The Shape of Sight: A Homological Framework for Unifying Visual Perception

TL;DR

This paper introduces a homological framework that unifies core problems in visual perception by modeling stable perceptual structures and dynamic flows through topological parity, linking neural dynamics to perception.

Contribution

It proposes a novel topological approach using homological parity to unify static and dynamic aspects of visual perception, supported by neural pathway evidence.

Findings

Homological parity distinguishes static scaffolds from dynamic flows in perception.

Supports ventral-dorsal pathway separation through topological structures.

Provides a mathematical foundation linking neural dynamics to perceptual processes.

Abstract

Visual perception, the brain's construction of a stable world from sensory data, faces several long-standing, fundamental challenges. While often studied separately, these problems have resisted a single, unifying computational framework. In this perspective, we propose a homological framework for visual perception. We argue that the brain's latent representations are governed by their topological parity. This parity interpretation functionally separates homological structures into two distinct classes: 1) Even-dimensional homology ($H_{even}$) acts as static, integrative scaffolds. These structures bind context and content into ``wholes'' or ``what'', serving as the stable, resonant cavities for perceptual objects; 2) Odd-dimensional homology ($H_{odd}$) acts as dynamic, recurrent flows. These structures represent paths, transformations, and self-sustaining ``traces'' or ``where'' that navigate the perceptual landscape. This scaffold-and-flow model is supported by the ventral-dorsal pathway separation and provides a unified solution to three core problems in visual perception. Homological parity hypothesis recasts visual perception not as a linear computation, but as a dynamic interaction between stable, integrative structures and the recurrent, self-sustaining flows that run on them. This perspective offers a new mathematical foundation for linking neural dynamics to perception and cognition.