Advanced Deep Learning with Python

Convolution as matrix multiplication

In this section, we'll describe the algorithm that we use to transform convolutions into matrix multiplication, just like how it's implemented in the cuDNN library (cuDNN: Efficient Primitives for Deep Learning, https://arxiv.org/abs/1410.0759). To understand this, let's assume that we perform a cross-channel 2D convolution over an RGB input image. Let's look at the following table for the parameters of the convolution:

Parameter	Notation	Value
Mini-batch size	N	1
Input feature maps (volume depth)	C	3 (one for each RGB channel)
Input image height	H	4
Input image width	W	4
Output feature maps (volume depth)	K	2
Filter height	R	2
Filter width	S	2
Output feature map height	P	2 (based on ...