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Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…

Neural and Evolutionary Computing · Computer Science 2017-09-19 Saarthak Sarup , Mingoo Seok

Place-cell networks, typically forced to pairwise synaptic interactions, are widely studied as models of cognitive maps: such models, however, share a severely limited storage capacity, scaling linearly with network size and with a very…

Disordered Systems and Neural Networks · Physics 2025-11-24 Adriano Barra , Martino S. Centonze , Michela Marra Solazzo , Daniele Tantari

Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…

Machine Learning · Computer Science 2020-01-28 Evgenii Tsymbalov , Sergei Makarychev , Alexander Shapeev , Maxim Panov

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

Optimization and Control · Mathematics 2024-03-25 Veronica Centorrino , Francesco Bullo , Giovanni Russo

We consider $L$-directional associative memories, composed of $L$ Hopfield networks, displaying imitative Hebbian intra-network interactions and anti-imitative Hebbian inter-network interactions, where couplings are built over a set of…

Disordered Systems and Neural Networks · Physics 2025-04-11 Elena Agliari , Andrea Alessandrelli , Paulo Duarte Mourao , Alberto Fachechi

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…

Disordered Systems and Neural Networks · Physics 2022-04-19 Miriam Aquaro , Francesco Alemanno , Ido Kanter , Fabrizio Durante , Elena Agliari , Adriano Barra

This paper studies the capability of a recurrent neural network model to memorize random dynamical firing patterns by a simple local learning rule. Two modes of learning/memorization are considered: The first mode is strictly online, with a…

Information Theory · Computer Science 2020-01-10 Patrick Murer , Hans-Andrea Loeliger

Continual learning is the problem of sequentially learning new tasks or knowledge while protecting previously acquired knowledge. However, catastrophic forgetting poses a grand challenge for neural networks performing such learning process.…

Machine Learning · Computer Science 2020-07-01 Vithursan Thangarasa , Thomas Miconi , Graham W. Taylor

We derive the Gardner storage capacity for associative networks of threshold linear units, and show that with Hebbian learning they can operate closer to such Gardner bound than binary networks, and even surpass it. This is largely achieved…

Disordered Systems and Neural Networks · Physics 2021-01-13 Francesca Schönsberg , Yasser Roudi , Alessandro Treves

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…

Neural and Evolutionary Computing · Computer Science 2011-05-03 C. Ramya , G. Kavitha , Dr. K. S. Shreedhara

Human Activity Recognition (HAR) is a challenging problem that needs advanced solutions than using handcrafted features to achieve a desirable performance. Deep learning has been proposed as a solution to obtain more accurate HAR systems…

Machine Learning · Computer Science 2020-07-08 Hamed Damirchi , Rooholla Khorrambakht , Hamid Taghirad

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…

Neurons and Cognition · Quantitative Biology 2007-06-19 Benoit Siri , Mathias Quoy , Bruno Delord , Bruno Cessac , Hugues Berry

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…

Disordered Systems and Neural Networks · Physics 2009-10-31 Leonid B. Litinskii

Deep reinforcement learning algorithms are usually impeded by sampling inefficiency, heavily depending on multiple interactions with the environment to acquire accurate decision-making capabilities. In contrast, humans rely on their…

Machine Learning · Computer Science 2024-03-07 Yonggang Jin , Chenxu Wang , Tianyu Zheng , Liuyu Xiang , Yaodong Yang , Junge Zhang , Jie Fu , Zhaofeng He

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models…

Neural and Evolutionary Computing · Computer Science 2024-02-20 Mingqing Xiao , Qingyan Meng , Zongpeng Zhang , Di He , Zhouchen Lin

Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…

Neural and Evolutionary Computing · Computer Science 2021-07-29 Dmitry Krotov

A feed-forward neural net with adaptable synaptic weights and fixed, zero or non-zero threshold potentials is studied, in the presence of a global feedback signal that can only have two values, depending on whether the output of the network…

Disordered Systems and Neural Networks · Physics 2009-11-10 J. Bedaux , W. A. van Leeuwen

To solve a navigation task based on experiences, we need a mechanism to associate places with objects and to recall them along the course of action. In a reward-oriented task, if the route to a reward location is simulated in mind after…

Neurons and Cognition · Quantitative Biology 2024-10-28 Hiroki Nakagawa , Katsumi Tateno , Kensuke Takada , Takashi Morie

Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…

Machine Learning · Computer Science 2025-04-11 Saul Santos , António Farinhas , Daniel C. McNamee , André F. T. Martins

In machine learning, error back-propagation in multi-layer neural networks (deep learning) has been impressively successful in supervised and reinforcement learning tasks. As a model for learning in the brain, however, deep learning has…

Machine Learning · Computer Science 2016-12-19 Thomas Mesnard , Wulfram Gerstner , Johanni Brea