Related papers: Cycle is All You Need: More Is Different

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…

What is intelligence? We argue for a structural-dynamical account rooted in a topological closure law: \emph{the boundary of a boundary vanishes} ($\partial^2=0$). This principle forces transient fragments to cancel while closed cycles…

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…

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},…

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,…

Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the…

Neuronal networks alternate between high- and low-activity regimes, known as up and down states. They also display rhythmic patterns essential for perception, memory consolidation, and sensory processing. Despite their importance, the…

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…

Cyclic patterns of neuronal activity are ubiquitous in animal nervous systems, and partially responsible for generating and controlling rhythmic movements such as locomotion, respiration, swallowing and so on. Clarifying the role of the…

Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…

Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large…

Memory systems can store vastly different amounts of information despite similar hardware constraints. Here, we show that superior spatial memory emerges from a discrete stiffening of hippocampal population geometry-a transition from…

This work introduces a novel Retention Layer mechanism for Transformer based architectures, addressing their inherent lack of intrinsic retention capabilities. Unlike human cognition, which can encode and dynamically recall symbolic…

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising…

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…

This paper proposes an extension of the traditional Central Dogma of molecular biology to a more dynamic model termed the Central Dogma Cycle (CDC) and a broader network called the Central Dogma Cyclic Network (CDCN). While the Central…

Codifying memories is one of the fundamental problems of modern Neuroscience. The functional mechanisms behind this phenomenon remain largely unknown. Experimental evidence suggests that some of the memory functions are performed by…

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…

The problem of consciousness faced several challenges for a few reasons: (a) a lack of necessary and sufficient conditions, without which we would not know how close we are to the solution, (b) a lack of a synthesis framework to build…

Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context…