Is it possible to decompose a neural network?
For some arbitrary configuration of a neural network, say a basic multi layer perceptron, is there a way to break down a network into a number of smaller networks, compute them individually, and recombine them?
For matrix multiplication, you can do something like this, where if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together, then add them together to get the same result as doing the 16x16 multiplication, without doing any unnecessary computation.
I am wondering if there is any kind of similar mechanism someone could use if they had some kind of hardware multiplier capable of computing a network of a fixed size and wanted to use it to compute a larger network.
Thanks for any help you can offer!
neural-networks
asked Dec 3 '18 at 20:37
Zephyr
1012
add a comment |
For some arbitrary configuration of a neural network, say a basic multi layer perceptron, is there a way to break down a network into a number of smaller networks, compute them individually, and recombine them?
For matrix multiplication, you can do something like this, where if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together, then add them together to get the same result as doing the 16x16 multiplication, without doing any unnecessary computation.
I am wondering if there is any kind of similar mechanism someone could use if they had some kind of hardware multiplier capable of computing a network of a fixed size and wanted to use it to compute a larger network.
Thanks for any help you can offer!
neural-networks
asked Dec 3 '18 at 20:37
Zephyr
1012
Maybe relevant: iphome.hhi.de/samek/pdf/MonICML16.pdf.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together... True but irrelevant. Your naive algorithm requires the same number of multiplications. The Strassen algorithm (en.wikipedia.org/wiki/Strassen_algorithm) is a bit better but more complex.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
That was kind of what I was getting at, I don't necessarily need a more efficient algorithm, if the best I can do is some kind of operation that has equal complexity, then that's fine as well. I just want to know what the best that can be done is.
– Zephyr
Dec 4 '18 at 13:39
add a comment |
For some arbitrary configuration of a neural network, say a basic multi layer perceptron, is there a way to break down a network into a number of smaller networks, compute them individually, and recombine them?
For matrix multiplication, you can do something like this, where if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together, then add them together to get the same result as doing the 16x16 multiplication, without doing any unnecessary computation.
I am wondering if there is any kind of similar mechanism someone could use if they had some kind of hardware multiplier capable of computing a network of a fixed size and wanted to use it to compute a larger network.
Thanks for any help you can offer!
neural-networks
asked Dec 3 '18 at 20:37
Zephyr
1012
For some arbitrary configuration of a neural network, say a basic multi layer perceptron, is there a way to break down a network into a number of smaller networks, compute them individually, and recombine them?
For matrix multiplication, you can do something like this, where if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together, then add them together to get the same result as doing the 16x16 multiplication, without doing any unnecessary computation.
I am wondering if there is any kind of similar mechanism someone could use if they had some kind of hardware multiplier capable of computing a network of a fixed size and wanted to use it to compute a larger network.
Thanks for any help you can offer!
neural-networks
neural-networks
asked Dec 3 '18 at 20:37
Zephyr
1012
asked Dec 3 '18 at 20:37
Zephyr
1012
asked Dec 3 '18 at 20:37
Zephyr
1012
asked Dec 3 '18 at 20:37
Zephyr
1012
asked Dec 3 '18 at 20:37
Zephyr
1012
1012
Maybe relevant: iphome.hhi.de/samek/pdf/MonICML16.pdf.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together... True but irrelevant. Your naive algorithm requires the same number of multiplications. The Strassen algorithm (en.wikipedia.org/wiki/Strassen_algorithm) is a bit better but more complex.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
That was kind of what I was getting at, I don't necessarily need a more efficient algorithm, if the best I can do is some kind of operation that has equal complexity, then that's fine as well. I just want to know what the best that can be done is.
– Zephyr
Dec 4 '18 at 13:39
add a comment |
Maybe relevant: iphome.hhi.de/samek/pdf/MonICML16.pdf.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together... True but irrelevant. Your naive algorithm requires the same number of multiplications. The Strassen algorithm (en.wikipedia.org/wiki/Strassen_algorithm) is a bit better but more complex.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
That was kind of what I was getting at, I don't necessarily need a more efficient algorithm, if the best I can do is some kind of operation that has equal complexity, then that's fine as well. I just want to know what the best that can be done is.
– Zephyr
Dec 4 '18 at 13:39
Maybe relevant: iphome.hhi.de/samek/pdf/MonICML16.pdf.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
Maybe relevant: iphome.hhi.de/samek/pdf/MonICML16.pdf.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together... True but irrelevant. Your naive algorithm requires the same number of multiplications. The Strassen algorithm (en.wikipedia.org/wiki/Strassen_algorithm) is a bit better but more complex.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together... True but irrelevant. Your naive algorithm requires the same number of multiplications. The Strassen algorithm (en.wikipedia.org/wiki/Strassen_algorithm) is a bit better but more complex.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
That was kind of what I was getting at, I don't necessarily need a more efficient algorithm, if the best I can do is some kind of operation that has equal complexity, then that's fine as well. I just want to know what the best that can be done is.
– Zephyr
Dec 4 '18 at 13:39
That was kind of what I was getting at, I don't necessarily need a more efficient algorithm, if the best I can do is some kind of operation that has equal complexity, then that's fine as well. I just want to know what the best that can be done is.
– Zephyr
Dec 4 '18 at 13:39
add a comment |
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Maybe relevant: iphome.hhi.de/samek/pdf/MonICML16.pdf.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
if you have two 16x16 matricies, you can break them into 8x8 blocks and multiply the individual blocks together... True but irrelevant. Your naive algorithm requires the same number of multiplications. The Strassen algorithm (en.wikipedia.org/wiki/Strassen_algorithm) is a bit better but more complex.
– Martín-Blas Pérez Pinilla
Dec 4 '18 at 8:03
That was kind of what I was getting at, I don't necessarily need a more efficient algorithm, if the best I can do is some kind of operation that has equal complexity, then that's fine as well. I just want to know what the best that can be done is.
– Zephyr
Dec 4 '18 at 13:39