If you could remember my last post about a self-driving car where I did a basic operation of multiply and sum of two arrays weights(W) and example(X):

[w1*x1 + w2*x2...... + w15*x15 + w16*x16]

[ 1*00 + -3*00 +...1*10 + -7*14 ] = 68

If we breakdown this equation, we have to do 16 multiplications and 15 addition, in total 30 CPU operations to complete this one, whereas in GPU it needed only 3 steps, let's see:

• First, Think these two above arrays as matrix of shape(1,16).
• Second, Transpose example matrix which will become (16,1).Transpose
• Third, Matrix multiplication of weight matrix and transposed example matrix will give the sum.

W × X^T

[ 1 , 16 ] × [ 16 , 1 ]

[ 1 , 1 ]

68

Nifty right! just in 3 steps, Let's do this for 6 examples, stacked into rows of a single table:

×

Still, in 3 steps, whetever be the number of examples. if you do the same thing with CPU it 180 steps as one example takes 30 steps and there are 6 of them so.