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We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to…

Optimization and Control · Mathematics 2024-07-24 Matteo Della Rossa , Raphaël M. Jungers

The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…

Machine Learning · Computer Science 2022-03-02 Zhijie Chen , Mingquan Feng , Junchi Yan , Hongyuan Zha

One successful model of interacting biological systems is the Boolean network. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self…

Molecular Networks · Quantitative Biology 2017-08-30 Haleh Ebadi , Meghdad Saeedian , Marcel Ausloos , GholamReza Jafari

Artificial neural networks, one of the most successful approaches to supervised learning, were originally inspired by their biological counterparts. However, the most successful learning algorithm for artificial neural networks,…

Machine Learning · Computer Science 2020-06-18 Matilde Tristany Farinha , Sérgio Pequito , Pedro A. Santos , Mário A. T. Figueiredo

Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…

Optimization and Control · Mathematics 2023-12-14 Virginie Debauche , Alec Edwards , Raphael M. Jungers , Alessandro Abate

While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student…

Disordered Systems and Neural Networks · Physics 2024-01-02 Francesco Alemanno , Luca Camanzi , Gianluca Manzan , Daniele Tantari

The common thread behind the recent Nobel Prize in Physics to John Hopfield and those conferred to Giorgio Parisi in 2021 and Philip Anderson in 1977 is disorder. Quoting Philip Anderson: "more is different". This principle has been…

Disordered Systems and Neural Networks · Physics 2025-10-16 Elena Agliari , Andrea Alessandrelli , Adriano Barra , Martino Salomone Centonze , Federico Ricci-Tersenghi

In the mammalian brain, newly acquired memories depend on the hippocampus for maintenance and recall, but over time the neocortex takes over these functions, rendering memories hippocampus-independent. The process responsible for this…

Neurons and Cognition · Quantitative Biology 2021-07-02 Peter Helfer , Thomas R. Shultz

Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…

Machine Learning · Statistics 2015-06-23 Yiyuan She , Yuejia He , Dapeng Wu

We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…

Neurons and Cognition · Quantitative Biology 2023-08-28 Louis Kang , Taro Toyoizumi

Neural networks are increasingly employed to model, analyze and control non-linear dynamical systems ranging from physics to biology. Owing to their universal approximation capabilities, they regularly outperform state-of-the-art…

Dynamical Systems · Mathematics 2023-12-27 Alessandro Corbetta , Thomas Geert de Jong

The nervous system reorganizes memories from an early site to a late site, a commonly observed feature of learning and memory systems known as systems consolidation. Previous work has suggested learning rules by which consolidation may…

Neurons and Cognition · Quantitative Biology 2025-02-11 Alireza Alemi , Emre R. F. Aksay , Mark S. Goldman

Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…

Disordered Systems and Neural Networks · Physics 2025-11-17 Miguel Aguilera , Daniele De Martino , Ivan Garashchuk , Dmitry Sinelshchikov

Neuroscience and Artificial Intelligence (AI) have progressed in tandem, each contributing to our understanding of the brain, and inspiring recent developments in biologically-plausible neural networks (NNs) and learning rules. Predictive…

Neural and Evolutionary Computing · Computer Science 2024-06-24 Ehsan Ganjidoost , Mallory Snow , Jeff Orchard

In biological systems, neuromodulation tunes synaptic plasticity based on the internal state of the organism, complementing stimulus-driven Hebbian learning. The algorithm recently proposed by Krotov and Hopfield \cite{krotov_2019} can be…

Disordered Systems and Neural Networks · Physics 2026-01-09 Başer Tambaş , A. Levent Subaşı , Alkan Kabakçıoğlu

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

When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…

Machine Learning · Computer Science 2022-03-21 Kenji Kashima , Ryota Yoshiuchi , Yu Kawano

Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…

Neurons and Cognition · Quantitative Biology 2018-04-03 Jason Kim , Jonathan M. Soffer , Ari E. Kahn , Jean M. Vettel , Fabio Pasqualetti , Danielle S. Bassett

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

Knowledge could be gained from experts, specialists in the area of interest, or it can be gained by induction from sets of data. Automatic induction of knowledge from data sets, usually stored in large databases, is called data mining. Data…

Logic in Computer Science · Computer Science 2008-04-28 Saratha Sathasivam , Wan Ahmad Tajuddin Wan Abdullah