Learning Using Thinned Networks: A Crowd Sourcing Phenomenon in Reservoir Computing

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The world of machine learning has quickly come to the forefront as a tool to aid numerous decision-making processes in areas of business, government, research, etc. A fundamental feature common to machine learning algorithms, and other real-world systems that process information, is an internal network structure. The challenge is to understand how this network structure affects an algorithm’s ability to process and learn from incoming data. The specific machine learning algorithms considered in this project are reservoir computers, which are used to learn and make predictions regarding dynamic processes. Recent discoveries indicate that improving reservoir performance can be achieved by using a network with few internal connections, i.e., a thinned network, which results in reservoir responses that are highly diverse. This is similar to phenomena observed in crowdsourcing where the decisions made by a group improve when group members respond independently and where decisions worsen when group pressure homogenizes individual responses. The goal of this project is to develop a mathematical framework describing how extremely sparse networks can be ideal for processing information and how the aggregation of this processed information results in structures that are ubiquitous in real-world networks. Having an explanation that untangles the impact of structure on learning in reservoirs will give the much broader area of machine learning a mathematical foothold for doing the same, contributing to basic scientific research and advancing the goals of machine learning. The project will also support the education and training of graduate and undergraduate students from different backgrounds to help foster a new generation of applied mathematicians working at the intersection of dynamics, machine learning, and network science. This will be done in a stratified research environment where mathematical scientists and domain experts will mentor both graduate and undergraduate students and graduate students will help mentor undergraduates. More concretely, the project will lay the groundwork for building a rigorous framework describing the effect of network structure on reservoir accuracy with the goal of removing as much of the black-box nature of reservoirs as possible. Taking inspiration from the social dynamics of crowdsourcing, one of the new perspectives the project hopes to infuse into this area of research is that collections of independently or nearly independently acting entities can be highly accurate in recreating the dynamics of complex systems. Towards this end the project aims to understand the distinction between processing data and aggregating data to train systems, which are often conflated in the analysis of machine learning algorithms but are easily separated in reservoir computers. A specific goal is to understand how response diversity is related to prediction accuracy and how to tune this diversity to improve learning in reservoir computers. The expected scientific benefit of the project is to provide new methods to analyze and specifically build reservoirs with decreased cost and increased predictive power using extremely sparse networks and to extend these principles to a larger class of machine learning algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.