Reformulating matrix multiplication scale equation to reduce math ops and improve power and performance. #6437
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
🔗 Helpful Links🧪 See artifacts and rendered test results at hud.pytorch.org/pr/pytorch/executorch/6437
Note: Links to docs will display an error until the docs builds have been completed. ❗ 1 Active SEVsThere are 1 currently active SEVs. If your PR is affected, please view them below: ✅ No FailuresAs of commit 9443a2b with merge base 4f12131 ( This comment was automatically generated by Dr. CI and updates every 15 minutes. |
facebook-github-bot
added
the
CLA Signed
Contributor
|
This pull request was exported from Phabricator. Differential Revision: D64479405 |
trivedivivek
added a commit
to trivedivivek/executorch
that referenced
this pull request
Oct 22, 2024
… and improve power and performance. (pytorch#6437) Summary: This diff simplifies the the matrix multiplication scale equation in q_linear op. The existing equation in q_linear op is: ``` for i in K / 4 sums[c] = mat1_tex . (qmat2(c) scales[c]) out += sums ``` where c = [0, 4), out, sums, mat1_tex and qmat2 are vectors and scales is a scalar. The dot product is associative with respect to scalar multiplication as mentioned in https://en.wikipedia.org/wiki/Dot_product ie. (ac1).(bc2) = c1c2(a.b) Thus, the multiplication can be rearranged as: ``` for i in K / 4 sums[c] = (mat1_tex . qmat2(c)) scales[c] out += sums ``` Using distributive property of multiplication ie. ab + ac + ad ... = a(b + c+ d...) the code can be further simplified to: ``` for i in K / 4 sums[c] = mat1_tex . qmat2(c) out += sums out *= scale ``` This rearrangement significantly reduces redundant multiplications. Reviewed By: SS-JIA Differential Revision: D64479405
trivedivivek
force-pushed
the
export-D64479405
branch
from
4257a44 to
2fcaa06
Compare
Contributor
|
This pull request was exported from Phabricator. Differential Revision: D64479405 |
trivedivivek
added a commit
to trivedivivek/executorch
that referenced
this pull request
Oct 23, 2024
… and improve power and performance. (pytorch#6437) Summary: This diff simplifies the the matrix multiplication scale equation in q_linear op. The existing equation in q_linear op is: ``` for i in K / 4 sums[c] = mat1_tex . (qmat2(c) scales[c]) out += sums ``` where c = [0, 4), out, sums, mat1_tex and qmat2 are vectors and scales is a scalar. The dot product is associative with respect to scalar multiplication as mentioned in https://en.wikipedia.org/wiki/Dot_product ie. (ac1).(bc2) = c1c2(a.b) Thus, the multiplication can be rearranged as: ``` for i in K / 4 sums[c] = (mat1_tex . qmat2(c)) scales[c] out += sums ``` Using distributive property of multiplication ie. ab + ac + ad ... = a(b + c+ d...) the code can be further simplified to: ``` for i in K / 4 sums[c] = mat1_tex . qmat2(c) out += sums out *= scale ``` This rearrangement significantly reduces redundant multiplications. Reviewed By: SS-JIA Differential Revision: D64479405
trivedivivek
force-pushed
the
export-D64479405
branch
from
2fcaa06 to
50f551d
Compare
Contributor
|
This pull request was exported from Phabricator. Differential Revision: D64479405 |
junpi3
approved these changes
Oct 23, 2024
… and improve power and performance. (pytorch#6437) Summary: This diff simplifies the the matrix multiplication scale equation in q_linear op. The existing equation in q_linear op is: ``` for i in K / 4 sums[c] = mat1_tex . (qmat2(c) scales[c]) out += sums ``` where c = [0, 4), out, sums, mat1_tex and qmat2 are vectors and scales is a scalar. The dot product is associative with respect to scalar multiplication as mentioned in https://en.wikipedia.org/wiki/Dot_product ie. (ac1).(bc2) = c1c2(a.b) Thus, the multiplication can be rearranged as: ``` for i in K / 4 sums[c] = (mat1_tex . qmat2(c)) scales[c] out += sums ``` Using distributive property of multiplication ie. ab + ac + ad ... = a(b + c+ d...) the code can be further simplified to: ``` for i in K / 4 sums[c] = mat1_tex . qmat2(c) out += sums out *= scale ``` This rearrangement significantly reduces redundant multiplications. Reviewed By: SS-JIA, jorgep31415 Differential Revision: D64479405
trivedivivek
force-pushed
the
export-D64479405
branch
from
50f551d to
9443a2b
Compare
Contributor
|
This pull request was exported from Phabricator. Differential Revision: D64479405 |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
3 participants
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Summary:
This diff simplifies the the matrix multiplication scale equation in q_linear op.
The existing equation in q_linear op is:
where c = [0, 4), out, sums, mat1_tex and qmat2 are vectors and scales is a scalar.
The dot product is associative with respect to scalar multiplication as mentioned in https://en.wikipedia.org/wiki/Dot_product ie. (ac1).(bc2) = c1c2(a.b)
Thus, the multiplication can be rearranged as:
Using distributive property of multiplication ie. ab + ac + ad ... = a(b + c+ d...) the code can be further simplified to:
This rearrangement significantly reduces redundant multiplications.
Reviewed By: SS-JIA
Differential Revision: D64479405