NeuSOGA3D is a hybrid neuro‑symbolic framework that reconstructs 3D geometry from unorganized point clouds by combining learned perceptual priors with explicit symbolic geometric reasoning. It projects point clouds onto orthographic planes, builds symbolic implicit spline representations, and fuses them via shape‑preserving constructive solid geometry to produce a coarse visual hull. Additional detail is added through cross‑sectional decomposition and volumetric reconstruction with Partial Shape‑Preserving Splines, yielding CAD‑compatible, structurally meaningful models across all 40 ModelNet40 categories.
By Qingde Li, Qingqi Hong, Zihan Li, Jie Tian
arXiv:2604. 18050v2 Announce Type: replace Abstract: AlphaGeometry represents a milestone in neuro-symbolic reasoning, yet its architecture faces a log-linear scaling bottleneck within its symbolic deduction engine that limits its efficiency as problem complexity increases.
By Anthony Bordg
arXiv:2606. 27926v1 Announce Type: new Abstract: Geometry Problem Solving have increasingly adopt the neuro-symbolic paradigm, combining neural intuition with symbolic rigor.
By Can Li, Ting Zhang, Junbo Zhao, Hua Huang
arXiv:2609.05575v1 Announce Type: new
Abstract: Understanding how concepts are encoded in the internal representations of machine learning models is a central problem in mechanistic interpretability,...
By Yiming Tang, Harshvardhan Saini, Samyak Jha, Huaming Chen, Xufeng Duan, Dianbo Liu
The paper introduces a framework that combines a Geometric Vision Parser and a Symbolic Solver to enable a Large Language Model to solve complex plane geometry problems. By translating diagrams into symbolic representations and performing formal deductions, the approach reduces hallucinations and produces interpretable, human-like solutions. Experiments on a new benchmark from 2025 Chinese Zhongkao exams show performance comparable to Gemini 2.5 Pro.
By Weichen Dai, Rafael Medeiros Cabral, Ziyi Shou, Yan Cao, Xin Shen, Dongcai Lu, Yi Zhou
arXiv:2512. 12225v3 Announce Type: replace Abstract: Developing artificial agents that unify representation, memory, adaptation, and prediction remains a fundamental challenge in artificial intelligence.
By Laha Ale
arXiv:2606. 04381v1 Announce Type: cross Abstract: Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space.
By Chen Chu, Bita Azarijoo, Li Xiong, Khurram Shafique, Cyrus Shahabi
arXiv:2606. 07007v1 Announce Type: cross Abstract: We propose a unified mathematical framework for a geometric understanding of concept learning and neuron interpretation in sparse autoencoders (SAEs).
By Chenhao Zhang, Chris Lin, Su-In Lee
arXiv:2609.12606v2 Announce Type: replace
Abstract: While multimodal reasoning has advanced rapidly, solving complex geometry problems critically hinges on active visual assistance, such as construct...
By Zhitong Dong, Jicai Pan, Yingguo Gao, Jingting Ding, Hao Chen, Jinjie Gu
Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators.
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
By Guangyu Meng, Pengfei Gu, Xueyang Li, Yiyu Shi, Erin Wolf Chambers, Danny Z. Chen
arXiv:2510. 24342v2 Announce Type: replace Abstract: Prior brain-AI alignment studies are typically constrained by specific inputs and tasks, limiting their ability to capture organizational properties across models with different modalities.
By Silin Chen, Yuzhong Chen, Caiwei Wang, Zifan Wang, Junhao Wang, Zifeng Jia, Keith M Kendrick, Tuo Zhang, Lin Zhao, Dezhong Yao, Tianming Liu, Xi Jiang