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

我的研究兴趣在于量化一组对象的相似性，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，建议工作的重点是结合我在描述性近集和使用gpu （GPGPU）的通用计算方面的专业知识，以增强和开发当前机器学习和深度神经网络（DNN）方法的新理论，并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，在2012年，A。Krizhevsky等人利用GPU驱动的卷积神经网络赢得了ILSVRC。他们的工作表明，gpu、大型标记数据集和深度神经网络的结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物体集合相似性的量化问题？答案是否定的，对新方法的探索构成了这项工作的基础。人类的行为不仅仅是对物体进行分类的能力。我们有一种强大的内在能力，可以对一组物体的相似性做出判断，我们每天都会无意识地进行很多次。因此，我们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。提出的工作的动机是发展理论和计算框架，以综合人类对物体集的相似性的感知。这项工作的数学基础是描述性拓扑和描述性邻近空间（即描述性近集理论），它基于表征对象固有属性的特征形式化了对象、对象集和这些集合的集合之间的关系。******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）的交集，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问题。深度神经网络已经彻底改变了社会的大部分领域。例子包括从自动驾驶汽车到实时语言翻译。从本质上讲，神经网络是模式分类器，这意味着它们将一个未知的模式放入有限数量的类中。提出的工作是量化对象集合的相似性。如果能够实现人类水平的算法，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.