Original title: Neuro-Symbolic Geometric Abstraction (NeuSOGA): From Observations to Symbolic Mathematical Representations
Qingde Li, Qingqi Hong, Jie Tian · September 2026
Modern artificial intelligence systems are great at perceiving the world, but they store what they learn inside hidden settings that humans cannot easily inspect or edit. To fix this, researchers built NeuSOGA, short for Neuro-Symbolic Geometric Abstraction. The system turns raw sensory observations into clear, symbolic mathematical formulas. It works by stepping through distinct stages. First, it extracts topological structure and uses a perception model called Segment AnythingA foundation model that can detect and separate objects in images with minimal input.. Next, it simplifies the shapes into geometric abstractions. Finally, it builds analytical mathematical equations using Implicit Area SplinesA method for generating smooth curves or surfaces using mathematical functions that implicitly define regions.. The researchers tested NeuSOGA on shapes, point clouds, and images from different viewing angles. They found that the framework successfully turns varied sensory inputs into compact, interpretable mathematical models while keeping the vital shape and structure fully intact.
Imagine trying to describe a complex sculpture to someone over the phone using only vague terms like 'pointy' or 'smooth.' It's hard to convey the exact shape without a clear system. In this paper, the framework takes visual observations and turns them into precise mathematical descriptions, much like creating a blueprint with exact measurements that anyone can follow and adjust.
Most AI systems hide their reasoning inside unreadable parameters, making them hard to trust or fix. This framework turns AI's understanding into clear equations, so humans can inspect and modify them. It's important for safety-critical fields like autonomous systems or medical diagnosis.
The abstract indicates experiments are conducted on ModelNet40 point clouds and optical observations, so broader applicability is not demonstrated. It focuses on geometric and topological aspects, potentially not covering other sensory data like color or texture. The framework's complexity or real-world scalability is not discussed.
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Neuro-Symbolic Geometric Abstraction (NeuSOGA): From Observations to Symbolic Mathematical Representations — Qingde Li, Qingqi Hong, Jie Tian
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.