相关论文: One+Infinite Dimensional Attractor Neural Networks

The Hubbard-Holstein model is one of the central models that describe the competition between electron-electron and electron-phonon interactions. In one dimension and at half-filling, the interplay between an electronic spin-density wave…

In this lecture I will present some models of neural networks that have been developed in the recent years. The aim is to construct neural networks which work as associative memories. Different attractors of the network will be identified…

We study the universal behavior associated with a Relativistic Boltzmann Transport (RBT) approach with the full collision integral in 0+1D conformal systems. We show that all momentum moments of the distribution function exhibit universal…

In the framework of the generalized Lotka Volterra model, solutions representing multispecies sequencial competition can be predictable with high probability. In this paper, we show that it occurs because the corresponding "heteroclinic…

A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation,…

We study a two-phase modified Stefan problem modeling solid combustion and nonequilibrium phase transition. The problem is known to exhibit a variety of non-trivial dynamical scenarios. We develop a priori estimates and establish…

We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Comp. 89 (2020), Calcolo 57 (2020)] satisfies an energy…

A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal…

Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the…

This paper discusses discrete-time maps of the form $x(k + 1) = F(x(k))$, focussing on equilibrium points of such maps. Under some circumstances, Lefschetz fixed-point theory can be used to establish the existence of a single locally…

Biological neural networks continuously adapt and modify themselves in response to experiences throughout their lifetime - a capability largely absent in artificial neural networks. Hebbian plasticity offers a promising path toward rapid…

We consider a pair of identical fermions with a short-range attractive interaction on a finite lattice cluster in the presence of strong site disorder. This toy model imitates a low density regime of the strongly disordered Hubbard model.…

A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…

We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics. We solve our model in the thermodynamic limit using generating functional analysis, and find (in contrast to the…

We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation…

In this paper, the existence, uniqueness, and positivity of solutions, as well as the asymptotic behavior through a finite fractal dimensional global attractor for a general Advection-Diffusion-Reaction (ADR) equation, are investigated. Our…

In this research, we introduce the concept of "computational entanglement," a phenomenon observed in overparameterized feedforward linear networks that enables the network to achieve zero loss by fitting random noise, even on previously…

The Hopfield associative memory model stores random patterns in synaptic couplings according to Hebb's rule and retrieves them through gradient descent on an energy function. This conventional setting, where neurons are assumed to have…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…

We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…