Understanding and Modifying Dynamical Hopfield Neural Networks for Generating Multiple Coherent Patterns

Abstract

Analysts have always been using classifications and predictions to deepen our understandings of the world we live in; and it is a fact that there has been a surge in the amount of data in the world with advancements in the internet and information management. For this reason, case-by-case qualitative analyses become inefficient and inevitably we start to rely on quantitative analyses. Quantitative analyses such as machine learning and deep learning have seen a lot success in industries; however they have been referred as black boxes because of their complexities. In this thesis, we aim to make one archetype of quantitative analytical technique, the recurrent dynamical Hopfield neural networks (RDHNN), transparent. We conduct rigorous experimental studies on Hopfield neural networks with David Sussillo’s FORCE mechanism via mathematical dynamical bifurcational studies. We compare his ideas with well-studied low dimensional systems and provide mathematical reconstructions and visualisations of the interactions among the network variables and the attractors (destinations of propagating in- formation). The result of this thesis is a computational scheme for RDHNNs with FORCE mechanism that can theoretically learn as many signals as possible at the same time. We provide the outputs for our final modification to show the successful simultaneous learning of four desired signals without human interference. We also show that our findings have very good forecastability with real life time series data.