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In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the fast Fourier transform (FFT), the fast multipole method (FMM), the geometric multigrid (GMG), and…

Numerical Analysis · Mathematics 2016-07-12 Amir Gholami , Dhairya Malhotra , Hari Sundar , George Biros

We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…

Numerical Analysis · Mathematics 2026-02-27 Pei-Chun Su , Ronald R. Coifman

Multimodal large language models have various practical applications that demand strong reasoning abilities. Despite recent advancements, these models still struggle to solve complex geometric problems. A key challenge stems from the lack…

Artificial Intelligence · Computer Science 2025-09-19 Yue Xin , Wenyuan Wang , Rui Pan , Ruida Wang , Howard Meng , Renjie Pi , Shizhe Diao , Tong Zhang

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

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…

Computation and Language · Computer Science 2025-06-06 Chengwu Liu , Ye Yuan , Yichun Yin , Yan Xu , Xin Xu , Zaoyu Chen , Yasheng Wang , Lifeng Shang , Qun Liu , Ming Zhang

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption…

Computer Vision and Pattern Recognition · Computer Science 2023-12-20 Mehran Kazemi , Hamidreza Alvari , Ankit Anand , Jialin Wu , Xi Chen , Radu Soricut

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and…

We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…

Machine Learning · Statistics 2015-06-02 Wesley Tansey , James G. Scott

We introduce fs1, a simple yet effective method that improves the factuality of reasoning traces by collecting them from large reasoning models and grounding them in knowledge graph (KG) paths. We fine-tune eight instruction-tuned Large…

Computation and Language · Computer Science 2026-04-21 Mike Zhang , Johannes Bjerva , Russa Biswas

Although most current large multimodal models (LMMs) can already understand photos of natural scenes and portraits, their understanding of abstract images, e.g., charts, maps, or layouts, and visual reasoning capabilities remains quite…

Computer Vision and Pattern Recognition · Computer Science 2024-10-04 Wenqi Zhang , Zhenglin Cheng , Yuanyu He , Mengna Wang , Yongliang Shen , Zeqi Tan , Guiyang Hou , Mingqian He , Yanna Ma , Weiming Lu , Yueting Zhuang

Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…

Computation and Language · Computer Science 2025-12-02 Felix Vossel , Till Mossakowski , Björn Gehrke

Current Visual-Language Navigation (VLN) methodologies face a trade-off between semantic understanding and control precision. While Multimodal Large Language Models (MLLMs) offer superior reasoning, deploying them as low-level controllers…

Robotics · Computer Science 2026-02-19 Zhenxing Xu , Brikit Lu , Weidong Bao , Zhengqiu Zhu , Junsong Zhang , Hui Yan , Wenhao Lu , Ji Wang

This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since…

Logic in Computer Science · Computer Science 2026-01-08 Josef Urban

The emergence of Multimodal Large Language Models (MLLMs) has propelled the development of autonomous agents that operate on Graphical User Interfaces (GUIs) using pure visual input. A fundamental challenge is robustly grounding natural…

We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…

Artificial Intelligence · Computer Science 2024-06-12 Maximilian Schäffeler , Mohammad Abdulaziz

LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…

As a core task in location-based services (LBS) (e.g., navigation maps), query and point of interest (POI) matching connects users' intent with real-world geographic information. Recently, pre-trained models (PTMs) have made advancements in…

Computation and Language · Computer Science 2023-05-25 Ruixue Ding , Boli Chen , Pengjun Xie , Fei Huang , Xin Li , Qiang Zhang , Yao Xu

We present miniF2F, a dataset of formal Olympiad-level mathematics problems statements intended to provide a unified cross-system benchmark for neural theorem proving. The miniF2F benchmark currently targets Metamath, Lean, Isabelle…

Artificial Intelligence · Computer Science 2022-03-01 Kunhao Zheng , Jesse Michael Han , Stanislas Polu

We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…

Computational Geometry · Computer Science 2025-01-03 Vítor Gomes Chagas , Elisa Dell'Arriva , Flávio Keidi Miyazawa

Large Language Models (LLMs) present massive inherent knowledge and superior semantic comprehension capability, which have revolutionized various tasks in natural language processing. Despite their success, a critical gap remains in…

Computation and Language · Computer Science 2025-02-11 Ben Liu , Jihai Zhang , Fangquan Lin , Cheng Yang , Min Peng