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In post-training for reasoning Large Language Models (LLMs), the current state of practice trains LLMs in two independent stages: Supervised Fine-Tuning (SFT) and Reinforcement Learning with Verifiable Rewards (RLVR, shortened as ``RL''…

Machine Learning · Computer Science 2025-10-03 Feiyang Kang , Michael Kuchnik , Karthik Padthe , Marin Vlastelica , Ruoxi Jia , Carole-Jean Wu , Newsha Ardalani

The evaluation and post-training of large language models (LLMs) rely on supervision, but strong supervision for difficult tasks is often unavailable, especially when evaluating frontier models. In such cases, models are demonstrated to…

Machine Learning · Computer Science 2026-01-29 Tianyi Alex Qiu , Micah Carroll , Cameron Allen

Large language models (LLMs) have been widely used for problem-solving tasks. Most recent work improves their performance through supervised fine-tuning (SFT) with labeled data or reinforcement learning (RL) from task feedback. In this…

Computation and Language · Computer Science 2025-09-29 Hang Li , Kaiqi Yang , Yucheng Chu , Hui Liu , Jiliang Tang

While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical…

Recent Language Models (LMs) have shown impressive capabilities in generating texts with the knowledge internalized in parameters. Yet, LMs often generate the factually incorrect responses to the given queries, since their knowledge may be…

Computation and Language · Computer Science 2023-10-20 Jinheon Baek , Soyeong Jeong , Minki Kang , Jong C. Park , Sung Ju Hwang

Many applications of large language models (LLMs) require deductive reasoning, yet models frequently produce incorrect or redundant inference steps. We frame natural language inference as a search problem where the final answer is the valid…

Artificial Intelligence · Computer Science 2026-05-26 Andreas Opedal , Francesco Ignazio Re , Abulhair Saparov , Mrinmaya Sachan , Bernhard Schölkopf , Ryan Cotterell

Formal specifications, such as pre- and post-conditions provide a solid basis for performing thorough program verification. However, developers rarely provide such formal specifications, hence if AI could help in constructing them, it would…

Software Engineering · Computer Science 2026-03-19 I. S. W. B. Prasetya , Fitsum Kifetew , Davide Prandi

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical…

Computation and Language · Computer Science 2023-10-20 Liangming Pan , Alon Albalak , Xinyi Wang , William Yang Wang

While large language models have made significant progress in mathematical reasoning, they remain unreliable at judging the correctness of their own solutions. Existing approaches that equip models with self-verification typically treat…

Computation and Language · Computer Science 2026-05-28 Haihui Pan , Junwei Bao , Hongfei Jiang , Yang Song

This paper investigates the ability of large language models (LLMs) to solve statistical tasks, as well as their capacity to assess the quality of reasoning. While state-of-the-art LLMs have demonstrated remarkable performance in a range of…

Computation and Language · Computer Science 2026-01-22 Crish Nagarkar , Leonid Bogachev , Serge Sharoff

While the reasoning capabilities of Large Language Models (LLMs) excel in analytical tasks such as mathematics and code generation, their utility for abstractive summarization remains widely assumed but largely unverified. To bridge this…

Computation and Language · Computer Science 2025-12-10 Haohan Yuan , Haopeng Zhang

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward…

Self-improvement is a significant techniques within the realm of large language model (LLM), aiming to enhance the LLM performance without relying on external data. Despite its significance, generally how LLM performances evolve during the…

Machine Learning · Computer Science 2026-02-10 Yifan Sun , Yushan Liang , Zhen Zhang , Xin Liu , Jiaye Teng

Extensive research on formal verification of machine learning (ML) systems indicates that learning from data alone often fails to capture underlying background knowledge. A variety of verifiers have been developed to ensure that a…

Logic in Computer Science · Computer Science 2023-11-17 Thomas Flinkow , Barak A. Pearlmutter , Rosemary Monahan

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…

Machine Learning · Computer Science 2026-02-16 Maria-Florina Balcan , Avrim Blum , Zhiyuan Li , Dravyansh Sharma

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates…

Artificial Intelligence · Computer Science 2025-05-20 Jianyuan Zhong , Zeju Li , Zhijian Xu , Xiangyu Wen , Kezhi Li , Qiang Xu

Recently, Large Language Models (LLMs) have drawn significant attention due to their outstanding reasoning capabilities and extensive knowledge repository, positioning them as superior in handling various natural language processing tasks…

Computation and Language · Computer Science 2023-11-30 Han Cao , Lingwei Wei , Mengyang Chen , Wei Zhou , Songlin Hu

Large Language Models (LLMs) are increasingly used for accessing information on the web. Their truthfulness and factuality are thus of great interest. To help users make the right decisions about the information they get, LLMs should not…

Computation and Language · Computer Science 2024-04-03 Chenglei Si , Navita Goyal , Sherry Tongshuang Wu , Chen Zhao , Shi Feng , Hal Daumé , Jordan Boyd-Graber

Self-improvement is a mechanism in Large Language Model (LLM) pre-training, post-training and test-time inference. We explore a framework where the model verifies its own outputs, filters or reweights data based on this verification, and…

Computation and Language · Computer Science 2025-02-26 Yuda Song , Hanlin Zhang , Carson Eisenach , Sham Kakade , Dean Foster , Udaya Ghai

Answer verification is crucial not only for evaluating large language models (LLMs) by matching their unstructured outputs against standard answers, but also serves as the reward model to guide LLM optimization. Most evaluation frameworks…

Computation and Language · Computer Science 2025-08-06 Shudong Liu , Hongwei Liu , Junnan Liu , Linchen Xiao , Songyang Gao , Chengqi Lyu , Yuzhe Gu , Wenwei Zhang , Derek F. Wong , Songyang Zhang , Kai Chen