Related papers: Finite Connectivity Attractor Neural Networks

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…

A formally exact set of equations is derived for the description of nonequilibrium phenomena in classical liquids and glasses. With the help of a non equilibrium projection operator formalism, the correlation functions and fluctuation…

Recurrent neural networks (RNN) are powerful tools to explain how attractors may emerge from noisy, high-dimensional dynamics. We study here how to learn the ~N^(2) pairwise interactions in a RNN with N neurons to embed L manifolds of…

We introduce and analytically study a generalized p-spin glass like model that captures some of the main features of attractive glasses, recently found by Mode Coupling investigations, such as a glass/glass transition line and dynamical…

Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…

Brain structural networks are often represented as discrete adjacency matrices with elements summarizing the connectivity between pairs of regions of interest (ROIs). These ROIs are typically determined a-priori using a brain atlas. The…

Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…

We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method…

We study analytically the equilibrium properties of the spherical hierarchical model in the presence of random fields. The expression for the critical line separating a paramagnetic from a ferromagnetic phase is derived. The critical…

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…

We use the density matrix renormalization group method (DMRG) to compute the frequency and momentum resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features…

We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the p-th power of the in-degree of b. We restrict to the…

Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…

We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an ansatz for the…

Glass networks are piecewise linear ODE systems that models an interactive system where there are 'switching points': the underlying dynamic changes qualitatively when a certain variable pass over a threshold. One of the most well-studied…

Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…

We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice which has frustration between the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction J2. In this paper,…

True ground states are evaluated for a 2d Ising model with random near neighbor interactions and ferromagnetic second neighbor interactions (the Randomly Coupled Ferromagnet). The spin glass stiffness exponent is positive when the absolute…

The inverse statistical problem of finding direct interactions in complex networks is difficult. In the natural sciences, well-controlled perturbation experiments are widely used to probe the structure of complex networks. However, our…

So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\text{SU}(2)_k$ and examine their…