Related papers: Neural Field Models with Transmission Delays and D…

Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (the…

Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time…

We are concerned with the numerical solution of a class integro-differential equations, known as Neural Field Equations, which describe the large-scale dynamics of spatially structured networks of neurons. These equations have many…

Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative…

Neural encoding is a field in neuroscience that focuses on characterizing how information from stimuli is encoded in the spiking activity of neurons. When more than one stimulus is present, a theory known as multiplexing posits that neurons…

We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph…

In this work, we investigate the dynamical properties of a reaction-diffusion system arising from tumor-therapy modelling that features both nonlinear interactions and nonlocal delay. By applying the Lyapunov-Schmidt reduction, we establish…

We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node…

Neural Style Transfer (NST) is the field of study applying neural techniques to modify the artistic appearance of a content image to match the style of a reference style image. Traditionally, NST methods have focused on texture-based image…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

We study a neural network model in which both neurons and synaptic interactions evolve in time simultaneously. The time evolution of synaptic interactions is described by a Langevin equation including a Hebbian learning term, and a bias…

Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…

Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…

The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…

Neural fields, a category of neural networks trained to represent high-frequency signals, have gained significant attention in recent years due to their impressive performance in modeling complex 3D data, such as signed distance (SDFs) or…

We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…

Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…

Visual illusions in humans arise when interpreting out-of-distribution stimuli: if the observer is adapted to certain statistics, perception of outliers deviates from reality. Recent studies have shown that artificial neural networks (ANNs)…