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

作为帮助商业、政府、研究等领域的众多决策过程的工具，机器学习的世界迅速走到了前列。机器学习算法和其他处理信息的真实世界系统的共同基本特征是内部网络结构。挑战在于了解这种网络结构如何影响算法处理和学习输入数据的能力。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，通过使用内部连接很少的网络，即稀疏网络，可以实现改善储集层动态，从而导致储集层响应高度多样化。这类似于在众包中观察到的现象，在这种现象中，当群体成员独立回应时，群体做出的决定会得到改善，而当群体压力使个人反应同质化时，决策会恶化。这个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才能理想地处理信息，以及这些处理过的信息的聚合如何产生现实世界网络中普遍存在的结构。有了一个解开结构对水库学习影响的解释，将为机器学习的更广泛领域提供一个同样的数学立足点，有助于基础科学研究和推进机器学习的目标。该项目还将支持对来自不同背景的研究生和本科生的教育和培训，以帮助培养在动力学、机器学习和网络科学的交叉点工作的新一代应用数学家。这将在分层的研究环境中进行，其中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储集层精度的影响，目标是尽可能消除储集层的黑箱性质。从众包的社会动力学中获得灵感，该项目希望向这一研究领域注入的新视角之一是，独立或几乎独立行动的实体的集合可以高度准确地再现复杂系统的动力学。为此，该项目旨在理解处理数据和将数据聚合到训练系统之间的区别，这两个系统在机器学习算法的分析中经常被混淆，但在油藏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水库计算机中的学习。该项目的预期科学收益是提供新的方法，利用极稀疏的网络以更低的成本和更高的预测能力来分析和具体构建水库，并将这些原则扩展到更大类别的机器学习算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.