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Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely…

Small-scale models offer various computational advantages, and yet to which extent size is critical for problem-solving abilities remains an open question. Specifically for solving grade school math, the smallest model size so far required…

Machine Learning · Computer Science 2023-12-15 Bingbin Liu , Sebastien Bubeck , Ronen Eldan , Janardhan Kulkarni , Yuanzhi Li , Anh Nguyen , Rachel Ward , Yi Zhang

Recent research has focused on enhancing the capability of smaller models through imitation learning, drawing on the outputs generated by large foundation models (LFMs). A number of issues impact the quality of these models, ranging from…

Computation and Language · Computer Science 2023-06-06 Subhabrata Mukherjee , Arindam Mitra , Ganesh Jawahar , Sahaj Agarwal , Hamid Palangi , Ahmed Awadallah

Small language models (SLMs) are more efficient, cost-effective, and customizable than large language models (LLMs), though they often underperform in specific areas like reasoning. Past methods for enhancing SLMs' reasoning, such as…

Computation and Language · Computer Science 2024-12-12 Kaiyuan Chen , Jin Wang , Xuejie Zhang

The use of Large Language Models (LLMs) in mathematical reasoning has become a cornerstone of related research, demonstrating the intelligence of these models and enabling potential practical applications through their advanced performance,…

Computation and Language · Computer Science 2024-12-20 Kathrin Seßler , Yao Rong , Emek Gözlüklü , Enkelejda Kasneci

The rapid advancement of Large Language Models (LLMs) in the realm of mathematical reasoning necessitates comprehensive evaluations to gauge progress and inspire future directions. Existing assessments predominantly focus on problem-solving…

Computation and Language · Computer Science 2024-06-05 Xiaoyuan Li , Wenjie Wang , Moxin Li , Junrong Guo , Yang Zhang , Fuli Feng

Large Language Models (LLMs) demonstrate capabilities in code generation, potentially boosting developer productivity. However, their adoption remains limited by high computational costs, among other factors. Small Language Models (SLMs)…

Software Engineering · Computer Science 2025-09-23 Débora Souza , Rohit Gheyi , Lucas Albuquerque , Gustavo Soares , Márcio Ribeiro

Large language models (LLMs) demonstrate strong mathematical reasoning, but reliance on closed-source APIs for OR tasks raises privacy concerns, and training open-source models from scratch incurs high compute costs. We introduce…

Artificial Intelligence · Computer Science 2025-10-03 Jianzhang Zhang , Jialong Zhou , Chuang Liu

Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already…

Computation and Language · Computer Science 2024-03-08 Chen Li , Weiqi Wang , Jingcheng Hu , Yixuan Wei , Nanning Zheng , Han Hu , Zheng Zhang , Houwen Peng

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from…

Computation and Language · Computer Science 2024-05-06 Longhui Yu , Weisen Jiang , Han Shi , Jincheng Yu , Zhengying Liu , Yu Zhang , James T. Kwok , Zhenguo Li , Adrian Weller , Weiyang Liu

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on…

Machine Learning · Computer Science 2025-08-28 Iman Mirzadeh , Keivan Alizadeh , Hooman Shahrokhi , Oncel Tuzel , Samy Bengio , Mehrdad Farajtabar

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods…

Machine Learning · Computer Science 2025-02-14 Safal Shrestha , Minwu Kim , Keith Ross

Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics. In wireless communications, where problems require precise manipulation of information-theoretic bounds,…

Machine Learning · Computer Science 2025-09-30 Xin Li , Mengbing Liu , Yiyang Zhu , Wenhe Zhang , Li Wei , Jiancheng An , Chau Yuen

The rapid advancement of large language models has opened new avenues for automating complex problem-solving tasks such as algorithmic coding and competitive programming. This paper introduces a novel evaluation technique, LLM-ProS, to…

Computation and Language · Computer Science 2026-03-03 Md Sifat Hossain , Anika Tabassum , Md. Fahim Arefin , Tarannum Shaila Zaman

Large Language Models (LLMs) have seen great advance in both academia and industry, and their popularity results in numerous open-source frameworks and techniques in accelerating LLM pre-training, fine-tuning, and inference. Training and…

Performance · Computer Science 2023-12-04 Longteng Zhang , Xiang Liu , Zeyu Li , Xinglin Pan , Peijie Dong , Ruibo Fan , Rui Guo , Xin Wang , Qiong Luo , Shaohuai Shi , Xiaowen Chu

Large language models (LLMs) have demonstrated significant potential in code generation tasks. However, there remains a performance gap between open-source and closed-source models. To address this gap, existing approaches typically…

Computation and Language · Computer Science 2025-04-18 Weijie Lv , Xuan Xia , Sheng-Jun Huang

Large Language Models (LLMs) are increasingly used in math education not only as problem solvers but also as assessors of learners' reasoning. However, it remains unclear whether stronger math problem-solving ability is associated with…

Artificial Intelligence · Computer Science 2026-03-27 Liang Zhang , Yu Fu , Xinyi Jin

Despite significant advancements in text generation and reasoning, Large Language Models (LLMs) still face challenges in accurately performing complex arithmetic operations. Language model systems often enable LLMs to generate code for…

Computation and Language · Computer Science 2024-09-04 Owen Dugan , Donato Manuel Jimenez Beneto , Charlotte Loh , Zhuo Chen , Rumen Dangovski , Marin Soljačić

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze…

Artificial Intelligence · Computer Science 2025-02-24 Johan Boye , Birger Moell

The ongoing evolution of language models has led to the development of large-scale architectures that demonstrate exceptional performance across a wide range of tasks. However, these models come with significant computational and energy…

Artificial Intelligence · Computer Science 2025-11-19 Xialie Zhuang , Peixian Ma , Zhikai Jia , Zane Cao , Shiwei Liu
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