Related papers: The Free Energy Principle drives neuromorphic deve…
The brain can be considered as a system that dynamically optimizes the structure of anatomical connections based on the efficiency requirements of functional connectivity. To illustrate the power of this principle in organizing the…
We construct a tensor model for nematic phases of bent-core molecules from molecular theory. The form of free energy is determined by molecular symmetry, which includes the couplings and derivatives of a vector and two second-order tensors,…
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…
Hardware-based neuromorphic computing remains an elusive goal with the potential to profoundly impact future technologies and deepen our understanding of emergent intelligence. The learning-from-mistakes algorithm is one of the few training…
It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given…
A thermodynamically motivated neural network model is described that self-organizes to transport charge associated with internal and external potentials while in contact with a thermal reservoir. The model integrates techniques for rapid,…
Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon our previous work on Ontology Neural Networks, we present an enhanced framework…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
We prove Goldschmidt's formula [Phys. Rev. B 47 (1990) 4858] for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the freezing transition in the phase diagram. The proof is…
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…
Motivated by the potential similarities between the underlying mechanisms of the enhanced memory storage capacity in black holes and in brain networks, we construct an artificial quantum neural network based on gravity-like synaptic…
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…
We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…
The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…
The free energy principle has been proposed as a unifying account of brain function. It is closely related, and in some cases subsumes, earlier unifying ideas such as Bayesian inference, predictive coding, and active learning. This article…
The emergence of cognition requires a framework that bridges evolutionary principles with neurocomputational mechanisms. This paper introduces the novel "thoughtseed" framework, proposing that cognition arises from the dynamic interaction…
We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric…
The term ``neuromorphic'' refers to systems that are closely resembling the architecture and/or the dynamics of biological neural networks. Typical examples are novel computer chips designed to mimic the architecture of a biological brain,…
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws.…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…