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Large language models (LLMs) frequently make errors when handling even simple numerical problems, such as comparing two small numbers. A natural hypothesis is that these errors stem from how LLMs represent numbers, and specifically, whether…

Machine Learning · Computer Science 2025-02-04 Amit Arnold Levy , Mor Geva

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

Tokenization is a fundamental component of large language models (LLMs), yet its influence on model scaling and performance is not fully explored. In this paper, we introduce Over-Tokenized Transformers, a novel framework that decouples…

Computation and Language · Computer Science 2025-05-26 Hongzhi Huang , Defa Zhu , Banggu Wu , Yutao Zeng , Ya Wang , Qiyang Min , Xun Zhou

Large language models (LLMs) achieve impressive results on advanced mathematics benchmarks but sometimes fail on basic arithmetic tasks, raising the question of whether they have truly grasped fundamental arithmetic rules or are merely…

Computation and Language · Computer Science 2025-09-18 Yang Yan , Yu Lu , Renjun Xu , Zhenzhong Lan

Variation in language is ubiquitous and often systematically linked to regional, social, and contextual factors. Tokenizers split texts into smaller units and might behave differently for less common linguistic forms. This might affect…

Computation and Language · Computer Science 2025-07-08 Anna Wegmann , Dong Nguyen , David Jurgens

Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to…

Computation and Language · Computer Science 2024-10-30 Xiang Zhang , Juntai Cao , Chenyu You

Scaling laws are useful guides for derisking expensive training runs, as they predict performance of large models using cheaper, small-scale experiments. However, there remain gaps between current scaling studies and how language models are…

Recent studies have demonstrated that the performance of transformers on the task of language modeling obeys a power-law relationship with model size over six orders of magnitude. While transformers exhibit impressive scaling, their…

Machine Learning · Computer Science 2021-10-07 Narsimha Chilkuri , Eric Hunsberger , Aaron Voelker , Gurshaant Malik , Chris Eliasmith

Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous…

Machine Learning · Computer Science 2025-06-24 Guhao Feng , Kai Yang , Yuntian Gu , Xinyue Ai , Shengjie Luo , Jiacheng Sun , Di He , Zhenguo Li , Liwei Wang

Tokenization, the division of input text into input tokens, is an often overlooked aspect of the large language model (LLM) pipeline and could be the source of useful or harmful inductive biases. Historically, LLMs have relied on byte pair…

Computation and Language · Computer Science 2024-02-26 Aaditya K. Singh , DJ Strouse

We introduce a scaling law for fine-tuning large language models (LLMs) under fixed compute budgets that explicitly accounts for data composition. Conventional approaches measure training data solely by total tokens, yet the number of…

Computation and Language · Computer Science 2025-06-04 Ryan Lagasse , Aidan Kierans , Avijit Ghosh , Shiri Dori-Hacohen

While scaling laws for Large Language Models (LLMs) traditionally focus on proxy metrics like pretraining loss, predicting downstream task performance has been considered unreliable. This paper challenges that view by proposing a direct…

Machine Learning · Computer Science 2025-12-10 Jakub Krajewski , Amitis Shidani , Dan Busbridge , Sam Wiseman , Jason Ramapuram

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which…

Computation and Language · Computer Science 2024-10-17 Andrea Pinto , Tomer Galanti , Randall Balestriero

Tokenization is a foundational step in the text process of Large Language Models (LLMs). Texts must be first tokenized into token IDs, which are then input to LLMs. Inefficient tokenization results in long token-ID sequences and will slow…

Computation and Language · Computer Science 2026-05-14 Chong Li , Yingzhuo Deng , Wen Yang , Jiajun Zhang , Chengqing Zong

Large Language Models (LLMs) have demonstrated remarkable generalization across diverse tasks, leading individuals to increasingly use them as personal assistants and universal computing engines. Nevertheless, a notable obstacle emerges…

Machine Learning · Computer Science 2023-09-13 Dimitris Spathis , Fahim Kawsar

Large Language Models (LLMs) have recently demonstrated strong performance in machine translation (MT). However, most prior work focuses on improving or benchmarking translation quality, offering limited insight into when and why LLM-based…

Computation and Language · Computer Science 2026-05-11 Shenbin Qian , Yves Scherrer

Large language models (LLMs) have recently attracted considerable interest for their ability to perform complex reasoning tasks, such as chain-of-thought (CoT) reasoning. However, most of the existing approaches to enhance this ability rely…

Computation and Language · Computer Science 2024-08-08 Xinyi Wang , Lucas Caccia , Oleksiy Ostapenko , Xingdi Yuan , William Yang Wang , Alessandro Sordoni

It is a common belief that large language models (LLMs) are better than smaller-sized ones. However, larger models also require significantly more time and compute during inference. This begs the question: what happens when both models…

Software Engineering · Computer Science 2024-07-26 Michael Hassid , Tal Remez , Jonas Gehring , Roy Schwartz , Yossi Adi

Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic…

Computation and Language · Computer Science 2022-08-11 Jing Qian , Hong Wang , Zekun Li , Shiyang Li , Xifeng Yan

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such…

Computation and Language · Computer Science 2023-01-31 Yao Fu , Hao Peng , Litu Ou , Ashish Sabharwal , Tushar Khot
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