Reverse convolution, transpose convolution

https://buptldy.github.io/2016/10/29/2016-10-29-deconv/

transposed convolution, fractionally strided convolution or deconvolution Posted on 2016-10-29




The concept of deconvolution (Deconvolution) was first presented by Zeiler in a paper published in 2010 Deconvolutional networks, but did not specify the name of the Deconvolution, which was formally used in the subsequent work ( Adaptive deconvolutional networks for mid and High Level feature learning). With the successful application of deconvolution in neural network visualization, it is adopted by more and more work, such as scene segmentation, generation model and so on. Deconvolution (deconvolution) also has many other names, such as: transposed convolution,fractional strided convolution and so on.

The purpose of this article is mainly in two aspects:
1. Explain the relationship between the convolution layer and the deconvolution layer;
2. Clarify the relationship between the input feature size and the output feature size of the deconvolution layer.

# # convolution Layer

We should all be familiar with the convolution layer, for the convenience of description, the definition is as follows:
-Two dimensional discrete convolution (n=2 n=2)
-square feature input (I1=i2=i i1=i2=i)
-Square convolution core dimensions (K1=k2=k k1=k2=k)
-the same step size per dimension (S1=s2=s s1=s2=s)
-Padding (p1=p2=p p1=p2=p) with the same dimensions per dimension

The following figure represents the convolution calculation process with the parameter (i=5,k=3,s=2,p=1) (i=5,k=3,s=2,p=1), which can be seen from the calculation result that the size of the output feature is