【專題演講】2025-01-06 11:00-12:00 The Manifold Hypothesis and its consequence in machine learning Yen-Hsi Richard Tsai (Department of Mathematics and Oden Institute for Computational Engineering and Sciences, UT-Austin)
數學跨領域研究中心 2025年專題演講
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DATE
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2025-01-06 11:00-12:00
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PLACE
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數學系館 3F會議室
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SPEAKER
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Yen-Hsi Richard Tsai
(Professor Department of Mathematics and Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin)
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The Manifold Hypothesis and its consequence in machine learning
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ABESTRACT
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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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SPONSOR
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國立成功大學數學系、國立成功大學數學跨領域研究中心
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