title: Hodge-Kodaira decomposition of evolving neural networks.
abstract: Although it is very important to scrutinize recurrent structures of neural networks for elucidating brain functions, conventional methods often have difficulty in characterizing global loops within a network systematically. Here we applied the Hodge-Kodaira decomposition, a topological method, to an evolving neural network model in order to characterize its loop structure. By controlling a learning rule parametrically, we found that a model with an STDP-rule, which tends to form paths coincident with causal firing orders, had the most loops. Furthermore, by counting the number of global loops in the network, we detected the inhomogeneity inside the chaotic region, which is usually considered intractable.
authors: Graduate School of Information Sciences, Tohoku University, Sendai, Japan. Electronic address: miura@ecei.tohoku.ac.jp.
authors: Keiji
authors: K
authors: Miura
authors: Faculty of Education, Kagawa University, Takamatsu, Japan. Electronic address: aoki@ed.kagawa-u.ac.jp.
authors: Takaaki
authors: T
authors: Aoki
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003198:Computer Simulation; D006801:Humans; D009415:Nerve Net / Q000502:physiology; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics
keywords: Chaos; Co-evolving network dynamics; Hodge–Kodaira decomposition; Phase oscillators; Spike-timing-dependent plasticity; Topology