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Large language models (LLMs) excel in many natural language tasks, yet they struggle with complex mathemat-ical problem-solving, particularly in symbolic reasoning and maintaining consistent output. This study evalu-ates 10 LLMs with 7 to 8…

Machine Learning · Computer Science 2025-01-29 Evgenii Evstafev

This paper presents a comprehensive study on the tokenization techniques employed by state-of-the-art large language models (LLMs) and their implications on the cost and availability of services across different languages, especially low…

Computation and Language · Computer Science 2024-10-07 Abrar Rahman , Garry Bowlin , Binit Mohanty , Sean McGunigal

Language models usually use left-to-right (L2R) autoregressive factorization. However, L2R factorization may not always be the best inductive bias. Therefore, we investigate whether alternative factorizations of the text distribution could…

Computation and Language · Computer Science 2025-07-01 Yizhe Zhang , Richard Bai , Zijin Gu , Ruixiang Zhang , Jiatao Gu , Emmanuel Abbe , Samy Bengio , Navdeep Jaitly

Tokenization is a fundamental component of language models for code. It involves breaking down the input into units that are later passed to the language model stack to learn high-dimensional representations used in various contexts, from…

Software Engineering · Computer Science 2025-07-22 Mootez Saad , Hao Li , Tushar Sharma , Ahmed E. Hassan

This study introduces a hypothesis-testing framework to assess whether large language models (LLMs) possess genuine reasoning abilities or primarily depend on token bias. We go beyond evaluating LLMs on accuracy; rather, we aim to…

Computation and Language · Computer Science 2024-10-07 Bowen Jiang , Yangxinyu Xie , Zhuoqun Hao , Xiaomeng Wang , Tanwi Mallick , Weijie J. Su , Camillo J. Taylor , Dan Roth

Tokenization significantly influences language models(LMs)' performance. This paper traces the evolution of tokenizers from word-level to subword-level, analyzing how they balance tokens and types to enhance model adaptability while…

Computation and Language · Computer Science 2024-03-04 Jinbiao Yang

Large reasoning models (LRMs) have led to new possibilities in terms of problem-solving, through the devising of a natural language thought process prior to answering a query. While their capabilities are well known across mathematics and…

Computation and Language · Computer Science 2025-10-15 Armel Zebaze , Rachel Bawden , Benoît Sagot

Large Language Models (LLMs) are pivotal in advancing natural language processing but often struggle with complex reasoning tasks due to inefficient attention distributions. In this paper, we explore the effect of increased computed tokens…

Computation and Language · Computer Science 2024-06-25 Bingli Liao , Danilo Vasconcellos Vargas

The widespread adoption of large language models (LLMs) has increased concerns about their robustness. Vulnerabilities in perturbations of tokenisation of the input indicate that models trained with a deterministic canonical tokenisation…

Computation and Language · Computer Science 2026-04-20 Sophie Steger , Rui Li , Sofiane Ennadir , Anya Sims , Arno Solin , Franz Pernkopf , Martin Trapp

In this paper, we investigate the phenomena of "selection biases" in Large Language Models (LLMs), focusing on problems where models are tasked with choosing the optimal option from an ordered sequence. We delve into biases related to…

Computation and Language · Computer Science 2024-06-06 Sheng-Lun Wei , Cheng-Kuang Wu , Hen-Hsen Huang , Hsin-Hsi Chen

Reasoning is critical for large language models (LLMs) to excel in a wide range of tasks. While methods like Chain-of-Thought (CoT) reasoning and enhance LLM performance by decomposing problems into intermediate steps, they also incur…

Computation and Language · Computer Science 2025-06-03 Tingxu Han , Zhenting Wang , Chunrong Fang , Shiyu Zhao , Shiqing Ma , Zhenyu Chen

Recent reasoning large language models (LLMs) have demonstrated remarkable improvements in mathematical reasoning capabilities through long Chain-of-Thought. The reasoning tokens of these models enable self-correction within reasoning…

Artificial Intelligence · Computer Science 2025-04-02 Yu Cui , Bryan Hooi , Yujun Cai , Yiwei Wang

Large Language Models (LLMs) perform well on reasoning benchmarks but often fail when inputs alter slightly, raising concerns about the extent to which their success relies on memorization. This issue is especially acute in Chain-of-Thought…

Computation and Language · Computer Science 2025-08-22 Huihan Li , You Chen , Siyuan Wang , Yixin He , Ninareh Mehrabi , Rahul Gupta , Xiang Ren

Training Large Language Models (LLMs) for chain-of-thought reasoning presents a significant challenge: supervised fine-tuning on a single "golden" rationale hurts generalization as it penalizes equally valid alternatives, whereas…

Computation and Language · Computer Science 2025-11-14 Mingye Zhu , Yi Liu , Zheren Fu , Quan Wang , Yongdong Zhang

Generative recommendation systems, driven by large language models (LLMs), present an innovative approach to predicting user preferences by modeling items as token sequences and generating recommendations in a generative manner. A critical…

Efficiency and safety of Large Language Models (LLMs), among other factors, rely on the quality of tokenization. A good tokenizer not only improves inference speed and language understanding but also provides extra defense against jailbreak…

Computation and Language · Computer Science 2026-04-16 Pavel Chizhov , Egor Bogomolov , Ivan P. Yamshchikov

Tokenization is a hardcoded compression step which remains in the training pipeline of Large Language Models (LLMs), despite a general trend towards architectures becoming increasingly end-to-end. Prior work has shown promising results at…

Machine Learning · Computer Science 2026-02-17 Sam Dauncey , Roger Wattenhofer

Chain-of-thought prompting has emerged as a powerful technique for enabling large language models (LLMs) to solve complex reasoning tasks. However, these reasoning chains can be verbose, raising concerns about efficiency. In response,…

Computation and Language · Computer Science 2025-04-02 Ayeong Lee , Ethan Che , Tianyi Peng

Large Language Models (LLMs) have demonstrated exceptional code generation capabilities, yet their token-level mechanisms remain underexplored, particularly in compressed models. Through systematic analysis of programming language token…

Software Engineering · Computer Science 2026-02-10 Viacheslav Siniaev , Iaroslav Chelombitko , Aleksey Komissarov

Large language models (LLMs) show strong reasoning abilities but often produce unnecessarily long explanations that reduce efficiency. Although reinforcement learning (RL) has been used to improve reasoning, most methods focus on accuracy…

Machine Learning · Computer Science 2026-04-20 Hanbing Liu , Lang Cao , Yuanyi Ren , Mengyu Zhou , Haoyu Dong , Xiaojun Ma , Shi Han , Dongmei Zhang