Publication

A Theoretical Argument for Complex-Valued Convolutional Networks

ArXiv PrePrint


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 several complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as “data-driven multiscale windowed power spectra,” “data-driven multiscale windowed absolute spectra,” “data-driven multiwavelet absolute values,” or (in their most general configuration) “data-driven nonlinear multiwavelet packets.” Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (for example, logistic or tanh) nonlinearities, max. pooling, etc., do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy).

Related Publications

All Publications

Spatially Aware Multimodal Transformers for TextVQA

Yash Kant, Dhruv Batra, Peter Anderson, Alexander Schwing, Devi Parikh, Jiasen Lu, Harsh Agrawal

ECCV - August 23, 2020

Perceiving 3D Human-Object Spatial Arrangements from a Single Image in the Wild

Jason Y. Zhang, Sam Pepose, Hanbyul Joo, Deva Ramanan, Jitendra Malik, Angjoo Kanazawa

ECCV - August 23, 2020

ContactPose: A Dataset of Grasps with Object Contact and Hand Pose

Samarth Brahmbhatt, Chengcheng Tang, Christopher D. Twigg, Charles C. Kemp, James Hays

ECCV - August 23, 2020

Learning to Generate Grounded Visual Captions without Localization Supervision

Chih-Yao Ma, Yannis Kalantidis, Ghassan AlRegib, Peter Vajda, Marcus Rohrbach, Zsolt Kira

ECCV - August 24, 2020

To help personalize content, tailor and measure ads, and provide a safer experience, we use cookies. By clicking or navigating the site, you agree to allow our collection of information on and off Facebook through cookies. Learn more, including about available controls: Cookies Policy