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经过训练以生成时空模式的递归脉冲神经网络中脉冲序列的拓扑特征。

Topological features of spike trains in recurrent spiking neural networks that are trained to generate spatiotemporal patterns.

作者信息

Maslennikov Oleg, Perc Matjaž, Nekorkin Vladimir

机构信息

Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia.

Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia.

出版信息

Front Comput Neurosci. 2024 Feb 23;18:1363514. doi: 10.3389/fncom.2024.1363514. eCollection 2024.

DOI:10.3389/fncom.2024.1363514
PMID:38463243
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10920356/
Abstract

In this study, we focus on training recurrent spiking neural networks to generate spatiotemporal patterns in the form of closed two-dimensional trajectories. Spike trains in the trained networks are examined in terms of their dissimilarity using the Victor-Purpura distance. We apply algebraic topology methods to the matrices obtained by rank-ordering the entries of the distance matrices, specifically calculating the persistence barcodes and Betti curves. By comparing the features of different types of output patterns, we uncover the complex relations between low-dimensional target signals and the underlying multidimensional spike trains.

摘要

在本研究中，我们专注于训练递归脉冲神经网络，以生成封闭二维轨迹形式的时空模式。使用Victor-Purpura距离，根据训练网络中的脉冲序列的差异对其进行检查。我们将代数拓扑方法应用于通过对距离矩阵的元素进行排序而获得的矩阵，具体计算持久条形码和贝蒂曲线。通过比较不同类型输出模式的特征，我们揭示了低维目标信号与底层多维脉冲序列之间的复杂关系。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/9e79d381d24a/fncom-18-1363514-g0007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/679230fe7a9f/fncom-18-1363514-g0001.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/e5573ad38596/fncom-18-1363514-g0003.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/d740cad75326/fncom-18-1363514-g0005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/92d7c444ccf0/fncom-18-1363514-g0006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/9e79d381d24a/fncom-18-1363514-g0007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/679230fe7a9f/fncom-18-1363514-g0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/badfa387a5b8/fncom-18-1363514-g0002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/e5573ad38596/fncom-18-1363514-g0003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/8db86af2dc49/fncom-18-1363514-g0004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/d740cad75326/fncom-18-1363514-g0005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/92d7c444ccf0/fncom-18-1363514-g0006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/82b8/10920356/9e79d381d24a/fncom-18-1363514-g0007.jpg

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