
TL;DR
This paper introduces Information Topology, a framework unifying information theory and algebraic topology, to explain how stable informational cycles underpin inference, learning, and prediction across various domains.
Contribution
It develops a novel topological approach to information, defining concepts like homological capacity and stability principles that connect entropy, invariants, and inference.
Findings
Homological capacity as a measure of sustainable informational cycles
Stable invariants underpin robust prediction and generalization
Application to visual binding, working memory, and consciousness
Abstract
We introduce \emph{Information Topology}: a framework that unifies information theory and algebraic topology by treating \emph{cycle closure} as the primitive operation of inference. The starting point is the \emph{dot-cycle dichotomy}, which separates pointwise, order-sensitive fluctuations (dots) from order-invariant, predictive structure (cycles). Algebraically, closure is the cancellation of boundaries (), which converts transient histories into stable invariants. Building on this, we derive the \emph{Structure-Before-Specificity} (SbS) principle: stable information resides in nontrivial homology classes that persist under perturbations, while high-entropy contextual details act as scaffolds. The \emph{Context-Content Uncertainty Principle} (CCUP) quantifies this balance by decomposing uncertainty into contextual spread and content precision, showing why prediction…
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Taxonomy
TopicsCCD and CMOS Imaging Sensors · Neural dynamics and brain function · Visual Attention and Saliency Detection
