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Interactive theorem provers (ITPs) require manual formalization, which is labor-intensive and demands expert knowledge. While automated formalization offers a potential solution, it faces two major challenges: model hallucination (e.g.,…

Artificial Intelligence · Computer Science 2026-03-24 Wangyue Lu , Lun Du , Sirui Li , Ke Weng , Haozhe Sun , Hengyu Liu , Minghe Yu , Tiancheng Zhang , Ge Yu

Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…

Artificial Intelligence · Computer Science 2025-11-12 Vishal Kumar , Shubhra Mishra , Rebecca Hao , Rizwaan Malik , David Broman , Dorottya Demszky

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS)…

Computation and Language · Computer Science 2025-04-18 Yicheng Pan , Zhenrong Zhang , Pengfei Hu , Jiefeng Ma , Jun Du , Jianshu Zhang , Quan Liu , Jianqing Gao , Feng Ma

While large language models (LLMs) have shown progress in mathematical reasoning, they still face challenges in formalizing theorems that arise from instantiating abstract structures in concrete settings. With the goal of auto-formalizing…

Artificial Intelligence · Computer Science 2025-11-14 Chenyi Li , Wanli Ma , Zichen Wang , Zaiwen Wen

Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate…

Computer Vision and Pattern Recognition · Computer Science 2026-01-27 Shasha Guo , Liang Pang , Xi Wang , Yanling Wang , Huawei Shen , Jing Zhang

Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…

Artificial Intelligence · Computer Science 2025-11-11 Albert Sadowski , Jarosław A. Chudziak

Multi-step theorem prediction is a central challenge in automated reasoning. Existing neural-symbolic approaches rely heavily on supervised parametric models, which exhibit limited generalization to evolving theorem libraries. In this work,…

Artificial Intelligence · Computer Science 2026-03-06 Junbo Zhao , Ting Zhang , Can Li , Wei He , Jingdong Wang , Hua Huang

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…

Artificial Intelligence · Computer Science 2025-10-02 Balaji Rao , William Eiers , Carlo Lipizzi

Automating the formalization of mathematical statements for theorem proving remains a major challenge for Large Language Models (LLMs). LLMs struggle to identify and utilize the prerequisite mathematical knowledge and its corresponding…

Artificial Intelligence · Computer Science 2026-04-08 Meiru Zhang , Philipp Borchert , Milan Gritta , Gerasimos Lampouras

Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies…

Machine Learning · Computer Science 2025-07-25 Neil He , Hiren Madhu , Ngoc Bui , Menglin Yang , Rex Ying

High-quality geometric diagram generation presents both a challenge and an opportunity: it demands strict spatial accuracy while offering well-defined constraints to guide generation. Inspired by recent advances in geometry problem solving…

Computer Vision and Pattern Recognition · Computer Science 2025-12-10 Xiaojing Wei , Ting Zhang , Wei He , Jingdong Wang , Hua Huang

Large Language Models (LLMs) are increasingly utilised in software engineering, yet their ability to generate structured artefacts such as UML diagrams remains underexplored. In this work we present NOMAD, a cognitively inspired, modular…

Software Engineering · Computer Science 2026-05-04 Polydoros Giannouris , Sophia Ananiadou

Autoformalization aims to convert informal mathematical proofs into machine-verifiable formats, bridging the gap between natural and formal languages. However, ensuring semantic alignment between the informal and formalized statements…

Computation and Language · Computer Science 2024-10-15 Jianqiao Lu , Yingjia Wan , Yinya Huang , Jing Xiong , Zhengying Liu , Zhijiang Guo

Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning…

Artificial Intelligence · Computer Science 2023-07-18 Adam Ishay , Zhun Yang , Joohyung Lee

Ultra Strong Machine Learning (USML) refers to symbolic learning systems that not only improve their own performance but can also teach their acquired knowledge to quantifiably improve human performance. We introduce LENS (Logic Programming…

Artificial Intelligence · Computer Science 2026-01-28 Lun Ai , Johannes Langer , Ute Schmid , Stephen Muggleton

Large Language Models (LLMs) have revolutionized natural language processing and demonstrated impressive capabilities in various tasks. Unfortunately, they are prone to hallucinations, where the model exposes incorrect or false information…

Computation and Language · Computer Science 2023-10-13 Patrik Puchert , Poonam Poonam , Christian van Onzenoodt , Timo Ropinski

Real-world geometry and 3D vision tasks are replete with challenging symmetries that defy tractable analytical expression. In this paper, we introduce Neural Isometries, an autoencoder framework which learns to map the observation space to…

Computer Vision and Pattern Recognition · Computer Science 2024-10-31 Thomas W. Mitchel , Michael Taylor , Vincent Sitzmann

While natural language understanding (NLU) is advancing rapidly, today's technology differs from human-like language understanding in fundamental ways, notably in its inferior efficiency, interpretability, and generalization. This work…

Computation and Language · Computer Science 2020-07-10 Ronen Tamari , Chen Shani , Tom Hope , Miriam R. L. Petruck , Omri Abend , Dafna Shahaf

A hallmark of intelligence is the ability to use a familiar domain to make inferences about a less familiar domain, known as analogical reasoning. In this article, we delve into the performance of Large Language Models (LLMs) in dealing…

Artificial Intelligence · Computer Science 2023-09-13 Thilini Wijesiriwardene , Amit Sheth , Valerie L. Shalin , Amitava Das

We report on our experience formalizing differential geometry with mathlib, the Lean mathematical library. Our account is geared towards geometers with no knowledge of type theory, but eager to learn more about the formalization of…

Logic in Computer Science · Computer Science 2021-08-03 Anthony Bordg , Nicolò Cavalleri