Wang , Lifeng Shang

Recent successes of reinforcement learning (RL) in training large reasoning models motivate the question of whether self-training - the process where a model learns from its own judgments - can be sustained within RL. In this work, we study…

Machine Learning · Computer Science 2025-10-10 Sheikh Shafayat , Fahim Tajwar , Ruslan Salakhutdinov , Jeff Schneider , Andrea Zanette

Large Language Models (LLMs) that can continually improve beyond their training budgets are able to solve increasingly difficult problems by adapting at test time, a property we refer to as extrapolation. However, standard reinforcement…

Machine Learning · Computer Science 2026-03-24 Ian Wu , Yuxiao Qu , Amrith Setlur , Aviral Kumar

Recent advancements in large language models (LLMs) have been driven by their emergent reasoning capabilities, particularly through long chain-of-thought (CoT) prompting, which enables thorough exploration and deliberation. Despite these…

Computation and Language · Computer Science 2026-04-09 Junnan Liu , Hongwei Liu , Songyang Zhang , Kai Chen

Large reasoning models (LRMs) have recently demonstrated impressive capabilities in complex reasoning tasks by leveraging increased test-time computation and exhibiting behaviors reminiscent of human-like self-reflection. While LRMs show a…

Computation and Language · Computer Science 2025-10-21 Qingcheng Zeng , Weihao Xuan , Leyang Cui , Rob Voigt

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or…

Artificial Intelligence · Computer Science 2024-12-30 Sijia Chen , Baochun Li

Large reasoning models (LRMs) already possess a latent capacity for long chain-of-thought reasoning. Prior work has shown that outcome-based reinforcement learning (RL) can incidentally elicit advanced reasoning behaviors such as…

Computation and Language · Computer Science 2025-05-28 Zhiyuan Hu , Yibo Wang , Hanze Dong , Yuhui Xu , Amrita Saha , Caiming Xiong , Bryan Hooi , Junnan Li

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in…

Machine Learning · Computer Science 2025-08-01 Tao He , Rongchuan Mu , Lizi Liao , Yixin Cao , Ming Liu , Bing Qin

Large language models (LLMs) have shown remarkable reasoning capabilities, especially when prompted to generate intermediate reasoning steps (e.g., Chain-of-Thought, CoT). However, LLMs can still struggle with problems that are easy for…

Computation and Language · Computer Science 2023-10-24 Shibo Hao , Yi Gu , Haodi Ma , Joshua Jiahua Hong , Zhen Wang , Daisy Zhe Wang , Zhiting Hu