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The Geometry of Intelligence: Deterministic Functional Topology as a Foundation for Real-World Perception

ArXivSource

Eduardo Di Santi

cs.LG
math.OC
|
Dec 4, 2025
5 views

One-line Summary

The paper proposes a deterministic functional-topological framework for understanding real-world perception, enabling systems to generalize from limited data by discovering the compact manifold structure of physical phenomena through self-supervised methods.

Plain-language Overview

This research explores how both biological and artificial systems can quickly learn from just a few examples by focusing on the geometric structure of real-world processes. The authors suggest that these processes form a compact and stable shape in a mathematical space, which helps in understanding and predicting them. They introduce a new framework that allows systems to identify the boundaries of this shape without prior knowledge of the underlying equations. The study is supported by experiments in various fields, showing that this method can help systems perceive and understand the world more effectively.

Technical Details