Related papers: Non-Convex Multi-species Hopfield models
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…
Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This…
Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…
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…
The modern Hopfield network, proposed by Krotov and Hopfield, is a mathematical generalization of the Hopfield network, which is a basic model of associative memory that employs higher-order interactions. This study introduces an open…
Modern Hopfield Neural Networks (HNNs), also known as Dense Associative Memories (DAMs), enhance the performance of simple recurrent neural networks by leveraging the nonlinearities in their energy functions. They have broad applications in…
The brain can reproduce memories from partial data; this ability is critical for memory recall. The process of memory recall has been studied using auto-associative networks such as the Hopfield model. This kind of model reliably converges…
The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and…
A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…
Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for…
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…
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…
In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an…
Associative memory or content-addressable memory is an important component function in computer science and information processing, and at the same time a key concept in cognitive and computational brain science. Many different neural…
Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…
Understanding both global and layer-specific group structures is useful for uncovering complex patterns in networks with multiple interaction types. In this work, we introduce a new model, the hierarchical multiplex stochastic blockmodel…
In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a…
Sequential learning involves learning tasks in a sequence, and proves challenging for most neural networks. Biological neural networks regularly conquer the sequential learning challenge and are even capable of transferring knowledge both…
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…
In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet…