On the Solvability of the {XOR} Problem by Spiking Neural Networks

Fuente: arXiv
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Autores principales: Moser, Bernhard A., Lunglmayr, Michael
Formato: Preprint
Publicado: 2024
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author Moser, Bernhard A.
Lunglmayr, Michael
author_facet Moser, Bernhard A.
Lunglmayr, Michael
contents The linearly inseparable XOR problem and the related problem of representing binary logical gates is revisited from the point of view of temporal encoding and its solvability by spiking neural networks with minimal configurations of leaky integrate-and-fire (LIF) neurons. We use this problem as an example to study the effect of different hyper parameters such as information encoding, the number of hidden units in a fully connected reservoir, the choice of the leaky parameter and the reset mechanism in terms of reset-to-zero and reset-by-subtraction based on different refractory times. The distributions of the weight matrices give insight into the difficulty, respectively the probability, to find a solution. This leads to the observation that zero refractory time together with graded spikes and an adapted reset mechanism, reset-to-mod, makes it possible to realize sparse solutions of a minimal configuration with only two neurons in the hidden layer to resolve all binary logic gate constellations with XOR as a special case.
format Preprint
id arxiv_https___arxiv_org_abs_2408_05845
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the Solvability of the {XOR} Problem by Spiking Neural Networks
Moser, Bernhard A.
Lunglmayr, Michael
Neural and Evolutionary Computing
82C32, 92B99, 41A65
C.1.3
The linearly inseparable XOR problem and the related problem of representing binary logical gates is revisited from the point of view of temporal encoding and its solvability by spiking neural networks with minimal configurations of leaky integrate-and-fire (LIF) neurons. We use this problem as an example to study the effect of different hyper parameters such as information encoding, the number of hidden units in a fully connected reservoir, the choice of the leaky parameter and the reset mechanism in terms of reset-to-zero and reset-by-subtraction based on different refractory times. The distributions of the weight matrices give insight into the difficulty, respectively the probability, to find a solution. This leads to the observation that zero refractory time together with graded spikes and an adapted reset mechanism, reset-to-mod, makes it possible to realize sparse solutions of a minimal configuration with only two neurons in the hidden layer to resolve all binary logic gate constellations with XOR as a special case.
title On the Solvability of the {XOR} Problem by Spiking Neural Networks
topic Neural and Evolutionary Computing
82C32, 92B99, 41A65
C.1.3
url https://arxiv.org/abs/2408.05845