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The Hopfield network serves as a fundamental energy-based model in machine learning, capturing memory retrieval dynamics through an ordinary differential equation (ODE). The model's output, the equilibrium point of the ODE, is traditionally…

Machine Learning · Computer Science 2024-08-22 Cédric Goemaere , Johannes Deleu , Thomas Demeester

Efficient state restoration in multi-turn conversations with large language models (LLMs) remains a critical challenge, primarily due to the overhead of recomputing or loading full key-value (KV) caches for all historical tokens. To address…

Computation and Language · Computer Science 2025-08-27 Junyi Wen , Junyuan Liang , Zicong Hong , Wuhui Chen , Ting Cai , Zibin Zheng

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…

Condensed Matter · Physics 2009-10-22 J. J. Arenzon , R. M. C. de Almeida

Mobile and embedded applications require neural networks-based pattern recognition systems to perform well under a tight computational budget. In contrast to commonly used synchronous, frame-based vision systems and CNNs, asynchronous,…

Neural and Evolutionary Computing · Computer Science 2019-06-24 Bodo Rückauer , Nicolas Känzig , Shih-Chii Liu , Tobi Delbruck , Yulia Sandamirskaya

Rehearsal-based Continual Learning (CL) has been intensely investigated in Deep Neural Networks (DNNs). However, its application in Spiking Neural Networks (SNNs) has not been explored in depth. In this paper we introduce the first…

Neural and Evolutionary Computing · Computer Science 2024-12-23 Alberto Dequino , Alessio Carpegna , Davide Nadalini , Alessandro Savino , Luca Benini , Stefano Di Carlo , Francesco Conti

We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…

Disordered Systems and Neural Networks · Physics 2026-02-17 Flavio Nicoletti , Francesco D'Amico , Matteo Negri

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,…

To improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the spurious memories (as in dreaming algorithms).…

Disordered Systems and Neural Networks · Physics 2025-06-03 Ludovica Serricchio , Dario Bocchi , Claudio Chilin , Raffaele Marino , Matteo Negri , Chiara Cammarota , Federico Ricci-Tersenghi

Despite their advantages in terms of computational resources, latency, and power consumption, event-based implementations of neural networks have not been able to achieve the same performance figures as their equivalent state-of-the-art…

Neural and Evolutionary Computing · Computer Science 2016-11-03 Jonathan Binas , Giacomo Indiveri , Michael Pfeiffer

The application of kernel-based Machine Learning (ML) techniques to discrete choice modelling using large datasets often faces challenges due to memory requirements and the considerable number of parameters involved in these models. This…

Machine Learning · Computer Science 2024-12-04 José Ángel Martín-Baos , Ricardo García-Ródenas , Luis Rodriguez-Benitez , Michel Bierlaire

The study of brain states, ranging from highly synchronous to asynchronous neuronal patterns like the sleep-wake cycle, is fundamental for assessing the brain's spatiotemporal dynamics and their close connection to behavior. However, the…

Neurons and Cognition · Quantitative Biology 2023-11-13 Arnau Marin-Llobet , Arnau Manasanch , Maria V. Sanchez-Vives

Hybrid architectures combining state-space models with attention have achieved strong efficiency-quality tradeoffs, yet existing approaches either apply attention uniformly or learn static sparse patterns. This misses a key opportunity:…

Machine Learning · Computer Science 2026-02-13 Ibne Farabi Shihab , Sanjeda Akter , Anuj Sharma

Biologically-inspired computing models have made significant progress in recent years, but the conventional von Neumann architecture is inefficient for the large-scale matrix operations and massive parallelism required by these models. This…

Hardware Architecture · Computer Science 2025-09-23 Siqing Fu , Lizhou Wu , Tiejun Li , Chunyuan Zhang , Jianmin Zhang , Sheng Ma

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…

Neural and Evolutionary Computing · Computer Science 2022-06-20 Beren Millidge , Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz

While a diverse collection of continual learning (CL) methods has been proposed to prevent catastrophic forgetting, a thorough investigation of their effectiveness for processing sequential data with recurrent neural networks (RNNs) is…

Large Language Models (LLMs) often falter in complex reasoning tasks due to their static, parametric knowledge, leading to hallucinations and poor performance in specialized domains like mathematics. This work explores a fundamental…

Machine Learning · Computer Science 2026-02-10 Srijan Shakya , Anamaria-Roberta Hartl , Sepp Hochreiter , Korbinian Pöppel

The Hopfield associative memory model stores random patterns in synaptic couplings according to Hebb's rule and retrieves them through gradient descent on an energy function. This conventional setting, where neurons are assumed to have…

Disordered Systems and Neural Networks · Physics 2026-01-23 Yoshiyuki Kabashima , Kazushi Mimura

Backpropagation through time (BPTT) is the standard algorithm for training recurrent neural networks (RNNs), which requires separate simulation phases for the forward and backward passes for inference and learning, respectively. Moreover,…

Machine Learning · Computer Science 2023-03-13 Anand Subramoney

Effective planning in model-based reinforcement learning (MBRL) and model-predictive control (MPC) relies on the accuracy of the learned dynamics model. In many instances of MBRL and MPC, this model is assumed to be stationary and is…

Machine Learning · Computer Science 2026-05-27 Yizhou Huang , Kevin Xie , Homanga Bharadhwaj , Florian Shkurti

Neuromorphic computing systems overcome the limitations of traditional von Neumann computing architectures. These computing systems can be further improved upon by using emerging technologies that are more efficient than CMOS for neural…