A Mathematical Motivation for Complex-valued Convolutional Networks

doi:doi:10.57702/ma0y5os0

A Mathematical Motivation for Complex-valued Convolutional Networks

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging.

BibTex:

@dataset{Joan_Bruna_and_Soumith_Chintala_and_Yann_LeCun_and_Serkan_Piantino_and_Arthur_Szlam_and_Mark_Tygert_2024,
    abstract = {A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging.},
    author = {Joan Bruna and Soumith Chintala and Yann LeCun and Serkan Piantino and Arthur Szlam and Mark Tygert},
    doi = {10.57702/ma0y5os0},
    institution = {No Organization},
    keyword = {'complex-valued convolutional networks', 'convolutional networks', 'harmonic analysis'},
    month = {dec},
    publisher = {TIB},
    title = {A Mathematical Motivation for Complex-valued Convolutional Networks},
    url = {https://service.tib.eu/ldmservice/dataset/a-mathematical-motivation-for-complex-valued-convolutional-networks},
    year = {2024}
}