Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#340082] of Guillermo Sapiro

Papers Published

  1. Qiu, Q; Cheng, X; Calderbank, R; Sapiro, G, DCFNet: Deep Neural Network with Decomposed Convolutional Filters, 35th International Conference on Machine Learning, Icml 2018, vol. 9 (January, 2018), pp. 6687-6696
    (last updated on 2019/07/24)

    ©35th International Conference on Machine Learning, ICML 2018.All Rights Reserved. Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficients remain learned from data. Such a structure not only reduces the number of trainable parameters and computation, but also imposes filter regularity by bases truncation. Through extensive experiments, we consistently observe that DCFNet maintains accuracy for image classification tasks with a significant reduction of model parameters, particularly with Fourier-Bessel (FB) bases, and even with random bases. Theoretically, we analyze the representation stability of DCFNet with respect to input variations, and prove representation stability under generic assumptions on the expansion coefficients. The analysis is consistent with the empirical observations.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320