Related papers: The Homological Brain: Parity Principle and Amorti…

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…

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…

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.…

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…

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 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…

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 brain achieves stability and plasticity in a topologically complex, shifting world through Metric-Topology Factorization (MTF), separating discrete topological indexing for context selection from continuous metric condensation for local…

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 proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…

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},…

Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…

This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing…

Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…

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…

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 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,…

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

The learning and recognition of object features from unregulated input has been a longstanding challenge for artificial intelligence systems. Brains are adept at learning stable representations given small samples of noisy observations;…