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政大典藏 > College of Science > Department of Mathematical Sciences > NSC Projects > Item 140.119/156614

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/156614

Title:	利用深度學習之流形重建之研究 Manifold Reconstruction with Deep Learning
Authors:	蔡炎龍
Contributors:	應數系
Keywords:	深度學習;流形重建;惠特尼擴問題;黎曼流形 Deep Learning;Manifold Reconstruction;Whitney’s extension problem;Riemannian manifolds
Date:	2021-10
Issue Date:	2025-04-16 14:28:19 (UTC+8)
Abstract:	本計畫為「新興或跨領域計畫」。我們以 Fefferman 最近流形重建的文章為藍本, 試圖以數學的角度去探討深度學習的問題。本計畫以深度學習, 並用一個類似 ResNet 的結構, 去取代 Fefferman 文章中演算法用到的重要部份。希望同樣在給定的條件之下, 我們也能用類似的手法, 透過深度學習建構一個合乎要求的流形。更進一步的, 我們希望能用更數學的語言, 去描述深度學習。其中一個例子我們希望運用「蒸餾」的手法, 討論是否可能找到某種意涵下的「最小模型」。 We are based on Fefferman's recent article on manifold reconstruction as an attempt to explore the theories of deep learning from a mathematical perspective. This project uses deep learning and a ResNet-like structure to replace the ones used in the algorithm in Fefferman's article. It is hoped that under the given conditions, we can also use a similar method to construct a desirable manifold through deep learning. Furthermore, we hope to describe deep learning in more mathematics way. For instance, we want to use the method of "distillation" to discuss whether it is possible to find a "minimum model" in some sense.
Relation:	科技部, MOST109-2115-M004-011, 109.08-110.07
Data Type:	report
Appears in Collections:	[Department of Mathematical Sciences] NSC Projects

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