Related papers: Generalization in the Hopfield Model

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…

This paper examines the memory capacity of generalized neural networks. Hopfield networks trained with a variety of learning techniques are investigated for their capacity both for binary and non-binary alphabets. It is shown that the…

We extend the existing work on Hopfield network state classification, employing more complex models that remain interpretable, such as densely-connected feed-forward deep neural networks and support vector machines. The states of the…

This article delves into the Hopfield neural network model, drawing inspiration from biological neural systems. The exploration begins with an overview of the model's foundations, incorporating insights from mechanical statistics to deepen…

Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…

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…

A set of fixed points of the Hopfield type neural network was under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…

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…

One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according to the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…

It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model. In this work we…

We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical…

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…

A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

Machine learning promises methods that generalize well from finite labeled data. However, the brittleness of existing neural net approaches is revealed by notable failures, such as the existence of adversarial examples that are…

Human eye movement mechanisms (saccades) are very useful for scene analysis, including object representation and pattern recognition. In this letter, a Hopfield neural network to emulate saccades is proposed. The network uses an energy…

In this paper we study the generalization capabilities of fully-connected neural networks trained in the context of time series forecasting. Time series do not satisfy the typical assumption in statistical learning theory of the data being…

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…