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

机器学习的世界已经迅速成为帮助商业、政府、研究等领域众多决策过程的工具，机器学习算法和其他处理信息的现实世界系统的一个共同的基本特征是内部网络结构。挑战在于理解这种网络结构如何影响算法处理和学习传入数据的能力。本项目中考虑的特定机器学习算法是水库计算机，用于学习和预测动态过程。最近的发现表明，可以通过使用具有很少内部连接的网络来实现改善储层性能，即，一个稀疏的网络，导致储层响应高度多样化。这类似于众包中观察到的现象，当群体成员独立响应时，群体做出的决策会得到改善，而当群体压力使个人响应均匀化时，决策会变得更糟。该项目的目标是开发一个数学框架，描述极其稀疏的网络如何成为处理信息的理想选择，以及这些处理过的信息如何聚合成在现实世界网络中无处不在的结构。有一个解释，解开结构对水库学习的影响，将为更广泛的机器学习领域提供一个数学立足点，为基础科研做出贡献，并推进机器学习的目标。该项目还将支持来自不同背景的研究生和本科生的教育和培训，以帮助培养新一代在动力学、机器学习和网络科学交叉领域工作的应用数学家。这将在分层的研究环境中进行，数学科学家和领域专家将指导研究生和本科生，研究生将帮助指导本科生。更具体地说，该项目将为建立一个严格的框架奠定基础，该框架描述了网络结构对水库精度的影响，目标是尽可能多地消除水库的黑箱性质。 从众包的社会动力学中获得灵感，该项目希望注入这一研究领域的新观点之一是，独立或几乎独立行动的实体的集合可以高度准确地重建复杂系统的动力学。为此，该项目旨在了解处理数据和聚合数据以训练系统之间的区别，这在机器学习算法的分析中经常被混淆，但在水库计算机中很容易分开。一个具体的目标是了解响应多样性如何与预测精度相关，以及如何调整这种多样性以改善油藏计算机的学习。该项目的预期科学效益是提供新的方法来分析和专门建造水库，降低成本，提高预测能力，使用极其稀疏的网络，并将这些原则扩展到更大的机器学习算法类别。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.