Fuzzy Spiking Neural Networks

Table of Contents

Chapter I: A Review of Neural Network

1.1 Brief History of Artificial Neural Networks

1.1.1 Logical Neural Networks

1.1.2 Early Computer Simulations

1.1.3 The Perceptron

1.1.4 Widrow & Hoff’s Delta Rule

1.1.5 The Significance of the XOR Problem

1.2 Summary of Terminology

1.2.1 Activation Functions

1.2.2 Learning

1.3 Backpropagation

1.3.1 Limitations of Backpropagation

1.4 Self-Organising Networks

1.4.1 Competitive Learning

1.5 Radial Basis Function Networks

1.6 Hybrid Topologies

1.6.1 Neuro Evolutionary Systems

1.6.2 Fuzzy Logic Systems

1.6.3 Neuro Fuzzy System

1.7 Summary

Chapter II: Preliminaries of Spiking Neural Networks

2.1 The Biological Neuron

2.1.1 The Role of Ions

2.1.2 Excitatory and Inhibitory Neurons

2.2 3rd Generation Neurons Models (Biophysical and Spiking Neurons model)

2.2.1 Encoding

2.2.2 Morphological Models

2.2.3 Integrate-and-Fire (IF) Model

2.2.4 Hodgkin-Huxley (HH) Model

2.2.5 Leaky Integrate-and-Fire (LIF) Model

2.2.6 Spike Response Model (SRM)

2.2.7 Conductance-based LIF Model

2.3 Unsupervised Learning

2.3.1 Bienenstock, Cooper and Munro’s Model

2.3.2 Hebbian Learning

2.3.3 Synaptic Scaling

2.3.4 Spike timing-dependent plasticity (STDP)

2.4 Supervised Learning

2.4.1 SpikeProp (Gradient Estimation)

2.4.2 Statistical Approach

2.4.3 Supervised Hebbian Learning (SHL)

2.5 Dynamic Synapse

2.6 Receptive Field

2.7 Spiking Neural Network Versus Traditional Neural Networks

2.8 Summary

Chapter III: Literature Review: Spiking Neural Networks

Chapter IV: Fuzzy based Spiking Neural Networks (FBSNN): A Theoretical Work

4.1 Introduction

4.2 Selection of Neuron Model and Topology

4.3 Solution of XOR by SNN

4.4 Using Fuzzy Reasoning

4.5 Summary

Chapter V: Fuzzy based Spiking Neural Networks (FBSNN): An Implementation and results

5.1 Introduction

5.2 Topology of the Network

5.3 Input Layer with Spikes

5.4 Hidden Layer and Receptive Field

5.5 Output Layer with Modified SHL

5.6 Using Fuzzy Reasoning

5.7 Summary

Research Objectives and Themes

This dissertation explores the integration of fuzzy reasoning capabilities into Spiking Neural Networks (SNNs), investigating how biological concepts like receptive fields and dynamic synapses can be utilized to model fuzzy logic within a spiking architecture. The work specifically addresses the challenge of creating a robust, frequency-selective network capable of solving non-linear classification problems like XOR, while maintaining biological plausibility and local learning constraints.

• Computational Neuroscience and Spiking Neural Networks (SNNs).
• Temporal encoding strategies and neuron dynamics.
• Implementation of fuzzy rules through receptive fields and synaptic plasticity.
• Supervised training algorithms for SNNs (e.g., modified SHL).
• Evaluation of network performance on non-linear classification (XOR).

Excerpt from the Book

Summary of Chapters

Chapter I: A Review of Neural Network: This chapter provides a historical overview of artificial neural networks, detailing key developments and the emergence of various network topologies and learning paradigms.

Chapter II: Preliminaries of Spiking Neural Networks: This section covers the biological foundations of spiking neurons, various neuron models, and fundamental learning mechanisms like STDP and supervised learning.

Chapter III: Literature Review: Spiking Neural Networks: This chapter summarizes essential academic literature and research contributions concerning spiking neural networks and their computational properties.

Chapter IV: Fuzzy based Spiking Neural Networks (FBSNN): A Theoretical Work: This chapter outlines the theoretical design of a spiking neural network that incorporates fuzzy reasoning, discussing how RBF topologies and biological mechanisms can be adapted.

Chapter V: Fuzzy based Spiking Neural Networks (FBSNN): An Implementation and results: This chapter presents the practical implementation and testing of the proposed fuzzy spiking neural network using the XOR classification problem to demonstrate its effectiveness.

Keywords

Spiking Neural Networks, Computational Neuroscience, Fuzzy Logic, Receptive Fields, Dynamic Synapses, XOR Problem, Synaptic Plasticity, Supervised Hebbian Learning, STDP, Pattern Classification, Neural Topology, Frequency Encoding, Neuron Selectivity, Membrane Potential, Computational Intelligence.

Frequently Asked Questions

What is the primary focus of this dissertation?

The dissertation primarily explores the intersection of Spiking Neural Networks (SNNs) and fuzzy logic systems, aiming to develop a biologically inspired spiking neural network architecture capable of fuzzy reasoning.

What are the central themes discussed in this work?

Central themes include computational neuroscience, spike train encoding, the biological plausibility of learning rules like STDP, and the integration of fuzzy rule-based inferencing into neural network layers.

What is the main research objective of this work?

The primary objective is to create an SNN topology that can perform non-linear mapping (specifically solving the XOR problem) by using receptive fields and supervised local learning mechanisms, thus bridging the gap between SNNs and fuzzy logic systems.

Which scientific methodologies are employed?

The research uses a theoretical framework inspired by RBF networks and biological neuroanatomy, implementing supervised Hebbian learning (SHL) and spike timing-dependent plasticity (STDP) to adjust network weights and demonstrate frequency selectivity.

What is covered in the main section of the dissertation?

The main sections analyze the theoretical design of fuzzy spiking neural networks, the selection of neuron and synapse models, and the practical implementation and evaluation of the network on the XOR problem.

Which terms characterize this research field?

Key terms include Spiking Neural Networks, Computational Intelligence, Synaptic Plasticity, Receptive Fields, and Fuzzy Inference Systems.

How does the author handle the credit assignment problem?

The author circumvents the credit assignment problem by utilizing a topology that restricts learning to the output layer, ensuring that learning remains locally-based and biologically plausible.

What role do receptive fields play in the proposed network?

Receptive fields act as frequency-selective filters in the hidden layer, allowing the network to categorize input spike trains based on their firing rates, thereby implementing a form of fuzzy antecedent processing.

How is the XOR classification problem solved?

The XOR problem is solved by routing spike trains through a hidden layer of frequency-selective neurons configured with receptive fields, with the output layer refined by a modified supervised Hebbian learning algorithm.