Exploring the Intersection of Set Proximity, Parallel Computing, and Machine Learning

探索集合邻近度、并行计算和机器学习的交叉点

• 批准号: RGPIN-2018-04088
• 负责人: Henry, Christopher
• 金额: $ 1.68万
• 依托单位: University of Winnipeg
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711193
• 关键词: Exploring; Intersection; Set; Proximity; Parallel

My research interest lies in quantifying the similarity of sets of objects, based on their characteristic attributes and features, in a manner similar to humans performing the same task. In this regard, the focus of the proposed work is to combine my expertise in descriptively near sets and general purpose computing using GPUs (GPGPU) to augment and develop new theory for current approaches to machine learning and deep neural networks (DNN), as well as to produce further gains in the accuracy and applicability of these techniques. As is well known, in 2012 A. Krizhevsky et al. won the ILSVRC using a convolutional neural network driven by GPU. Their work demonstrated that the combination of GPUs, large labelled datasets, and DNN could solve a real-world image classification problem. This event, and the subsequent progress, raised the following question: had the problem of quantifying the similarity of sets of objects been effectively solved by these networks? The answer is No, and the search for new approaches forms the foundation of the proposed work. Human behaviour is much richer than simply its ability to classify objects. We have a powerfully inherent ability to make judgements on the similarity of groups of objects, which we perform seamlessly and unconsciously many times a day. Thus, there is a strong need for the combination of theoretical frameworks for quantifying similarity and the current exciting developments in the field of machine learning. The motivation of the proposed work is to develop theoretical and computational frameworks for the synthesis of human perception of the similarity of sets of objects. The mathematical foundation of this work is descriptive topology and descriptive proximity spaces (i.e. descriptive near set theory), which formalize relationships between objects, sets of objects, and collections of these sets based on features that characterize intrinsic object attributes. As the field of descriptive topology and descriptive proximity spaces is quite new, as well as computational approaches to these concepts, the novelty of the proposed work is very high. Further, no one is working at the intersection of descriptive approaches and high performance computing (HPC) or considering how these techniques can enrich and extend current deep learning algorithms to the problem of quantifying the similarity of objects, sets of objects, and families of sets. Deep neural networks have revolutionized large swathes of society. Examples range from self-driving cars to real-time language translation. At their heart, neural networks are pattern classifiers, meaning they take an unknown pattern and place it into one of a finite number of classes. The proposed work is to quantify the similarity of sets of objects. This simple, yet different, concept has the potential to be as revolutionary as neural networks if algorithms capable of human-level performance can be achieved.

我的研究兴趣在于量化对象集合的相似性，基于它们的特征属性和特征，以类似于人类执行相同任务的方式。在这方面，拟议工作的重点是结合我在描述性近集和使用GPU的通用计算(GPGPU)方面的专业知识，为当前的机器学习和深度神经网络(DNN)方法补充和发展新的理论，以及在这些技术的准确性和适用性方面取得进一步的进展。 众所周知，2012年，A.Krizevsky等人。使用由GPU驱动的卷积神经网络赢得了ILSVRC。他们的工作表明，GPU、大型标记数据集和DNN的组合可以解决现实世界的图像分类问题。这一事件以及随后的进展提出了以下问题：这些网络是否有效地解决了量化目标集合相似性的问题？答案是否定的，寻找新的方法是拟议工作的基础。人类的行为远比简单地将物体分类的能力丰富得多。我们有一种强大的与生俱来的能力来判断一组对象的相似性，我们每天都会无缝地、无意识地执行很多次。因此，迫切需要将量化相似性的理论框架与当前机器学习领域令人兴奋的发展相结合。这项拟议工作的动机是开发理论和计算框架，用于合成人类对对象集合的相似性的感知。这项工作的数学基础是描述性拓扑和描述性邻近空间(即描述性接近集理论)，它基于表征对象固有属性的特征来形式化对象、对象集合和这些集合之间的关系。 由于描述性拓扑学和描述性邻近性空间领域是一个相当新的领域，以及对这些概念的计算方法，所提出的工作的新颖性非常高。此外，没有人研究描述性方法和高性能计算(HPC)的交叉点，也没有人考虑这些技术如何丰富和扩展当前的深度学习算法，以量化对象、对象集和集合族的相似性。深度神经网络已经彻底改变了社会的大片领域。从自动驾驶汽车到实时语言翻译，例子很多。从本质上讲，神经网络是模式分类器，这意味着它们接受未知模式，并将其归入有限数量的类别中的一个。建议的工作是量化对象集之间的相似性。这个简单但不同的概念有可能像神经网络一样具有革命性，如果能够实现能够达到人类水平的算法的话。