视觉的形态：视觉感知的同调框架
The Shape of Sight: A Homological Framework for Unifying Visual Perception
AI总结：
本文提出基于同调框架的视觉感知模型，通过偶维和奇维同调结构区分静态支架与动态流动，统一解决视觉感知的核心问题。
摘要：
视觉感知是大脑从感官数据构建稳定世界的进程，面临几个长期存在的根本性挑战。尽管通常被单独研究，这些问题一直缺乏一个统一的计算框架。在本文中，我们提出了一种视觉感知的同调框架。我们主张大脑的潜在表征由其拓扑奇偶性所支配。这种奇偶性解释将同调结构分为两类：1) 偶维同调（H_even）作为静态、整合的支架。这些结构将上下文和内容结合为“整体”或“什么”，作为感知对象的稳定、共振空腔；2) 奇维同调（H_odd）作为动态、循环的流动。这些结构代表路径、变换和自我维持的“轨迹”或“哪里”，在感知景观中导航。这种支架与流动模型得到了腹侧-背侧通路分离的支持，并为视觉感知的三个核心问题提供了统一的解决方案。同调奇偶性假说将视觉感知重新定义为稳定整合结构与运行在其上的循环、自我维持流动之间的动态交互。这一视角为将神经动态与感知和认知联系起来提供了新的数学基础。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
