Understanding deep learning is increasingly emergent as it penetrates more and more into
industry and science. In recent years, a research line from Fourier analysis sheds light on …

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, ie, loss landscape of an …

In this paper, an adaptive multi-scale neural network with Resnet blocks (adaptive-MS-
Resnet) architecture is constructed for solving the Poisson equation, Helmholtz equation …

It is important to understand how dropout, a popular regularization method, aids in achieving
a good generalization solution during neural network training. In this work, we present a …

α-clustering structure is a significant topic in light nuclei. A Bayesian convolutional neural
network (BCNN) is applied to classify initial nonclustered and clustered configurations …

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 the …

In this work, we investigate the mechanism underlying loss spikes observed during neural
network training. When the training enters a region with a lower-loss-as-sharper (LLAS) …

Understanding transformer-based language models is becoming increasingly crucial,
particularly as they play pivotal roles in advancing towards artificial general intelligence …

Generative adversarial networks (GANs) are a class of machine-learning models that use
adversarial training to generate new samples with the same (potentially very complex) …

Deep learning has achieved wide success in solving Partial Differential Equations (PDEs),
with particular strength in handling high dimensional problems and parametric problems …