Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Cai, Yuhang; Wu, Tianyi; Tao, Louis; Xiao, Zhuo-Cheng

doi:10.3389/fncom.2021.678688

Cited by 3 publications

(2 citation statements)

References 91 publications

(133 reference statements)

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“…This gives us confidence that the dynamics in MFEs can be described by a lower dimensional dynamical system. We remark that the low dimensional characteristics of MFE dynamics is corroborated by the recent model reduction study in Cai et al (2021). We will further investigate this model reduction problem in our future studies.…”

Section: Discussionsupporting

confidence: 77%

“…Despite the intuitive mechanism of MFEs and some early investigation about the low dimension nature of MFEs Cai et al (2021), it is very difficult to find a low dimensional dynamical system to accurately approximate the MFEs. Known results about MFE mechanism in Zhang et al (2014); Li and Xu (2019); Cai et al (2021) do not provide a full answer to that. Spiking activities in MFEs can range from quite homogeneous to very synchronous.…”

Section: Introductionmentioning

confidence: 99%

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Supervised Parameter Estimation of Neuron Populations from Multiple Firing Events

Le¹,

Li²

2022

Preprint

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The firing dynamics of biological neurons in mathematical models is often determined by the model's parameters, representing the neurons' underlying properties. The parameter estimation problem seeks to recover those parameters of a single neuron or a neuron population from their responses to external stimuli and interactions between themselves. Most common methods for tackling this problem in the literature use some mechanistic models in conjunction with either a simulation-based or solution-based optimization scheme. In this paper, we study an automatic approach of learning the parameters of neuron populations from a training set consisting of pairs of spiking series and parameter labels via supervised learning. Unlike previous work, this automatic learning does not require additional simulations at inference time nor expert knowledge in deriving an analytical solution or in constructing some approximate models. We simulate many neuronal populations with different parameter settings using a stochastic neuron model. Using that data, we train a variety of supervised machine learning models, including convolutional and deep neural networks, random forest, and support vector regression. We then compare their performance against classical approaches including a genetic search, Bayesian sequential estimation, and a random walk approximate model. The supervised models almost always outperform the classical methods in parameter estimation and spike reconstruction

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Section: Discussionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Supervised Parameter Estimation of Neuron Populations from Multiple Firing Events

Le¹,

Li²

2022

Preprint

View full text Add to dashboard Cite

show abstract

Learning spiking neuronal networks with artificial neural networks: neural oscillations

Zhang,

Wang,

et al. 2024

J. Math. Biol.

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Multi-band oscillations emerge from a simple spiking network

Cai

Zhang

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8–12 Hz), beta (12.5–30 Hz), and gamma (30–120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales (e.g., various ion channels or multiple types of inhibitory neurons) or oscillatory inputs to produce rhythms in multi-bands. Here, we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincaré section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then, we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus, our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities.

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Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Cited by 3 publications

References 91 publications

Supervised Parameter Estimation of Neuron Populations from Multiple Firing Events

Supervised Parameter Estimation of Neuron Populations from Multiple Firing Events

Learning spiking neuronal networks with artificial neural networks: neural oscillations

Multi-band oscillations emerge from a simple spiking network

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