神经符号几何抽象框架（NeuSOGA）：从观测到符号数学表示
Neuro-Symbolic Geometric Abstraction (NeuSOGA): From Observations to Symbolic Mathematical Representations
- University of Hull（赫尔大学）
- Xiamen University（厦门大学）
- Chinese Academy of Sciences（中国科学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出NeuSOGA框架，结合多种技术将观测转化为符号数学表示，在多类数据集上验证其能保留几何拓扑结构，为观测到符号提供可解释路径。
AI中文摘要：
人工智能的一个核心挑战是将观测结果转化为适用于抽象、解释和推理的显式符号表示。尽管现代AI系统通过大规模统计学习获得了卓越的感知能力，但由此产生的知识通常编码在潜在参数中，难以进行分析检查或操作。受神经符号AI和人类抽象理论的启发，本文研究从几何观测中形成符号数学表示的过程。我们提出NeuSOGA（神经符号几何抽象框架），这一框架逐步将观测转化为拓扑抽象、几何抽象，最终得到符号数学表示。该架构结合了基于欧氏距离变换的拓扑引导结构发现、使用Segment Anything的基础模型感知、自适应多尺度几何抽象，以及通过隐式样条的符号合成。生成的表示是支持任意阶平滑性、加法组合和闭式评估的分析隐式模型。与神经潜在编码不同，该生成的表示保持可解释性、可编辑性和数学明确性。在ModelNet40点云、任意视角投影和分割光学观测上的实验表明，NeuSOGA可将不同观测转化为紧凑的符号表示，同时在不同传感模态和视角方向上保留基本几何和拓扑结构。NeuSOGA提供了从观测到符号的可解释、可解释路径，并建立
英文摘要：
A fundamental challenge in artificial intelligence is the transformation of observations into explicit symbolic representations suitable for abstraction, interpretation, and reasoning. While modern AI systems achieve remarkable perceptual capabilities through large-scale statistical learning, the resulting knowledge is typically encoded within latent parameters that are difficult to inspect or manipulate analytically. Inspired by Neuro-Symbolic AI and theories of human abstraction, this paper investigates the formation of symbolic mathematical representations from geometric observations. We propose NeuSOGA (Neuro-Symbolic Geometric Abstraction), a framework that progressively transforms observations into topological abstractions, geometric abstractions, and ultimately symbolic mathematical representations. The architecture combines topology-guided structural discovery using Euclidean Distance Transforms, foundation-model perception using Segment Anything, adaptive multi-scale geometric abstraction, and symbolic synthesis through Implicit Area Splines. The resulting representation is an analytical implicit model supporting arbitrary-order smoothness, additive composition, and closed-form evaluation. Unlike neural latent encodings, the generated representation remains interpretable, editable, and mathematically explicit. Experiments on ModelNet40 point clouds, arbitrary-view projections, and segmented optical observations demonstrate that NeuSOGA transforms diverse observations into compact symbolic representations while preserving essential geometric and topological structure across sensing modalities and viewing directions. NeuSOGA provides an interpretable and explainable pathway from observation to symbol and establishes
