Training of spiking neural networks based on information theoretic costs

📝 Abstract

Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal dynamics and responds to the history of inputs as opposed to the current inputs only. Because of such properties a spiking neural network has rich intrinsic capabilities to process spatiotemporal data. However, because the spikes are discontinuous ‘yes or no’ events, it is not trivial to apply traditional training procedures such as gradient descend to the spiking neurons. In this thesis we propose to use stochastic spiking neuron models in which probability of a spiking output is a continuous function of parameters. We formulate several learning tasks as minimization of certain information-theoretic cost functions that use spiking output probability distributions. We develop a generalized description of the stochastic spiking neuron and a new spiking neuron model that allows to flexibly process rich spatiotemporal data. We formulate and derive learning rules for the following tasks: - a supervised learning task of detecting a spatiotemporal pattern as a minimization of the negative log-likelihood (the surprisal) of the neuron’s output - an unsupervised learning task of increasing the stability of neurons output as a minimization of the entropy - a reinforcement learning task of controlling an agent as a modulated optimization of filtered surprisal of the neuron’s output. We test the derived learning rules in several experiments such as spatiotemporal pattern detection, spatiotemporal data storing and recall with autoassociative memory, combination of supervised and unsupervised learning to speed up the learning process, adaptive control of simple virtual agents in changing environments.

💡 Analysis

Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal dynamics and responds to the history of inputs as opposed to the current inputs only. Because of such properties a spiking neural network has rich intrinsic capabilities to process spatiotemporal data. However, because the spikes are discontinuous ‘yes or no’ events, it is not trivial to apply traditional training procedures such as gradient descend to the spiking neurons. In this thesis we propose to use stochastic spiking neuron models in which probability of a spiking output is a continuous function of parameters. We formulate several learning tasks as minimization of certain information-theoretic cost functions that use spiking output probability distributions. We develop a generalized description of the stochastic spiking neuron and a new spiking neuron model that allows to flexibly process rich spatiotemporal data. We formulate and derive learning rules for the following tasks: - a supervised learning task of detecting a spatiotemporal pattern as a minimization of the negative log-likelihood (the surprisal) of the neuron’s output - an unsupervised learning task of increasing the stability of neurons output as a minimization of the entropy - a reinforcement learning task of controlling an agent as a modulated optimization of filtered surprisal of the neuron’s output. We test the derived learning rules in several experiments such as spatiotemporal pattern detection, spatiotemporal data storing and recall with autoassociative memory, combination of supervised and unsupervised learning to speed up the learning process, adaptive control of simple virtual agents in changing environments.

📄 Content

Moscow Power Engineering Institute
(Technical University)

Training of spiking neural networks based on information theoretic costs by Sinyavskiy Oleg Y.

A thesis for the candidate degree of technical sciences
Specialty: 05.13.17 “Theoretical Foundations of Informatics”

Supervisor: Prof. Kobrin A.I.

Moscow, 2011 2

Abstract

Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal dynamics and responds to the history of inputs as opposed to the current inputs only. Because of such properties a spiking neural network has rich intrinsic capabilities to process spatiotemporal data. However, because the spikes are discontinuous “yes or no” events, it is not trivial to apply traditional training procedures such as gradient descend to the spiking neurons. In this thesis we propose to use stochastic spiking neuron models in which probability of a spiking output is a continuous function of parameters. We formulate several learning tasks as minimization of certain information-theoretic cost functions that use spiking output probability distributions.

We develop a generalized description of the stochastic spiking neuron and a new spiking neuron model that allows to flexibly process rich spatiotemporal data. We formulate and derive learning rules for the following tasks:

a supervised learning task of detecting a spatiotemporal pattern as a minimization of the negative log-likelihood (the surprisal) of the neuron’s output

an unsupervised learning task of increasing the stability of neurons output as a minimization of the entropy

a reinforcement learning task of controlling an agent as a modulated optimization of filtered surprisal of the neuron’s output We test the derived learning rules in several experiments such as spatiotemporal pattern detection, spatiotemporal data storing and recall with autoassociative memory, combination of supervised and unsupervised learning to speed up the learning process, adaptive control of simple virtual agents in changing environments.

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Acknowledgements

The thesis was done at the subdepartment of theoretical mechanics and mechatronics in Moscow Power Engineering Institue. I would like to express the deepest gratitude to my supervisor professor Alexander I. Kobrin for the invaluable help and advices during the preparation of the thesis. I would like to thank all my colleagues from the subdepartment for the warm support and help with the thesis. Especially, I would like to deeply thank professor Witali L. Dunin-Barkowski for numerous valuable advices and discussions.

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Table of Contents Introduction …………………………………………………………………………………………………………………………… 5 Chapter 1. Generalized spiking neuron model …………………………………………………………………… 14 1.1. The space of spiking patterns ……………………………………………………………………………………………… 15 1.2. A distance function on the spiking patterns space ……………………………………………………………….. 16 1.3. A generalized spiking neuron model …………………………………………………………………………………… 19 1.4. Formulating learning tasks for the generalized spiking neuron ……………………………………………. 24 1.4.1. Supervised learning of the generalized spiking neuron ……………………………………………………… 25 1.4.2. Unsupervised learning of the generalized spiking neuron ………………………………………………….. 28 1.4.3. Reinforcement learning of the generalized spiking neuron ………………………………………………… 29 1.5. Spike Multi Response Model ………………………………………………………………………………………………. 30 Chapter 2. Supervised learning of spiking neurons ……………………………………………………………. 37 2.1. Supervised learning of the generalized spiking neuron in discrete time ………………………………… 38 2.2. Implementation of the supervised learning rules …………………………………………………………………. 40 2.3. Learning a desired delay between an input and output spike ……………………………………………….. 42 2.4. A pattern detection task ……………………………………………………………………………………………………… 44 2.5. The spatiotemporal autoassociative memory …………………………………………………………………..

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