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Working memory requires the brain to maintain information from the recent past to guide ongoing behavior. Neurons can contribute to this capacity by slowly integrating their inputs over time, creating persistent activity that outlasts the…

Neurons and Cognition · Quantitative Biology 2025-11-20 Nicoas Zucchet , Qianqian Feng , Axel Laborieux , Friedemann Zenke , Walter Senn , João Sacramento

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…

Mathematical Physics · Physics 2017-08-02 Elena Agliari , Adriano Barra , Chiara Longo , Daniele Tantari

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…

Disordered Systems and Neural Networks · Physics 2009-10-30 G. Lattanzi , G. Nardulli , G. Pasquariello , S. Stramaglia

Fixed points of recurrent neural networks can be leveraged to store and generate information. These fixed points can be captured by the Boltzmann-Gibbs measure, which leads to neural Langevin dynamics that can be used for sampling and…

Neurons and Cognition · Quantitative Biology 2025-07-01 Zhendong Yu , Weizhong Huang , Haiping Huang

An important open question in computational neuroscience is how various spatially tuned neurons, such as place cells, are used to support the learning of reward-seeking behavior of an animal. Existing computational models either lack…

Neurons and Cognition · Quantitative Biology 2022-05-18 Yuanxiang Gao

Conversion of temporal to spatial correlations in the cortex is one of the most intriguing functions in the brain. The learning at synapses triggering the correlation conversion can take place in a wide integration window, whose influence…

Disordered Systems and Neural Networks · Physics 2021-12-21 Zijian Jiang , Jianwen Zhou , Tianqi Hou , K. Y. Michael Wong , Haiping Huang

Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…

Neurons and Cognition · Quantitative Biology 2021-12-02 Ulises Pereira-Obilinovic , Johnatan Aljadeff , Nicolas Brunel

We numerically demonstrate a network of coupled oscillators that can learn to solve a classification task from a set of examples -- performing both training and inference through the nonlinear evolution of the system. We accomplish this by…

Mesoscale and Nanoscale Physics · Physics 2026-01-07 Daan de Bos , Marc Serra-Garcia

Molecular processes of neuronal learning have been well-described. However, learning mechanisms of non-neuronal cells have not been fully understood at the molecular level. Here, we discuss molecular mechanisms of cellular learning,…

Molecular Networks · Quantitative Biology 2020-03-18 Péter Csermely , Nina Kunsic , Péter Mendik , Márk Kerestély , Teodóra Faragó , Dániel V. Veres , Péter Tompa

We study some features of learning models based on "delayed" and undifferentiated reinforcement and realized by simple algorithms which may be considered of a very elementary nature. We show that a modification of the Hebb-rule works well…

Condensed Matter · Physics 2007-05-23 Ion-Olimpiu Stamatescu

Learning in the brain is poorly understood and learning rules that respect biological constraints, yet yield deep hierarchical representations, are still unknown. Here, we propose a learning rule that takes inspiration from neuroscience and…

Neural and Evolutionary Computing · Computer Science 2021-10-27 Bernd Illing , Jean Ventura , Guillaume Bellec , Wulfram Gerstner

In neural network's Literature, Hebbian learning traditionally refers to the procedure by which the Hopfield model and its generalizations store archetypes (i.e., definite patterns that are experienced just once to form the synaptic…

Disordered Systems and Neural Networks · Physics 2024-02-21 Francesco Alemanno , Miriam Aquaro , Ido Kanter , Adriano Barra , Elena Agliari

In realistic neural circuits, both neurons and synapses are coupled in dynamics with separate time scales. The circuit functions are intimately related to these coupled dynamics. However, it remains challenging to understand the intrinsic…

Neurons and Cognition · Quantitative Biology 2025-11-11 Wenkang Du , Haiping Huang

We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences…

Neurons and Cognition · Quantitative Biology 2015-01-28 Ashish Kapoor , E. Paxon Frady , Stefanie Jegelka , William B. Kristan , Eric Horvitz

Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of non-zero…

Neurons and Cognition · Quantitative Biology 2008-09-10 Alexei Koulakov , Tomas Hromadka , Anthony M. Zador

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the…

Neural and Evolutionary Computing · Computer Science 2017-09-26 Eliott Coyac , Vincent Gripon , Charlotte Langlais , Claude Berrou

A fundamental aspect of learning in biological neural networks is the plasticity property which allows them to modify their configurations during their lifetime. Hebbian learning is a biologically plausible mechanism for modeling the…

Neural and Evolutionary Computing · Computer Science 2021-03-16 Anil Yaman , Giovanni Iacca , Decebal Constantin Mocanu , Matt Coler , George Fletcher , Mykola Pechenizkiy

There is an analogy that is often made between deep neural networks and actual brains, suggested by the nomenclature itself: the "neurons" in deep neural networks should correspond to neurons (or nerve cells, to avoid confusion) in the…

Machine Learning · Computer Science 2021-11-03 David I. Spivak , Timothy Hosgood

In this paper, a mathematical theory of learning is proposed that has many parallels with information theory. We consider Vapnik's General Setting of Learning in which the learning process is defined to be the act of selecting a hypothesis…

Machine Learning · Computer Science 2014-05-08 Ibrahim Alabdulmohsin

Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a…

Machine Learning · Statistics 2026-05-12 Alessio Giorlandino , Sebastian Goldt , Antoine Maillard