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Expressivity in Neural Networks: Theory and Applications
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Reporter:
Juncai He, Assistant Professor, Yau Mathematical Sciences Center, Tsinghua University
Inviter:
Shuo Zhang, Associate Professor
Subject:
Expressivity in Neural Networks: Theory and Applications
Time and place:
14:30-15:30 February 27(Thursday), Z311
Abstract:

I will present recent results on the expressivity of neural networks and its applications. First, we will recall the connections between linear finite elements and ReLU deep neural networks (DNNs), as well as between spectral methods and ReLUk$^k$ DNNs. Next, we will share our latest findings on whether DNNs can precisely recover continuous piecewise polynomials of arbitrary order on any simplicial mesh in any dimension. Furthermore, we will discuss a specific result on the optimal expressivity of ReLU DNNs and its applications, incorporating the Kolmogorov-Arnold representation theorem. Finally, I will conclude with a remark on studying convolutional neural networks from an expressivity perspective.