Transposed Convolutions

As we may have inferred directly from its formula, the convolution operation leads either to a decrease or no change in the size of the output. This’s helpful in classification problems, but there are some instances where we need to go the other way.

Note: The animations to explain the convolution mechanics are used here with special thanks from Vincent Dumoulin, Francesco Visin - A guide to convolution arithmetic for deep learning [arXiv:1603.07285]

Introduction

In transposed convolution, we go the other way around, where the input image is upsampled and usually increases in size. This is often helpful in image generation using a GAN/VAE or superresolution, and so on.

We’ll continue with the following assumptions:

• The input image I (shown in blue) has the dimensions $m\times n$.
• The convolving kernel/filter, F has the dimensions $f\times f$ (square kernels are the usual standard).
• The output image O (shown in green) has the dimensions $x\times y$

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