Related papers: The Free Energy Principle drives neuromorphic deve…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general…
The human brain represents the only known example of general intelligence that naturally aligns with human values. On a mere 20-watt power budget, the brain achieves robust learning and adaptive decision-making in ways that continue to…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to…
We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by…
It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero mode…
Multiscale synergy -- the interplay of a system's distinct characteristic length, time, and energy scales -- is becoming a unifying thread across many contemporary branches of science. Ranging from moir\'e and super-moir\'e materials and…
The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its roots in the nonextensive nature of…
We analyze the force-extension curve for a general class of systems, which are described at the mesoscopic level by a free energy depending on the extension of its components. Similarly to what is done in real experiments, the total length…
We propose a concept of autonomous energy transducer at a molecular scale, where output is produced with small input energy, of the same order of the thermal energy, without restriction of magnitude or timing of input, and without any…
Atomic-scale phase-field modeling formulates the probability densities of atomic vibrations as Gaussian distributions and derives a free energy functional using variational Gaussian theory and interatomic potentials. This framework permits…
The 'free energy principle' (FEP) has been suggested to provide a unified theory of the brain, integrating data and theory relating to action, perception, and learning. The theory and implementation of the FEP combines insights from…
We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over…
Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…
The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…
A critical mystery in neuroscience lies in determining how anatomical structure impacts the complex functional dynamics of human thought. How does large-scale brain circuitry constrain states of neuronal activity and transitions between…
Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks…
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to…
The nucleation process under different external conditions is considered. It is shown that the duration of this process can be connected with the microscopic corrections to the free energy of the critical embryo. Connection between…