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

我的研究兴趣在于量化对象集的相似性，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，拟议工作的重点是联合收割机我在近距离集合和使用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）方法扩展和开发新理论，并进一步提高这些技术的准确性和适用性。 众所周知，2012年A. Krizhevsky等人使用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对象集相似性的问题？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对物体进行分类的能力丰富得多。我们有一种强大的内在能力，可以对物体组的相似性做出判断，我们每天都会无缝地、无意识地执行很多次。因此，迫切需要将用于量化相似性的理论框架与机器学习领域当前令人兴奋的发展相结合。所提出的工作的动机是开发的理论和计算框架的合成人类感知的相似性的对象集。这项工作的数学基础是描述性拓扑和描述性邻近空间（即描述性近集理论），它形式化了对象之间的关系，对象集，以及这些集合的集合基于表征内在对象属性的特征。 由于描述性拓扑和描述性邻近空间领域是相当新的，以及这些概念的计算方法，所提出的工作的新奇是非常高的。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，以解决量化对象、对象集和集合族的相似性问题。深度神经网络已经彻底改变了社会的大部分。例子从自动驾驶汽车到实时语言翻译。神经网络的核心是模式分类器，这意味着它们采用未知模式并将其放入有限数量的类中。建议的工作是量化的相似性的对象集。如果能够实现具有人类水平性能的算法，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。

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.