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Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…

Machine Learning · Computer Science 2024-12-02 Xueyan Niu , Bo Bai , Lei Deng , Wei Han

We analyze continuous Hopfield associative memories augmented by additional, rapid short-term associative synaptic plasticity. Through the cavity method, we determine the boundary between the retrieval and forgetting, or spin-glass phase,…

Neurons and Cognition · Quantitative Biology 2026-02-10 Martina Del Gaudio , Federico Ghimenti , Surya Ganguli

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

It has been shown that a neural network model recently proposed to describe basic memory performance is based on a ternary/binary coding/decoding algorithm which leads to a new neural network assembly memory model (NNAMM) providing…

Artificial Intelligence · Computer Science 2007-05-23 Petro M. Gopych

In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the…

General Physics · Physics 2008-01-28 Maxim Budaev

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…

Machine Learning · Computer Science 2024-11-01 Benjamin Hoover , Duen Horng Chau , Hendrik Strobelt , Parikshit Ram , Dmitry Krotov

Classical autoassociative memory models have been central to understanding emergent computations in recurrent neural circuits across diverse biological contexts. However, they typically neglect neuromodulatory agents that are known to…

Neurons and Cognition · Quantitative Biology 2025-12-17 Daiki Goto , Hector Manuel Lopez Rios , Monika Scholz , Suriyanarayanan Vaikuntanathan

We study a fully connected Hopfield-type associative memory network with online activity-dependent synaptic plasticity, where neural states and synaptic couplings coevolve during retrieval. Using the generating-functional formalism, we…

Disordered Systems and Neural Networks · Physics 2026-05-22 Yoshinori Hara , Yoshiyuki Kabashima

High-order extensions of the Hopfield model are known to exhibit dramatically enhanced storage capacity at equilibrium, while their dynamical retrieval properties remain less well understood. In our previous work, we carried out a dynamical…

Statistical Mechanics · Physics 2026-04-06 Yuto Sumikawa , Yoshiyuki Kabashima

We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to…

Neural and Evolutionary Computing · Computer Science 2016-05-20 Ivo Danihelka , Greg Wayne , Benigno Uria , Nal Kalchbrenner , Alex Graves

The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…

Neural and Evolutionary Computing · Computer Science 2018-10-30 Alberto Fachechi , Elena Agliari , Adriano Barra

Associative memory architectures such as the Hopfield network have long been important conceptual and theoretical models for neuroscience and artificial intelligence. However, translating these abstract models into spiking neural networks…

Neurons and Cognition · Quantitative Biology 2025-07-02 William F. Podlaski , Christian K. Machens

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…

Neurons and Cognition · Quantitative Biology 2016-02-17 Alireza Alemi , Carlo Baldassi , Nicolas Brunel , Riccardo Zecchina

Natural memories are associative, declarative and distributed. Symbolic computing memories resemble natural memories in their declarative character, and information can be stored and recovered explicitly; however, they lack the associative…

Artificial Intelligence · Computer Science 2020-09-29 Luis A. Pineda , Gibrán Fuentes , Rafael Morales

Energy-based probabilistic models learned by maximizing the likelihood of the data are limited by the intractability of the partition function. A widely used workaround is to maximize the pseudo-likelihood, which replaces the global…

Statistical Mechanics · Physics 2026-03-31 Francesco D'Amico , Dario Bocchi , Luca Maria Del Bono , Saverio Rossi , Matteo Negri

We analyze a variant of the Hopfield model that incorporates an unlearning mechanism based on spin correlations in the high-temperature regime. In the large system limit where extensively many patterns are stored, we employ the replica…

Disordered Systems and Neural Networks · Physics 2026-02-10 Shuta Takeuchi , Takashi Takahashi , Yoshiyuki Kabashima

In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different…

Disordered Systems and Neural Networks · Physics 2018-07-11 Elena Agliari , Danila Migliozzi , Daniele Tantari

We introduce a three-dimensional vectorial extension of the Hopfield associative-memory model in which each neuron is a unit vector on $S^2$ and synaptic couplings are $3\times 3$ blocks generated through a vectorial Hebbian rule. The…

Disordered Systems and Neural Networks · Physics 2025-12-10 F. Gallavotti , A. Zaccone

In the context of attractor neural networks, we study how the equilibrium analog neural activities, reached by the network dynamics during memory retrieval, may improve storage performance by reducing the interferences between the recalled…

Condensed Matter · Physics 2009-10-22 Nicolas Brunel , Riccardo Zecchina

Neural networks are susceptible to catastrophic forgetting. They fail to preserve previously acquired knowledge when adapting to new tasks. Inspired by human associative memory system, we propose a brain-like approach that imitates the…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 Yi Gu , Jie Li , Yuting Gao , Ruoxin Chen , Chentao Wu , Feiyang Cai , Chao Wang , Zirui Zhang