Eigenvalue spectrum of neural networks with arbitrary Hebbian length

Autor:	Zhou, Jianwen, Jiang, Zijian, Hou, Tianqi, Chen, Ziming, Wong, K Y Michael, Huang, Haiping
Rok vydání:	2021
Předmět:	Condensed Matter - Disordered Systems and Neural Networks Condensed Matter - Statistical Mechanics Quantitative Biology - Neurons and Cognition
Zdroj:	Physical Review E 104, 064307 (2021)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevE.104.064307
Popis:	Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In our model, the Hebbian length can be arbitrarily large. The spectral density of the coupling matrix is derived using the replica method, which is also shown to be consistent with the results obtained by applying the free probability method. The maximal eigenvalue is then obtained by an iterative equation, related to the paramagnetic to spin glass transition in the model. Altogether, this work establishes the connection between the associative memory with arbitrary Hebbian length and the asymptotic eigen-spectrum of the neural-coupling matrix. Comment: 19 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.14324 Zobrazit plný text záznamu View this record from Arxiv