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This paper introduces several techniques that improve the scalability of the deductive verification of data-level programs working on arrays and matrices. First of all, we introduce a technique to rewrite expressions with (nested)…

Software Engineering · Computer Science 2026-05-14 Lars B. van den Haak , Anton Wijs , Marieke Huisman

Reinforcement learning is widely used to improve the reasoning ability of large language models, especially when answers can be automatically checked. Standard GRPO-style training updates the model using only the current step, while full…

Machine Learning · Computer Science 2026-05-11 Ismam Nur Swapnil , Aranya Saha , Tanvir Ahmed Khan , Mohammad Ariful Haque , Ser-Nam Lim

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes…

Artificial Intelligence · Computer Science 2025-05-26 Muzhi Dai , Shixuan Liu , Qingyi Si

Retrieval-augmented large language models, when optimized with outcome-level rewards, can achieve strong answer accuracy on multi-hop questions. However, under noisy retrieval, models frequently suffer from "right-answer-wrong-reason…

Computation and Language · Computer Science 2026-03-17 Yu Liu , Wenxiao Zhang , Diandian Guo , Cong Cao , Fangfang Yuan , Qiang Sun , Yanbing Liu , Jin B. Hong , Zhiyuan Ma

The evolution of Large Language Models (LLMs) has catalyzed a paradigm shift from superficial instruction following to rigorous long-horizon reasoning. While Group Relative Policy Optimization (GRPO) has emerged as a pivotal mechanism for…

Artificial Intelligence · Computer Science 2026-01-01 Xuan Xie , Xuan Wang , Wenjie Wang , Shuai Chen , Wei Lin

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, even when arriving at a correct final answer, their rationales are often logically unsound or inconsistent. This is a major issue when…

Artificial Intelligence · Computer Science 2023-11-09 Gabriel Poesia , Kanishk Gandhi , Eric Zelikman , Noah D. Goodman

Large language models (LLMs) present an opportunity to scale high-quality personalized education to all. A promising approach towards this means is to build dialog tutoring models that scaffold students' problem-solving. However, even…

Computation and Language · Computer Science 2024-07-15 Nico Daheim , Jakub Macina , Manu Kapur , Iryna Gurevych , Mrinmaya Sachan

Uncertainty estimation is a significant issue for current large language models (LLMs) that are generally poorly calibrated and over-confident, especially with reinforcement learning from human feedback (RLHF). Unlike humans, whose…

Computation and Language · Computer Science 2024-05-13 Ruixin Yang , Dheeraj Rajagopal , Shirley Anugrah Hayati , Bin Hu , Dongyeop Kang

Reinforcement fine-tuning improves the reasoning ability of large language models, but it can also encourage them to answer unanswerable queries by guessing or hallucinating missing information. Existing abstention methods either train…

Computation and Language · Computer Science 2026-04-21 Skylar Zhai , Jingcheng Liang , Dongyeop Kang

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts…

Machine Learning · Computer Science 2026-03-02 Yuyang Ding , Chi Zhang , Juntao Li , Haibin Lin , Min Zhang

Generating low-level robot task plans from high-level natural language instructions remains a challenging problem. Although large language models have shown promising results in generating plans, the accuracy of the output remains…

Reinforcement learning with verifiable rewards (RLVR) has recently enhanced the reasoning capabilities of large language models (LLMs), particularly for mathematical problem solving. However, a fundamental limitation remains: as the…

Machine Learning · Computer Science 2025-11-03 Wenhao Deng , Long Wei , Chenglei Yu , Tailin Wu

Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that…

Artificial Intelligence · Computer Science 2026-02-10 Kaleem Ullah Qasim , Jiashu Zhang , Hao Li , Muhammad Kafeel Shaheen

Sequence generation models are increasingly being used to translate natural language into programs, i.e. to perform executable semantic parsing. The fact that semantic parsing aims to predict programs that can lead to executed actions in…

Computation and Language · Computer Science 2023-07-10 Elias Stengel-Eskin , Benjamin Van Durme

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy…

Machine Learning · Computer Science 2026-02-09 Pengyi Li , Elizaveta Goncharova , Andrey Kuznetsov , Ivan Oseledets

Large language models (LLMs) trained with reinforcement objectives often achieve superficially correct answers via shortcut strategies, pairing correct outputs with spurious or unfaithful reasoning and degrading under small causal…

Machine Learning · Computer Science 2025-09-30 Xiangqi Wang , Yue Huang , Yujun Zhou , Xiaonan Luo , Kehan Guo , Xiangliang Zhang

Latent reasoning offers a more efficient alternative to explicit reasoning by compressing intermediate reasoning into continuous representations and substantially shortening reasoning chains. However, existing latent reasoning methods…

Machine Learning · Computer Science 2026-05-01 Jingcheng Deng , Zihao Wei , Liang Pang , Junhong Wu , Shicheng Xu , Zenghao Duan , Huawei Shen

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…

Computation and Language · Computer Science 2024-12-18 Vernon Y. H. Toh , Deepanway Ghosal , Soujanya Poria

Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…

Machine Learning · Statistics 2022-10-25 David Widmann , Fredrik Lindsten , Dave Zachariah

Intelligent coding systems are transforming software development by enabling users to specify code behavior in natural language. However, the opaque decision-making of AI-driven coders raises trust and usability concerns, particularly for…

Software Engineering · Computer Science 2025-08-11 Xiangzhe Xu , Shiwei Feng , Zian Su , Chengpeng Wang , Xiangyu Zhang