Projects
Thesis for Bachelor's in Mathematics - Memory and Pattern Recognition in the Abstract Neuron

Abstract:
Memory recollection and the ability to reconstruct signals from partial input is one of the most important capabilities and deepest mysteries of the biological neuron. A suite of models have been designed to understand and imitate this power of the brain, based on the hypothesis that learning occurs through the changing of synaptic connections in the neuron. Here, we pursue the analysis of Hebbian-based models (the Simple Hebbian Model, Oja's Rule, and the BCM Model), all based on the notion that if a neuron persistently takes part in the firing of another neuron, their connection will become stronger. We analyze the utility of each of these rules in both a biological and computational context. Through stability analysis and simulation, we show the instability and shortcomings of the Hebbian Rule, the stability and ability to recognize patterns of Oja's Rule, and the BCM Model's unique ability to both reconstruct and recollect patterns.

A full copy of the thesis.
A fun demonstration of the models explored in this project.
A MATLAB Live Script with simulations run for the thesis.