Understand Vector Convolution: A Beginner Guide

Vector Convolution is a special operation for vector. In this tutorial, we will use some simple examples to illustrate it for deep learning beginners.

What is vector convolution?

As to n dimension vector A and B

A = [a₀, a₁, a₂, …, a_n-1]

B = [b₀, b₁, b₂, …, b_n-1]

The convolution of f(A,B) is C:

C = [c₀, c₁, …, c_2n-2]

where

From the equation above, we can find:

• The dimension of vector A and B must be the same.
• The dimension of result C is 2n-1

We can understand the vector C as following:

Here is an example.

A = [1,2,3,4]
B = [2,3,4,5]

Here vector A and B is 4 dimension. It means the dimension of convolutional C is 2 * 4 – 1 = 7.

A * B^T =

[2, 3, 4, 5
 4, 6, 8, 10
 6, 9, 12, 15
 8, 12, 16, 20]

c₀ = 2

c₁ = 3 + 4 = 7

c₂ = 4 + 6 + 6 = 16

c₃ = 5 + 8 + 9 + 8 = 30

c₄ = 10 + 12 + 12 = 34

c₅ = 15 + 16 = 31

c₆ = 20

It menas C is:

[2,7,16,30,34,31,20]