演講公告

演講主題：Side-effects of Learning from Low Dimensional Data
主講人：Yen-Hsi Richard Tsai 教授(The University of Texas at Austin)
演講日期：2022年12月27日(二) 14:00 - 15:00
演講地點：(光復校區) 科學一館223室
摘要內容：
Abstract. The low dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input. However, one often needs to consider evaluating the optimized network at points outside the training distribution. We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace. We study the potential regularization effects associated with the network's depth and noise in the codimension of the data manifold. Finally, we discuss some implications of an embedded data manifold’s curvatures for solving linear regression problems.
相關檔案：Talk_1111227.pdf

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