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The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation…

Neural and Evolutionary Computing · Computer Science 2007-05-23 Xiaofei Huang

Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to…

Neurons and Cognition · Quantitative Biology 2015-05-19 Harold P. de Vladar , Eörs Szathmáry

The neuronal paradigm of studying the brain has left us with limitations in both our understanding of how neurons process information to achieve biological intelligence and how such knowledge may be translated into artificial intelligence…

Neurons and Cognition · Quantitative Biology 2020-05-12 Leo Kozachkov , Konstantinos P. Michmizos

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…

Dynamical Systems · Mathematics 2022-08-18 Matthew E. Levine , Andrew M. Stuart

Continual learning aims to empower artificial intelligence (AI) with strong adaptability to the real world. For this purpose, a desirable solution should properly balance memory stability with learning plasticity, and acquire sufficient…

Machine Learning · Computer Science 2023-11-10 Liyuan Wang , Xingxing Zhang , Qian Li , Mingtian Zhang , Hang Su , Jun Zhu , Yi Zhong

Deep neural networks give us a powerful method to model the training dataset's relationship between input and output. We can regard that as a complex adaptive system consisting of many artificial neurons that work as an adaptive memory as a…

Disordered Systems and Neural Networks · Physics 2024-05-08 Kenichi Nakazato

Modern autonomous systems are driving the critical need for next-generation adaptive materials and structures with embodied intelligence, i.e., the embodiment of memory, perception, learning, and decision-making within the mechanical…

Applied Physics · Physics 2025-11-18 Yuning Zhang , K. W. Wang

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors…

Neural and Evolutionary Computing · Computer Science 2014-03-14 Amin Karbasi , Amir Hesam Salavati , Amin Shokrollahi , Lav R. Varshney

Neural circuits exhibit remarkable computational flexibility, enabling adaptive responses to noisy and ever-changing environmental cues. A fundamental question in neuroscience concerns how a wide range of behaviors can emerge from a…

Statistical Mechanics · Physics 2025-09-18 Giacomo Barzon , Daniel M. Busiello , Giorgio Nicoletti

Models of interacting complex systems provide the fundamental statistical physics reference frame for the study and the understanding of associative memories, machine learning, and the dynamics of neural networks. On the other hand,…

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

In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…

Analysis of PDEs · Mathematics 2025-10-27 Yuncheng You

Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…

Neurons and Cognition · Quantitative Biology 2026-01-30 Tala Fakhoury , Elia Turner , Sushrut Thorat , Athena Akrami

Learning is based on synaptic plasticity, which affects and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic…

Neurons and Cognition · Quantitative Biology 2026-01-14 Jakob Stubenrauch , Naomi Auer , Richard Kempter , Benjamin Lindner

The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space---a cognitive map. These cells do not only exhibit location-specific spiking during…

Neurons and Cognition · Quantitative Biology 2018-11-05 Andrey Babichev , Dmitriy Morozov , Yuri Dabaghian

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

Humans excel at continually acquiring, consolidating, and retaining information from an ever-changing environment, whereas artificial neural networks (ANNs) exhibit catastrophic forgetting. There are considerable differences in the…

Neural and Evolutionary Computing · Computer Science 2023-04-17 Fahad Sarfraz , Elahe Arani , Bahram Zonooz

Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening…

Numerical Analysis · Mathematics 2024-03-11 Aleksandr Dekhovich , O. Taylan Turan , Jiaxiang Yi , Miguel A. Bessa

Various work has suggested that the memorability of an image is consistent across people, and thus can be treated as an intrinsic property of an image. Using computer vision models, we can make specific predictions about what people will…

Computer Vision and Pattern Recognition · Computer Science 2022-01-11 Coen D. Needell , Wilma A. Bainbridge

Memory and forgetting constitute two sides of the same coin, and although the first has been rigorously investigated, the latter is often overlooked. A number of experiments under the realm of psychology and experimental neuroscience have…

Neurons and Cognition · Quantitative Biology 2019-07-23 Antonios Georgiou , Mikhail Katkov , Misha Tsodyks