Abstract
A Spiking Neural Network (SNN) is trained with Spike Timing Dependent Plasticity (STDP), which is a neuro-inspired unsupervised learning method for various machine learning applications. This paper studies the generalizability properties of the STDP learning processes using the Hausdorff dimension of the trajectories of the learning algorithm. The paper analyzes the effects of STDP learning models and associated hyper-parameters on the generalizability properties of an SNN. The analysis is used to develop a Bayesian optimization approach to optimize the hyper-parameters for an STDP model for improving the generalizability properties of an SNN.
Highlights
A Spiking Neural Network (SNN) (Maass, 1997; Gerstner and Kistler, 2002b; Pfeiffer and Pfeil, 2018) is a neuro-inspired machine learning (ML) model that mimics the spike-based operation of the human brain (Bi and Poo, 1998)
We provide a theoretical background for the motivation of the work treating the Spike Timing Dependent Plasticity (STDP) learning process as a stochastic process and modeling it using a stochastic differential equation
We observed that the lognormal weight distribution obtained from the log-STDP learning process leads to a more generalizable STDP-trained SNN with a minimal decrease in testing accuracy
Summary
A Spiking Neural Network (SNN) (Maass, 1997; Gerstner and Kistler, 2002b; Pfeiffer and Pfeil, 2018) is a neuro-inspired machine learning (ML) model that mimics the spike-based operation of the human brain (Bi and Poo, 1998). Gurbuzbalaban et al (2020) and Hodgkinson and Mahoney (2021) have simultaneously shown that the law of the SGD iterates can converge to a heavy-tailed stationary distribution with infinite variance when the step-size η is large and/or the batch-size B is small. These results form a theoretical basis for the origins of the observed heavy-tailed behavior of SGD in practice.
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