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Applied Math and Comp Sci Colloquium

Friday, December 6, 2019 - 2:00pm

Xiuyuan Cheng

Duke University


University of Pennsylvania


Filters in a Convolutional Neural Network (CNN) contain model parameters learned from data. The properties of convolutional filters in a trained deep network directly affect the quality of the data representation being learned. In this talk, we introduce a framework of decomposing convolutional filters over a truncated set of bases to reduce the model and computational complexity of deep CNNs with automatically imposed filter regularity. This includes efficient group equivariant convolutional layers, which explicitly encode rotation and scaling group actions in image data with provable representation stability, by adopting a joint basis decomposition over space and group geometry simultaneously. When allowing the light-weighted basis layer to be adapted to varying modals and enforcing the coefficient layer to be shared across environments, the filter decomposed CNN provides a new way of invariant feature learning, where we introduce applications in domain adaptation and conditional generative networks in computer vision. Joint work with Qiang Qiu, Wei Zhu, Ze Wang, Robert Calderbank, and Guillermo Sapiro.

Xiuyuan Cheng is an Assistant Professor of Mathematics at Duke University. She works on theoretical and computational techniques to solve problems in high-dimensional statistics, signal processing, and machine learning. Cheng received her Ph.D. from Princeton University in 2013 and held a postdoctoral position at École Normale Supérieure in Paris and a Gibbs Assistant Professorship at Yale University. She joined the Duke Department of Mathematics in 2017. Cheng's work is supported by NSF, NIH, and the Alfred P. Sloan Foundation.