冷拓｜上海大学｜学者主页

2026

FGeo-GCG: Hybrid Validation-Enhanced Geometric Data Synthesis with Human-like Proof

Cheng Qin, Xiaokai Zhang, Yuchang Yang, Zhenhai Sun, Yang Li, Zhengyu Hu, Tuo Leng

Symmetry

DOI

2026

FGeo-ISRL: A MCTS-Enhanced Deep Reinforcement Learning System for Plane Geometry Problem-Solving via Inverse Search

Yang Li, Xiaokai Zhang, Cheng Qin, Zhengyu Hu, Tuo Leng

Symmetry

DOI

2026

A Hybrid Framework for Automated Geometric Problem-Solving by Integrating Formal Symbolic Systems and Deep Learning

Zheng Hu, Xiaokai Zhang, Cheng Qin, Yang Li, Tuo Leng

Symmetry

DOI

2026

Reconstruct Exact Solution via Numerical and Symbolic Computation: A Case Study of AMM Problem 11984

Zhen-Bing Zeng, Tuo Leng, Jian Lu, Yao-Chen Xu

2026 9th International Conference on Artificial Intelligence and Big Data (ICAIBD)

DOI

2025

FGeo-Eval: Evaluation System for Plane Geometry Problem Solving

Qike Huang, Xiaokai Zhang, Na Zhu, Fangzhen Zhu, Tuo Leng

Symmetry

DOI

2024

Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver

Zeren Zhang, Jo-Ku Cheng, Jingyang Deng, Lu Tian, Jinwen Ma, Ziran Qin, Xiaokai Zhang, Na Zhu, Tuo Leng

IEEE International Conference on Acoustics, Speech, and Signal Processing

DOI

2024

FGeo-TP: A Language Model-Enhanced Solver for Euclidean Geometry Problems

Yi-Ming He, Jia Zou, Xiaokai Zhang, Na Zhu, Tuo Leng

Symmetry

DOI

2024

FGeo-Parser: Autoformalization and Solution of Plane Geometric Problems

Na Zhu, Xiaokai Zhang, Qike Huang, Fangzhen Zhu, Zhen Zeng, Tuo Leng

Symmetry

DOI

2024

FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network

Xiaokai Zhang, Yang Li, Na Zhu, Cheng Qin, Zhen Zeng, Tuo Leng

International Joint Conference on Artificial Intelligence

DOI

2024

Floating-Point Embedding: Enhancing the Mathematical Comprehension of Large Language Models

Xiaoxiao Jin, Chenyang Mao, Dengfeng Yue, Tuo Leng

Symmetry

DOI

2024

FGeo-DRL: Deductive Reasoning for Geometric Problems through Deep Reinforcement Learning

Jia Zou, Xiaokai Zhang, Yiming He, Na Zhu, Tuo Leng

Symmetry

DOI

2024

FGeo-SSS: A Search-Based Symbolic Solver for Human-like Automated Geometric Reasoning

Xiaokai Zhang, Na Zhu, Yi-Ming He, Jia Zou, Cheng Qin, Yang Li, Tuo Leng

Symmetry

DOI

2023

半球面上四点距离之和的最大值问题

王玉铮，冷拓，曾振柄

《数学年刊A辑(中文版)》

2023

FormalGeo: The First Step Toward Human-like IMO-level Geometric Automated Reasoning

Xiaokai Zhang, Na Zhu, Yi-Ming He, Jia Zou, Qike Huang, Xiaoxiao Jin, Yanjun Guo, Chenyang Mao, Zhe Zhu, Dengfeng Yue, Fangzhen Zhu, Yang Li, Yifan Wang, Yi-Wen Huang, Runan Wang, Cheng Qin, Zhen Zeng, Shao-Rong Xie, Xiangfeng Luo, Tuo Leng

arXiv.org

DOI

2022

A reverse Thomson problem on the unit circle

Tuo Leng, Yuchi Wu

Proceedings of the American Mathematical Society

DOI

2019

On discrete Wirtinger-Northcott problems

Tuo Leng, Qingyu Zhao, Xiaolin Qin

Linear Algebra and its Applications

DOI

2019

The Fermat-Torricelli Problem of Triangles on the Sphere with Euclidean Metric: A Symbolic Solution with Maple

Xiaofeng Guo, Tuo Leng, Z. Zeng

IEEE Workshop on Memetic Computing

DOI

2018

球面欧氏度量下Fermat-Torricelli点的问题

郭小丰，冷拓，曾振柄

《系统科学与数学》

2016

Discrete Wirtinger type inequality under non-periodic end conditions

Tuo Leng

DOI

2015

Generalizations of Cauchy-Schwarz inequality in unitary spaces

Tuo Leng

DOI

2015

The sharp upper bound for the ratio between the arithmetic and the geometric mean

Tuo Leng, Xiao Qin

DOI

2014

Computing the Determinant of a Matrix with Polynomial Entries by Approximation

Xiao-Lin Qin, Zhi Sun, Tuo Leng, Yong Feng

Journal of Systems Science and Complexity

DOI

2014

CONVERSES OF A DISCRETE WIRTINGER TYPE INEQUALITY

Tuo Leng, Yong Feng

DOI

2012

Finding the Symbolic Solution of a Geometric Problem Through Numerical Computations

Liangyu Chen, Tuo Leng, Li-Yong Shen, Min Wu, Zhengfeng Yang, Z. Zeng

Asian Symposium on Computer Mathematics

DOI

2007

Note on an inequality of Vicente Gonçalves

Jun Yuan, Tuo Leng

DOI

冷拓

精选作品

期刊论文

FGeo-GCG: Hybrid Validation-Enhanced Geometric Data Synthesis with Human-like Proof

FGeo-ISRL: A MCTS-Enhanced Deep Reinforcement Learning System for Plane Geometry Problem-Solving via Inverse Search

A Hybrid Framework for Automated Geometric Problem-Solving by Integrating Formal Symbolic Systems and Deep Learning

Reconstruct Exact Solution via Numerical and Symbolic Computation: A Case Study of AMM Problem 11984

FGeo-Eval: Evaluation System for Plane Geometry Problem Solving

Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver

FGeo-TP: A Language Model-Enhanced Solver for Euclidean Geometry Problems

FGeo-Parser: Autoformalization and Solution of Plane Geometric Problems

FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network

Floating-Point Embedding: Enhancing the Mathematical Comprehension of Large Language Models

FGeo-DRL: Deductive Reasoning for Geometric Problems through Deep Reinforcement Learning

FGeo-SSS: A Search-Based Symbolic Solver for Human-like Automated Geometric Reasoning

半球面上四点距离之和的最大值问题

FormalGeo: The First Step Toward Human-like IMO-level Geometric Automated Reasoning

A reverse Thomson problem on the unit circle

On discrete Wirtinger-Northcott problems

The Fermat-Torricelli Problem of Triangles on the Sphere with Euclidean Metric: A Symbolic Solution with Maple

球面欧氏度量下Fermat-Torricelli点的问题

Discrete Wirtinger type inequality under non-periodic end conditions

Generalizations of Cauchy-Schwarz inequality in unitary spaces

The sharp upper bound for the ratio between the arithmetic and the geometric mean

Computing the Determinant of a Matrix with Polynomial Entries by Approximation

CONVERSES OF A DISCRETE WIRTINGER TYPE INEQUALITY

Finding the Symbolic Solution of a Geometric Problem Through Numerical Computations

Note on an inequality of Vicente Gonçalves

研究方向