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Large Language Models (LLMs) are demonstrating rapid improvements on complex reasoning benchmarks, particularly when allowed to utilize intermediate reasoning steps before converging on a final solution. However, current literature often…

Computation and Language · Computer Science 2026-01-01 Ákos Prucs , Márton Csutora , Mátyás Antal , Márk Marosi

Reinforcement learning (RL)-based fine-tuning has become a crucial step in post-training language models for advanced mathematical reasoning and coding. Following the success of frontier reasoning models, recent work has demonstrated that…

Machine Learning · Computer Science 2025-08-11 Rosie Zhao , Alexandru Meterez , Sham Kakade , Cengiz Pehlevan , Samy Jelassi , Eran Malach

Many common estimators in machine learning and causal inference are linear smoothers, where the prediction is a weighted average of the training outcomes. Some estimators, such as ordinary least squares and kernel ridge regression, allow…

Machine Learning · Computer Science 2026-04-02 David Arbour , Harsh Parikh , Bijan Niknam , Elizabeth Stuart , Kara Rudolph , Avi Feller

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search…

Information Retrieval · Computer Science 2022-08-05 Jingtao Zhan , Xiaohui Xie , Jiaxin Mao , Yiqun Liu , Jiafeng Guo , Min Zhang , Shaoping Ma

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

Despite the efficacy of Direct Preference Optimization (DPO) in aligning Large Language Models (LLMs), reward hacking remains a pivotal challenge. This issue emerges when LLMs excessively reduce the probability of rejected completions to…

Computation and Language · Computer Science 2025-08-26 Chenxu Yang , Ruipeng Jia , Mingyu Zheng , Naibin Gu , Zheng Lin , Siyuan Chen , Weichong Yin , Hua Wu , Weiping Wang

Reinforcement learning with verifiable rewards (RLVR) is a practical, scalable way to improve large language models on math, code, and other structured tasks. However, we argue that many headline RLVR gains are not yet well validated…

Effective reward design is a central challenge in Reinforcement Learning (RL) for code generation. Mainstream test-suite-level outcome rewards enforce functional correctness but induce sparsity, while external Reward Models (RMs) provide…

Machine Learning · Computer Science 2026-05-27 Longwen Wang , Yirui Liu , Xuan'er Wu , Xiaohui Hu , Yuankai Fan , Kaidong Yu , Qizhen Weng , Wei Xi , Xuelong Li

Reinforcement learning with verifiable rewards (RLVR) has improved the reasoning ability of large language models, yet training remains costly because many rollouts contribute little to optimization, considering the amount of computation…

Machine Learning · Computer Science 2026-02-20 Yan Sun , Jia Guo , Stanley Kok , Zihao Wang , Zujie Wen , Zhiqiang Zhang

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, with Group Relative Policy Optimization (GRPO) serving as the dominant algorithm. We identify two overlooked…

Machine Learning · Computer Science 2026-05-13 Mingxiong Lin , Zhangquan Gong , Maowen Tang , Qian Li , Chuangchuang Wang , Jian Ma , Sutian Huang , Kai Tang , Haonan Lu

In practice, rigorous reasoning is often a key driver of correct code, while Reinforcement Learning (RL) for code generation often neglects optimizing reasoning quality. Bringing process-level supervision into RL is appealing, but it faces…

Software Engineering · Computer Science 2026-05-06 Lishui Fan , Yu Zhang , Mouxiang Chen , Zhongxin Liu

Recent reinforcement learning (RL) techniques have yielded impressive reasoning improvements in language models, yet it remains unclear whether post-training truly extends a model's reasoning ability beyond what it acquires during…

Computation and Language · Computer Science 2025-12-09 Charlie Zhang , Graham Neubig , Xiang Yue

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

Methodology · Statistics 2011-03-31 Guillaume Bouchard , Stéphane Girard , Anatoli Iouditski , Alexander Nazin

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…

Machine Learning · Statistics 2018-10-29 Mikhail Belkin , Daniel Hsu , Partha Mitra

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from…

Machine Learning · Computer Science 2025-10-02 Tao Ren , Jinyang Jiang , Hui Yang , Wan Tian , Minhao Zou , Guanghao Li , Zishi Zhang , Qinghao Wang , Shentao Qin , Yanjun Zhao , Rui Tao , Hui Shao , Yijie Peng

Reinforcement learning with verifiable rewards has driven recent advances in LLM post-training, in particular for reasoning. Policy optimization algorithms generate a number of responses for a given prompt and then effectively weight the…

Machine Learning · Computer Science 2026-02-12 Reinhard Heckel , Mahdi Soltanolkotabi , Christos Thramboulidis

Recent advances highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing LLMs' capabilities. However, it remains unclear whether the current practice of RLVR truly expands a model's reasoning…

Machine Learning · Computer Science 2026-02-05 Fang Wu , Weihao Xuan , Ximing Lu , Mingjie Liu , Yi Dong , Zaid Harchaoui , Yejin Choi

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning…

Artificial Intelligence · Computer Science 2025-09-30 Guanxu Chen , Yafu Li , Yuxian Jiang , Chen Qian , Qihan Ren , Jingyi Yang , Yu Cheng , Dongrui Liu , Jing Shao

Performance optimization of deep learning models is conducted either manually or through automatic architecture search, or a combination of both. On the other hand, their performance strongly depends on the target hardware and how…

Machine Learning · Computer Science 2022-09-23 Vahid Partovi Nia , Alireza Ghaffari , Mahdi Zolnouri , Yvon Savaria

Test-time scaling offers a promising path to improve LLM reasoning by utilizing more compute at inference time; however, the true promise of this paradigm lies in extrapolation (i.e., improvement in performance on hard problems as LLMs keep…

Machine Learning · Computer Science 2025-06-16 Amrith Setlur , Matthew Y. R. Yang , Charlie Snell , Jeremy Greer , Ian Wu , Virginia Smith , Max Simchowitz , Aviral Kumar
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