Identifying the dynamical transitions of a stochastic spiking neural network by topological data analysis

Xiaotian Bai; Chaojun Yu; Jian Zhai

doi:10.1117/12.3049787

8 November 2024 Identifying the dynamical transitions of a stochastic spiking neural network by topological data analysis

Xiaotian Bai, Chaojun Yu, Jian Zhai

Author Affiliations +

Proceedings Volume 13416, Fourth International Conference on Advanced Algorithms and Neural Networks (AANN 2024); 134161G (2024) https://doi.org/10.1117/12.3049787
Event: 2024 4th International Conference on Advanced Algorithms and Neural Networks, 2024, Qingdao, China

Abstract

The relationship between the structures of neural networks and their dynamics is yet not well understood, and studies on this topic are still greatly needed. Changes in the parameters of a network can cause its state to shift between different regimes, and in this work, we studied a neural network of stochastic spiking neurons, whose dynamics change when the control parameter varies. More specifically, as showed by some numerical results, a bistable region appears and eventually disappears when the control parameter increases in an interval, and a critical-like transition appears. However, this kind of transition is always difficult to be detected. Here we used a new approach based on topological data analysis (TDA) that uses superlevel persistence to visualize this transition through a "homological bifurcation plot", which shows the changes of the 0th Betti numbers of the KDE (kernel density estimate) of the activities of the network.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Xiaotian Bai, Chaojun Yu, and Jian Zhai "Identifying the dynamical transitions of a stochastic spiking neural network by topological data analysis", Proc. SPIE 13416, Fourth International Conference on Advanced Algorithms and Neural Networks (AANN 2024), 134161G (8 November 2024); https://doi.org/10.1117/12.3049787

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