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Reasoning in large language models has long been a central research focus, and recent studies employing reinforcement learning (RL) have introduced diverse methods that yield substantial performance gains with minimal or even no external…

Machine learning models increasingly influence decisions in high-stakes settings such as finance, law and hiring, driving the need for transparent, interpretable outcomes. However, while explainable approaches can help understand the…

Artificial Intelligence · Computer Science 2025-08-26 Sopam Dasgupta , Sadaf MD Halim , Joaquín Arias , Elmer Salazar , Gopal Gupta

Reasoning models have demonstrated impressive performance on difficult tasks that traditional language models struggle at. However, many are plagued with the problem of overthinking--generating large amounts of unnecessary tokens which…

Computation and Language · Computer Science 2025-04-21 Xiao Pu , Michael Saxon , Wenyue Hua , William Yang Wang

In mathematical proof education, there remains a need for interventions that help students learn to write mathematical proofs. Research has shown that timely feedback can be very helpful to students learning new skills. While for many years…

Artificial Intelligence · Computer Science 2025-07-15 Chenyan Zhao , Mariana Silva , Seth Poulsen

Multiple-choice questions (MCQs) are commonly used across all levels of math education since they can be deployed and graded at a large scale. A critical component of MCQs is the distractors, i.e., incorrect answers crafted to reflect…

Computers and Society · Computer Science 2024-05-15 Alexander Scarlatos , Wanyong Feng , Digory Smith , Simon Woodhead , Andrew Lan

Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation…

Computation and Language · Computer Science 2024-10-08 Zhihan Zhang , Tao Ge , Zhenwen Liang , Wenhao Yu , Dian Yu , Mengzhao Jia , Dong Yu , Meng Jiang

While large models pre-trained on high-quality data exhibit excellent performance on mathematical reasoning (e.g., GSM8k, MultiArith), it remains challenging to specialize smaller models for these tasks. Common approaches to address this…

Computation and Language · Computer Science 2026-03-19 Neeraj Gangwar , Suma P Bhat , Nickvash Kani

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term \textit{reasoning rigidity}.…

Artificial Intelligence · Computer Science 2025-05-26 Doohyuk Jang , Yoonjeon Kim , Chanjae Park , Hyun Ryu , Eunho Yang

We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…

Logic · Mathematics 2020-12-16 David H. Wolpert , David Kinney

Overfitting is a well-known issue in machine learning that occurs when a model struggles to generalize its predictions to new, unseen data beyond the scope of its training set. Traditional techniques to mitigate overfitting include early…

Machine Learning · Computer Science 2025-12-09 Flavio Giorgi , Fabiano Veglianti , Fabrizio Silvestri , Gabriele Tolomei

Generative AI challenges traditional assessments by allowing students to produce correct answers without demonstrating understanding or reasoning. Rather than prohibiting AI, this work argues that one way to integrate AI into education is…

Computers and Society · Computer Science 2026-02-03 Ahmad Samer Wazan

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user…

Computation and Language · Computer Science 2024-10-10 Zihao Zhou , Shudong Liu , Maizhen Ning , Wei Liu , Jindong Wang , Derek F. Wong , Xiaowei Huang , Qiufeng Wang , Kaizhu Huang

Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…

Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present…

Machine Learning · Computer Science 2024-03-13 Danny Halawi , Jean-Stanislas Denain , Jacob Steinhardt

Recent advances in multi-modal generative models have driven substantial improvements in image editing. However, current generative models still struggle with handling diverse and complex image editing tasks that require implicit reasoning,…

Computer Vision and Pattern Recognition · Computer Science 2025-11-25 Feng Han , Yibin Wang , Chenglin Li , Zheming Liang , Dianyi Wang , Yang Jiao , Zhipeng Wei , Chao Gong , Cheng Jin , Jingjing Chen , Jiaqi Wang

Many recent developments on generative models for natural images have relied on heuristically-motivated metrics that can be easily gamed by memorizing a small sample from the true distribution or training a model directly to improve the…

Machine Learning · Computer Science 2021-06-08 Ching-Yuan Bai , Hsuan-Tien Lin , Colin Raffel , Wendy Chih-wen Kan

Inductive reasoning is an essential capability for large language models (LLMs) to achieve higher intelligence, which requires the model to generalize rules from observed facts and then apply them to unseen examples. We present MIRAGE, a…

Computation and Language · Computer Science 2025-03-03 Jiachun Li , Pengfei Cao , Zhuoran Jin , Yubo Chen , Kang Liu , Jun Zhao

Multifidelity and multioutput optimisation algorithms are of active interest in many areas of computational design as they allow cheaper computational proxies to be used intelligently to aid experimental searches for high-performing…

Machine Learning · Statistics 2022-08-29 Clyde Fare , Peter Fenner , Edward O. Pyzer-Knapp

Large language models can perform various reasoning tasks by using chain-of-thought prompting, which guides them to find answers through step-by-step demonstrations. However, the quality of the prompts depends on the demonstrations given to…

Computation and Language · Computer Science 2023-02-02 Zhihong Shao , Yeyun Gong , Yelong Shen , Minlie Huang , Nan Duan , Weizhu Chen

Modern generative models have demonstrated the ability to solve challenging mathematical problems. In many real-world settings, however, mathematical solutions must be expressed visually through diagrams, plots, geometric constructions, and…

Computer Vision and Pattern Recognition · Computer Science 2026-04-01 Ruiyao Liu , Hui Shen , Ping Zhang , Yunta Hsieh , Yifan Zhang , Jing Xu , Sicheng Chen , Junchen Li , Jiawei Lu , Jianing Ma , Jiaqi Mo , Qi Han , Zhen Zhang , Zhongwei Wan , Jing Xiong , Xin Wang , Ziyuan Liu , Hangrui Cao , Ngai Wong