zbMATH — the first resource for mathematics

Spontaneous dynamics of asymmetric random recurrent spiking neural networks. (English) Zbl 1089.68110
Summary: We study the effect of a unique initial stimulation on random recurrent networks of leaky integrate-and-fire neurons. Indeed, given a stochastic connectivity, this so-called spontaneous mode exhibits various nontrivial dynamics. This study is based on a mathematical formalism that allows us to examine the variability of the afterward dynamics according to the parameters of the weight distribution. Under the independence hypothesis (e.g., in the case of very large networks), we are able to compute the average number of neurons that fire at a given time – the spiking activity. In accordance with numerical simulations, we prove that this spiking activity reaches a steady state. We characterize this steady state and explore the transients.

68T05 Learning and adaptive systems in artificial intelligence
Full Text: DOI arXiv
[1] DOI: 10.1088/0954-898X/8/4/003 · Zbl 0904.92013
[2] DOI: 10.1093/cercor/7.3.237
[3] DOI: 10.1023/A:1008925309027 · Zbl 1036.92008
[4] DOI: 10.1162/089976699300016179
[5] DOI: 10.1016/S0167-2789(98)00082-7 · Zbl 1194.35469
[6] DOI: 10.1162/089976699300016601
[7] DOI: 10.1162/089976600300015899
[8] DOI: 10.1088/0954-898X/3/2/004 · Zbl 0825.92051
[9] DOI: 10.1016/0167-2789(94)90214-3 · Zbl 0809.92003
[10] DOI: 10.1103/PhysRevE.66.051917
[11] DOI: 10.1162/08997660252741167 · Zbl 0987.92007
[12] DOI: 10.1023/A:1013775115140 · Zbl 1057.68667
[13] DOI: 10.1007/s004400100182 · Zbl 1004.60023
[14] DOI: 10.1162/089976600300015835
[15] DOI: 10.1126/science.274.5293.1724
[16] DOI: 10.1214/aoms/1177731118 · Zbl 0060.30207
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.