EAGER:Topological Machine Learning

1989年首次提出的深度学习仍然是从大型数据集中提取特定信息的最有效方法。这种方法利用许多非线性处理层，在不断增加的抽象层次上开发数据的表示。深度学习在一系列应用中表现出了一流的性能，包括图像和语音识别，并在基于自然语言理解和翻译的任务中展示了有希望的结果。粗略地说，深度学习通过在监督学习阶段调整大量（Ý200）拟合参数来获取“知识”。然后使用这些参数从以前“看不见的”数据中提取信息。最终，深度学习的前提是使用大量的调优参数来开发非线性特征检测器，能够在抽象层面上有效地表示数据的内在结构。这个项目将研究两种潜在的强大的，但高度投机的从数据中提取信息的替代方法。这些方法利用数据的内在属性，而不是一组广泛的调优参数。这两种方法都是基于pi对成功应用于不同数学分支的技术的可能扩展所做的推测。第一个问题涉及从随机目击物体中提取特定结构信息；第二，预测动力系统的行为。该项目的最终目标是确定上述用于预测高维时间序列或其某些变体的代数拓扑方法或技术是否可以用于创建一类新的非迭代无监督学习算法。该项目更广泛的影响是在抽象数学和机器学习的交叉点培养年轻科学家，并将其应用于科学、技术和商业。

Deep learning, first proposed in 1989, still represents the most effective means for extracting specific information from large datasets. This approach exploits many nonlinear processing layers to develop representations of data at increasing levels of abstraction. Deep learning has demonstrated best-in-class performance in a range of applications, including image and speech recognition, and demonstrated promising results for tasks based on natural language understanding and translation. Crudely speaking, deep learning acquires ¡®knowledge¡¯ by tuning large numbers (¡Ý200) of fitting parameters during a supervised learning phase. These parameters are then used to extract information from previously ¡®unseen¡¯ data. Ultimately, deep learning is premised on using a large number of tuning parameters to develop nonlinear feature detectors capable of efficiently representing the intrinsic structure of the data at an abstract level.¡±This project will examine two potentially powerful, but highly speculative alternative approaches to extract information from data. These approaches exploit the intrinsic properties of the data rather than an extensive set of tuning parameters. Both approaches are based on conjectures made by the PIs regarding possible extensions of techniques successfully applied in very different branches of mathematics. The first concerns the extraction of specific structural information from random sightings of objects; the second, forecasting the behavior of dynamical systems [6]. The ultimate goal of this project is to determine whether the aforementioned algebraic topological approaches or techniques developed for the forecasting of high-dimensional time-series or some variations thereof, can be exploited to create a new class of non-iterative unsupervised learning algorithms. The broader impact of the project is the training of young scientists at the hitherto unexplored intersection of abstract mathematics and machine learning, with possible applications in science,technology, and commerce.