Related papers: Finite size effects for spiking neural networks wi…
Information propagation characterizes how input correlations evolve across layers in deep neural networks. This framework has been well studied using mean-field theory, which assumes infinitely wide networks. However, these assumptions…
This work theoretically studies stochastic neural networks, a main type of neural network in use. We prove that as the width of an optimized stochastic neural network tends to infinity, its predictive variance on the training set decreases…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study…
For small training set sizes $P$, the generalization error of wide neural networks is well-approximated by the error of an infinite width neural network (NN), either in the kernel or mean-field/feature-learning regime. However, after a…
We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free…
Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic boundary conditions are investigated by means of the $1/N$ expansion and by Monte Carlo simulations. Analytic and numerical results for magnetic susceptibility and…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells…
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for…
We propose a general procedure for extracting the running coupling constants of the underlying field theory of a given classical statistical model on a two-dimensional lattice, combining tensor network renormalization (TNR) and the…
A new perturbation theory is proposed for studying finite-size effects near critical point of the $\phi^4$ model with a one-component order parameter. The new approach is based on the techniques of generating functional and functional…
Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact…
Neurons are spatially extended cells; different parts of a neuron have specific voltage dynamics. Important types of neurons even generate different spikes in different parts of the cell. Neurons' inputs are also often spatially…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary…
Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid…
Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be…
The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…