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Progressive Feedforward Collapse of ResNet Training
Overall, this study extends NC to PFC to model the collapse phenomenon of intermediate layers and its dependence on the input data, shedding light on the theoretical understanding of ResNet in classification problems.
A Mathematical Principle of Deep Learning: Learn the Geodesic Curve in the Wasserstein Space
In a word, we conclude a mathematical principle of deep learning is to learn the geodesic curve in the Wasserstein space; and deep learning is a great engineering realization of continuous transformation in high-dimensional space.
Tessellated Wasserstein Auto-Encoders
Non-adversarial generative models such as variational auto-encoder (VAE), Wasserstein auto-encoders with maximum mean discrepancy (WAE-MMD), sliced-Wasserstein auto-encoder (SWAE) are relatively easy to train and have less mode collapse compared to Wasserstein auto-encoder with generative adversarial network (WAE-GAN).
Matrix Normal PCA for Interpretable Dimension Reduction and Graphical Noise Modeling
However, most of the existing methods only assume that the noise is correlated in the feature space while there may exist two-way structured noise.
