相关论文: Some Exact Results of Hopfield Neural Networks and…

In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory. Studying random binary patterns, he also uncovered that, if a small…

We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…

We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…

The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…

The Dense Associative Memory generalizes the Hopfield network by allowing for sharper interaction functions. This increases the capacity of the network as an autoassociative memory as nearby learned attractors will not interfere with one…

In neuroscience, classical Hopfield networks are the standard biologically plausible model of long-term memory, relying on Hebbian plasticity for storage and attractor dynamics for recall. In contrast, memory-augmented neural networks in…

A general scheme to realize a perceptron for hardware neural networks is presented, where multiple interconnections are achieved by a superposition of Schrodinger waves. Spatially patterned potentials process information by coupling…

A recurrent artificial neural network known as Hopfield network is used for pattern storage. Here we have applied this associative memory type network for pattern recognition for predictive controls and diagnostics in accelerator based…

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…

This paper continues on the work of the B-Matrix approach in hebbian learning proposed by Dr. Kak. It reports the results on methods of improving the memory retrieval capacity of the hebbian neural network which implements the B-Matrix…

The exponential rise in data generation has led to vast, heterogeneous datasets crucial for predictive analytics and decision-making. Ensuring data quality and semantic integrity remains a challenge. This paper presents a brain-inspired…

Neural network models offer a theoretical testbed for the study of learning at the cellular level. The only experimentally verified learning rule, Hebb's rule, is extremely limited in its ability to train networks to perform complex tasks.…

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…

Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour…

It turned out that the set of the fixed points is not necessarily the same as the set of the local minima of the energy functional. It depends on the diagonal elements of the connection matrix. The simple method which allows to cut off…

Hopfield networks (HNs) and Restricted Boltzmann Machines (RBMs) are two important models at the interface of statistical physics, machine learning, and neuroscience. Recently, there has been interest in the relationship between HNs and…

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native…

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…

Modern Hopfield networks have enjoyed recent interest due to their connection to attention in transformers. Our paper provides a unified framework for sparse Hopfield networks by establishing a link with Fenchel-Young losses. The result is…

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…