Related papers: Memory as Structured Trajectories: Persistent Homo…
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…
We propose a formal foundation for cognition rooted in algebraic topology, built on a Homological Parity Principle. This posits that even-dimensional homology represents stable Structure/Context (e.g., generative models), while…
Sequence learning, prediction and replay have been proposed to constitute the universal computations performed by the neocortex. The Hierarchical Temporal Memory (HTM) algorithm realizes these forms of computation. It learns sequences in an…
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…
In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…
We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence…
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…
We propose an information-topological framework in which cycle closure is the fundamental mechanism of memory and consciousness. Memory is not a static store but the ability to re-enter latent cycles in neural state space, with invariant…
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…
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…
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 \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},…
We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…
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,…
The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space---a cognitive map. These cells do not only exhibit location-specific spiking during…
The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis…
Memory consolidation, the process by which transient experiences are transformed into stable, structured representations, is a foundational organizing principle in the human brain, yet it remains largely unexplored as a design principle for…
The spiking activity of principal cells in mammalian hippocampus encodes an internalized neuronal representation of the ambient space---a cognitive map. Once learned, such a map enables the animal to navigate a given environment for a long…
Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine…
Associative memory architectures such as the Hopfield network have long been important conceptual and theoretical models for neuroscience and artificial intelligence. However, translating these abstract models into spiking neural networks…