【114/1/6】11:00-12:00 Applied Mathematics Seminar：Prof. Yen-Hsi Richard Tsai(Department of Mathematics and Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin)
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| Date | 2025-1-6 11:00-12:00 |
| Place | Mathtmatics Building 3F Conference Room O301 |
| Speaker | Prof. Yen-Hsi Richard Tsai(Department of Mathematics and Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin) |
| Title | The Manifold Hypothesis and Its Consequence in Machine Learning |
| Abstract | The 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. Since a typical neural network is constructed to be a function on the whole embedding space, one must consider the stability of an optimized network function when evaluating at points outside the training distribution. In this talk, we will discuss some consequences of the data manifold's curvatures and the arbitrariness of the high-dimensional ambient space. We will also discuss the regularization effects by introducing noise to the data. Finally, we discuss the multiscale properties of the empirical loss function induced by data distributions supported on a low dimensional submanifold. |
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