70 citations · 164 across the 35 of their papers we have counts for
5 papers · 2 filters
Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs
Xi-An Li, Zhi-Qin John Xu, Lei Zhang
While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by t…
Embedding Principle: a hierarchical structure of loss landscape of deep neural networks
Yaoyu Zhang, Yuqing Li, Zhongwang Zhang +2
We prove a general Embedding Principle of loss landscape of deep neural networks (NNs) that unravels a hierarchical structure of the loss landscape of NNs, i.e., loss landscape of…
Embedding Principle of Loss Landscape of Deep Neural Networks
Yaoyu Zhang, Zhongwang Zhang, Tao Luo +1
Understanding the structure of loss landscape of deep neural networks (DNNs)is obviously important. In this work, we prove an embedding principle that the loss landscape of a DNN "…
Towards Understanding the Condensation of Neural Networks at Initial Training
Hanxu Zhou, Qixuan Zhou, Tao Luo +2
Empirical works show that for ReLU neural networks (NNs) with small initialization, input weights of hidden neurons (the input weight of a hidden neuron consists of the weight from…
An Upper Limit of Decaying Rate with Respect to Frequency in Deep Neural Network
Tao Luo, Zheng Ma, Zhiwei Wang +2
Deep neural network (DNN) usually learns the target function from low to high frequency, which is called frequency principle or spectral bias. This frequency principle sheds light…