Much slower valid convolution using complementary size of kernels.

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Shen Zhao 2020-12-13

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编辑： Shen Zhao 2020-12-24

I am using the valid convolution using convn( T, a, 'valid').

I have run the code below:

T = randn(384,384,8);
a = randn(5,5,8);
b = randn(380,380,1);
tic; convn(T,a,'valid'); toc
tic; convn(T,b,'valid'); toc

The reuslt in my computer is

Elapsed time is 0.002837 seconds.
Elapsed time is 0.016301 seconds.

Thus the the latter is much slower compared to fomer one.

However, in terms of flops, or only in terms of multiplications

convn(T,a,'valid')

takes 5*5*8*(384-5+1)*(384-5+1)*(8-8+1) = 28880000 multiplications

convn(T,b,'valid')

also takes 380*380*1*(384-380+1)*(384-380+1)*(8-1+1) = 28880000 multiplications

So why are the two computing time so different?

And is there some ways to implement the convn(T,b,'valid') much faster?

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Shen Zhao 2020-12-24

编辑：Shen Zhao 2020-12-24

I understand your first point, this seems to infer that the difference between the two convolution using GPU will be more severe.

However, in which perspective convn(T,a,'valid') is harder? FLOPS? or hardware implementation?

Bruno Luong 2020-12-24

编辑：Bruno Luong 2020-12-24

No not FLOPS. As you said the FLOPS are more or less indentical.

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Answer 1

Bjorn Gustavsson 2020-12-21

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No, n-dimensional fourier-transforms, multiplication of the Fourier-transforms of 5-5-8 a with T will be a fair bit faster than the multiplication of the 380-by-380-by-1 b with T.

HTH

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Answer 2

Roshan Hingnekar 2020-12-22

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编辑：Walter Roberson 2020-12-22

T and 'a' are 3 dimensional where as 'b' is 2 dimensional, convolution of 3-dimensional with 2-dimensional will be slower than a 3-dimensional with a 3-dimensional.

refer to the below links for further insight on randn and convn functions.

https://www.mathworks.com/help/matlab/ref/randn.html

https://www.mathworks.com/help/matlab/ref/convn.html?searchHighlight=convn&s_tid=srchtitle

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Shen Zhao 2020-12-24

I read the corredponding webpages, could you explain more on why the same dimensional convolution will be faster?

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Answer 3

Bruno Luong 2020-12-22

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I would suggest to do specific conv with MEX programing.

Not sure the chance to beat MATLAB though.

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Shen Zhao 2020-12-24

We once tried to write some C++ code to compete with matlab convn especially for 'valid' convolution, we found it really hard to beat Matalb convn. The matlab convn is really well-optimized.

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Much slower valid convolution using complementary size of kernels.

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Much slower valid convolution using complementary size of kernels.

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