Related papers: Finite Connectivity Attractor Neural Networks
In this article, we explore the potential of artificial neural networks, which are trained using an exceptionally simplified catalog of ideal configurations encompassing both order and disorder. We explore the generalisation power of these…
Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning.…
The attention interaction matrix $QK^{\top}$ contains two entangled computations: a skew-symmetric component that redistributes information between positions (routing) and a symmetric component that scales mutual relevance (filtering). We…
In this work we reveal and explore a new class of attractor neural networks, based on inborn connections provided by model molecular markers, the molecular marker based attractor neural networks (MMBANN). We have explored conditions for the…
We study spin 3/2 fermionic cold atoms with attractive interactions confined in a one-dimensional optical lattice. Using numerical techniques, we determine the phase diagram for a generic density. For the chosen parameters, one-particle…
The phase diagram of two interacting planar arrays of directed lines in random media is obtained by a renormalization group analysis. The results are discussed in the contexts of the roughening of reconstructed crystal surfaces, and the…
The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p \to \infty$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that…
Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints.…
Bifurcation theory is a powerful tool for studying how the dynamics of a neural network model depends on its underlying neurophysiological parameters. However, bifurcation theory has been developed mostly for smooth dynamical systems and…
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
We analyze the properties of the energy landscape of {\it finite-size} fully connected p-spin-like models whose high temperature phase is described, in the thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled liquids.…
The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on…
In this paper, we introduce a novel approach to neural learning: the Feature-Imitating-Network (FIN). A FIN is a neural network with weights that are initialized to reliably approximate one or more closed-form statistical features, such as…
We present, as a very general method, an effective field theory to analyze models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it gives the exact…
In this paper we study a fully connected planted spin glass named the planted XY model. Motivation for studying this system comes both from the spin glass field and the one of statistical inference where it models the angular…
The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions $(d\to \infty)$. In spite of its simplicity the model displays a rich…
We study fully occupied lattice systems of classical magnetic dipoles which point along random axes. Only dipolar interactions are considered. From tempered Monte Carlo simulations, we obtain numerical evidence that supports the following…
This paper addresses the problem of finding cycles in the state transition graphs of synchronous Boolean networks. Synchronous Boolean networks are a class of deterministic finite state machines which are used for the modeling of gene…
Inferring synaptic connectivity from neural population activity is a fundamental challenge in computational neuroscience, complicated by partial observability and mismatches between inference models and true circuit dynamics. In this study,…
One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…