EuclidNet：面向几何可构造问题的深度视觉推理
EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry
AI总结：
本文提出EuclidNet框架，利用Mask R-CNN视觉推理和递归回溯机制求解直尺圆规几何构造问题，并在日本算额几何问题上验证了其有效性。
摘要：
本文提出了一个基于深度学习的框架，通过视觉推理求解几何构造问题，可用于自动化几何定理证明。几何中的可构造问题通常要求在给定初始配置的情况下，给出使用直尺和圆规构造某一给定目标的步骤序列。我们的EuclidNet框架利用神经网络架构Mask R-CNN，从初始配置和带额外交点的目标配置中提取视觉特征，然后生成可能的构造步骤作为中间数据模型，这些中间数据模型在训练过程中作为反馈，用于进一步细化构造步骤序列。该过程递归重复，直到找到解（此时我们回溯路径以生成逐步构造指南），或判定问题不可解。我们的EuclidNet框架在复杂的日本算额几何问题上得到验证，展示了其利用回溯对具有挑战性的问题进行深度视觉推理的能力。
英文摘要：
In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
