报告题目：Exploiting Data Low-Dimensional Structures by Deep Neural Networks: Error Analysis and Neural Scaling Laws

报告人：刘皓助理教授 香港浸会大学

时间：2024.11.12 上午09:00-11:00

腾讯会议号：521-228-968

报告摘要： Deep neural networks have demonstrated a great success on many applications, especially on problems with high-dimensional data sets. In spite of that, most existing statistical theories are cursed by data dimension and cannot explain such a success. To bridge the gap between theories and practice, we exploit the low-dimensional  structures of dataset and establish theoretical guarantees with a fast rate that is only cursed by the intrinsic dimension of the dataset. This presentation addresses our recent work on theories of deep neural networks that exploits low-dimensional data structures. Specifically, we establish approximation and generalization error bounds for learning functions and operators. Our results provide fast rates depending on the intrinsic dimension of data sets and show that deep neural networks are adaptive to low-dimensional structures of data sets. Our results partially provide theoretical explanations of neural scaling laws

报告人简介：刘皓博士现为香港浸会大学助理教授。刘博士于2018年在香港科技大学取得博士学位，并于2018-2021年在佐治亚理工大学做博士后。在2021年夏天，刘博士加入香港浸会大学。刘博士的主要研究方向包括图像处理，深度学习理论，偏微分方程识别以及数值偏微分方程。