Related papers: Formalized Hopfield Networks and Boltzmann Machine…

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…

The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…

It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be…

We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

We present the first proof of principle that normalizing flows can accurately learn the Boltzmann distribution of the fermionic Hubbard model - a key framework for describing the electronic structure of graphene and related materials.…

Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest…

These are lecture notes for a course on machine learning with neural networks for scientists and engineers that I have given at Gothenburg University and Chalmers Technical University in Gothenburg, Sweden. The material is organised into…

Boltzmann Machines (BMs) are graphical models with interconnected binary units, employed for the unsupervised modeling of data distributions. When trained on real data, BMs show the tendency to behave like critical systems, displaying a…

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…

In this paper we propose a novel neural network model for learning stochastic Hamiltonian systems (SHSs) from observational data, termed the stochastic generating function neural network (SGFNN). SGFNN preserves symplectic structure of the…

The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…

Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…

A number of recent papers have provided evidence that practical design questions about neural networks may be tackled theoretically by studying the behavior of random networks. However, until now the tools available for analyzing random…

In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…

Statistical mechanics has made significant contributions to the study of biological neural systems by modeling them as recurrent networks of interconnected units with adjustable interactions. Several algorithms have been proposed to…

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…

The process of training feedforward neural networks (FFNNs) can benefit from an automated process where the best heuristic to train the network is sought out automatically by means of a high-level probabilistic-based heuristic. This…

We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor…

For the Hopfield model with the Hebb connection matrix we investigate the case of $p$ memorized patterns that are distorted copies of the same {\it standard}. In other words, we try to simulate that learning always takes place by means of…