Related papers: On the Topological Foundation of Learning and Memo…
Biological intelligence emerges from substrates that are slow, noisy, and energetically constrained, yet it performs rapid and coherent inference in open-ended environments. Classical computational theories, built around vector-space…
We introduce the delta-homology model of memory, a unified framework in which recall, learning, and prediction emerge from cycle closure, the completion of topologically constrained trajectories within the brain's latent manifold. A…
Contemporary ML separates the static structure of parameters from the dynamic flow of inference, yielding systems that lack the sample efficiency and thermodynamic frugality of biological cognition. In this theoretical work, we propose…
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.…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
The Context-Content Uncertainty Principle (CCUP) proposes that inference under uncertainty is governed by an entropy asymmetry between context and content: high-entropy contexts must be interpreted through alignment with low-entropy,…
We propose a topological framework for memory and inference grounded in the structure of spike-timing dynamics, persistent homology, and the Context-Content Uncertainty Principle (CCUP). Starting from the observation that polychronous…
This paper introduces a unifying framework that links the Context-Content Uncertainty Principle (CCUP) with optimal transport (OT) via primal-dual inference. We propose that cognitive representations are not static encodings but active dual…
Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…
Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…
Just as the arrow of time structures physics, the arrow of inference organizes cognition, directing the flow of information in perception, action, and memory. The Context-Content Uncertainty Principle (CCUP) formalizes this asymmetry,…
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},…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Computation fundamentally separates time from space: nondeterministic search is exponential in time but polynomially simulable in space (Savitch's Theorem). We propose that the brain physically instantiates a biological variant of this…
Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…
Spatial awareness in mammals is based on internalized representations of the environment---cognitive maps---encoded by networks of spiking neurons. Although behavioral studies suggest that these maps can remain stable for long periods, it…
Human cognition spans perception, memory, intuitive judgment, deliberative reasoning, action selection, and social inference, yet these capacities are often explained through distinct computational theories. Here we present a unified…
A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a…
This review presents recent and older results on elementary quantitative and qualitative aspects of consciousness and cognition and tackles the question "What is consciousness?" conjointly from biological, neuroscience-cognitive, physical…
In this article, we present a cognitive architecture that is built from powerful yet simple neural models. Specifically, we describe an implementation of the common model of cognition grounded in neural generative coding and holographic…