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Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity.…

Neurons and Cognition · Quantitative Biology 2009-05-15 Michael A. Buice , Jack D. Cowan , Carson C. Chow

Neurons within a population are strongly correlated, but how to simply capture these correlations is still a matter of debate. Recent studies have shown that the activity of each cell is influenced by the population rate, defined as the…

Neurons and Cognition · Quantitative Biology 2016-12-26 Christophe Gardella , Olivier Marre , Thierry Mora

RNNs have been shown to be excellent models for sequential data and in particular for data that is generated by users in an session-based manner. The use of RNNs provides impressive performance benefits over classical methods in…

Machine Learning · Computer Science 2018-08-29 Balázs Hidasi , Alexandros Karatzoglou

Primates utilize distributed neural circuits to learn habits in uncertain environments, but the underlying mechanisms remain poorly understood. We propose a formal theory of network energetics explaining how brain states influence…

Animals are known to make efficient probabilistic inferences based on uncertain and noisy information from the outside world. Although it is known that generic neural networks can perform near-optimal point estimation by probabilistic…

Neurons and Cognition · Quantitative Biology 2021-11-10 Kohei Ichikawa , Asaki Kataoka

Neural Combinatorial Optimization (NCO) has mostly focused on learning policies, typically neural networks, that operate on a single candidate solution at a time, either by constructing one from scratch or iteratively improving it. In…

Neural and Evolutionary Computing · Computer Science 2026-01-14 Andoni Irazusta Garmendia , Josu Ceberio , Alexander Mendiburu

To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging…

Neurons and Cognition · Quantitative Biology 2020-03-10 Alexandre René , André Longtin , Jakob H. Macke

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world…

Machine Learning · Computer Science 2022-02-15 Nate Gruver , Marc Finzi , Samuel Stanton , Andrew Gordon Wilson

The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…

Probability · Mathematics 2025-05-27 James MacLaurin , Pedro Vilanova

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…

Neurons and Cognition · Quantitative Biology 2017-05-05 Christian Donner , Klaus Obermayer , Hideaki Shimazaki

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on…

Machine Learning · Computer Science 2025-10-30 Elia Torre , Michele Viscione , Lucas Pompe , Benjamin F Grewe , Valerio Mante

Encoding models are used for predicting brain activity in response to sensory stimuli with the objective of elucidating how sensory information is represented in the brain. Encoding models typically comprise a nonlinear transformation of…

Neurons and Cognition · Quantitative Biology 2017-03-13 Umut Güçlü , Marcel A. J. van Gerven

Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks…

Neurons and Cognition · Quantitative Biology 2026-03-30 Timothy Doyeon Kim , Ulises Pereira-Obilinovic , Yiliu Wang , Eric Shea-Brown , Uygar Sümbül

To be effective in sequential data processing, Recurrent Neural Networks (RNNs) are required to keep track of past events by creating memories. While the relation between memories and the network's hidden state dynamics was established over…

Machine Learning · Computer Science 2019-09-17 Doron Haviv , Alexander Rivkind , Omri Barak

Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal…

Neurons and Cognition · Quantitative Biology 2023-11-07 Lu Mi , Trung Le , Tianxing He , Eli Shlizerman , Uygar Sümbül

Although recurrent neural networks (RNNs) trained on cognitive tasks have become a widely used framework for studying neural computation, the internal mechanisms by which RNNs switch between rhythms across multiple frequency bands, and how…

Neurons and Cognition · Quantitative Biology 2026-05-15 Yutaka Yamaguti , Shota Nakamura

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating - i.e. multiplicative -…

Disordered Systems and Neural Networks · Physics 2021-12-02 Kamesh Krishnamurthy , Tankut Can , David J. Schwab

Generative neural networks can produce data samples according to the statistical properties of their training distribution. This feature can be used to test modern computational neuroscience hypotheses suggesting that spontaneous brain…

Neural and Evolutionary Computing · Computer Science 2025-07-29 Lorenzo Tausani , Alberto Testolin , Marco Zorzi

Neuroscience research has made immense progress over the last decade, but our understanding of the brain remains fragmented and piecemeal: the dream of probing an arbitrary brain region and automatically reading out the information encoded…

Stimulus from the environment that guides behavior and informs decisions is encoded in the firing rates of neural populations. Each neuron in the populations, however, does not spike independently: spike events are correlated from cell to…

Neurons and Cognition · Quantitative Biology 2012-07-24 Nicholas Cain , Eric Shea-Brown