TY - JOUR
T1 - Hodge-Kodaira decomposition of evolving neural networks
AU - Miura, Keiji
AU - Aoki, Takaaki
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Nos. 24120701 and 24120708 .
Publisher Copyright:
© 2014 Elsevier Ltd.
PY - 2015/2/1
Y1 - 2015/2/1
N2 - 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.
AB - 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.
KW - Chaos
KW - Co-evolving network dynamics
KW - Hodge-Kodaira decomposition
KW - Phase oscillators
KW - Spike-timing-dependent plasticity
KW - Topology
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U2 - 10.1016/j.neunet.2014.05.021
DO - 10.1016/j.neunet.2014.05.021
M3 - Article
AN - SCOPUS:84921354882
VL - 62
SP - 20
EP - 24
JO - Neural Networks
JF - Neural Networks
SN - 0893-6080
ER -