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Calculating axis's local wg size based on global workload and making it as close as possible to warp size of 32.#6409

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facebook-github-bot merged 1 commit intopytorch:mainfrom
trviv:export-D64418632
Oct 22, 2024
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Calculating axis's local wg size based on global workload and making it as close as possible to warp size of 32.#6409
facebook-github-bot merged 1 commit intopytorch:mainfrom
trviv:export-D64418632

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@trviv trviv commented Oct 21, 2024

Summary:
This diff changes the local workgroup size calculation logic in the Vulkan backend of Executorch.

The workgroup size of the largest axis is kept largest so workgroups are better occupied.
The workgroup size is calculated based on the warp size of 32. When kernel is 2 dimensional largest axis is kept close to warp size it, so threads in the same warp Read / Write to consecutive memory locations, thus improving performance.

Reviewed By: SS-JIA

Differential Revision: D64418632

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@facebook-github-bot facebook-github-bot added the CLA Signed This label is managed by the Facebook bot. Authors need to sign the CLA before a PR can be reviewed. label Oct 21, 2024
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This pull request was exported from Phabricator. Differential Revision: D64418632

trviv added a commit to trviv/executorch that referenced this pull request Oct 22, 2024
…it as close as possible to warp size of 32. (pytorch#6409)

Summary:

This diff changes the local workgroup size calculation logic in the Vulkan backend of Executorch.

The workgroup size of the largest axis is kept largest so workgroups are better occupied.
The workgroup size is calculated based on the warp size of 32. When kernel is 2 dimensional largest axis is kept close to warp size it, so threads in the same warp Read / Write to consecutive memory locations, thus improving performance.

Reviewed By: SS-JIA

Differential Revision: D64418632
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This pull request was exported from Phabricator. Differential Revision: D64418632

trviv added a commit to trviv/executorch that referenced this pull request Oct 22, 2024
…it as close as possible to warp size of 32. (pytorch#6409)

Summary:

This diff changes the local workgroup size calculation logic in the Vulkan backend of Executorch.

The workgroup size of the largest axis is kept largest so workgroups are better occupied.
The workgroup size is calculated based on the warp size of 32. When kernel is 2 dimensional largest axis is kept close to warp size it, so threads in the same warp Read / Write to consecutive memory locations, thus improving performance.

Reviewed By: SS-JIA

Differential Revision: D64418632
@facebook-github-bot
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This pull request was exported from Phabricator. Differential Revision: D64418632

trviv added a commit to trviv/executorch that referenced this pull request Oct 22, 2024
…it as close as possible to warp size of 32. (pytorch#6409)

Summary:

This diff changes the local workgroup size calculation logic in the Vulkan backend of Executorch.

The workgroup size of the largest axis is kept largest so workgroups are better occupied.
The workgroup size is calculated based on the warp size of 32. When kernel is 2 dimensional largest axis is kept close to warp size it, so threads in the same warp Read / Write to consecutive memory locations, thus improving performance.

Reviewed By: SS-JIA

Differential Revision: D64418632
@facebook-github-bot
Copy link
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This pull request was exported from Phabricator. Differential Revision: D64418632

trviv added a commit to trviv/executorch that referenced this pull request Oct 22, 2024
…it as close as possible to warp size of 32. (pytorch#6409)

Summary:

This diff changes the local workgroup size calculation logic in the Vulkan backend of Executorch.

The workgroup size of the largest axis is kept largest so workgroups are better occupied.
The workgroup size is calculated based on the warp size of 32. When kernel is 2 dimensional largest axis is kept close to warp size it, so threads in the same warp Read / Write to consecutive memory locations, thus improving performance.

Reviewed By: SS-JIA

Differential Revision: D64418632
@facebook-github-bot
Copy link
Contributor

This pull request was exported from Phabricator. Differential Revision: D64418632

…it as close as possible to warp size of 32. (pytorch#6409)

Summary:

This diff changes the local workgroup size calculation logic in the Vulkan backend of Executorch.

The workgroup size of the largest axis is kept largest so workgroups are better occupied.
The workgroup size is calculated based on the warp size of 32. When kernel is 2 dimensional largest axis is kept close to warp size it, so threads in the same warp Read / Write to consecutive memory locations, thus improving performance.

Reviewed By: SS-JIA

Differential Revision: D64418632
@facebook-github-bot
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This pull request was exported from Phabricator. Differential Revision: D64418632

@facebook-github-bot facebook-github-bot merged commit fe20be9 into pytorch:main Oct 22, 2024
SS-JIA added a commit that referenced this pull request Aug 7, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

[ghstack-poisoned]
SS-JIA added a commit that referenced this pull request Aug 7, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

ghstack-source-id: 301415132
Pull Request resolved: #13185
SS-JIA pushed a commit that referenced this pull request Aug 11, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

[ghstack-poisoned]
SS-JIA pushed a commit that referenced this pull request Aug 11, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

[ghstack-poisoned]
SS-JIA pushed a commit that referenced this pull request Aug 13, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

[ghstack-poisoned]
SS-JIA pushed a commit that referenced this pull request Aug 13, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

[ghstack-poisoned]
SS-JIA pushed a commit that referenced this pull request Aug 13, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

[ghstack-poisoned]
SS-JIA pushed a commit that referenced this pull request Aug 13, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)

[ghstack-poisoned]
SS-JIA pushed a commit that referenced this pull request Aug 13, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / #6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)
agrima1304 pushed a commit to agrima1304/executorch that referenced this pull request Aug 26, 2025
## Context

Currently `default_pick_local_wg_size()` (which internally calls `ComputeGraph::create_local_wg_size`) is used to select the local work group size for matrix multiplication ops. However, these functions currently bias the size of the local work group towards the largest dim of the global work group producing local wg sizes like

```
shader                                                                          globalwg size            localwg size
===========                                                                     =====================    ====================                 =============
linear_qga4w_tiled_texture3d_texture3d_texture2d_float                          {256, 29, 1}             {32, 2, 1}                                    1487
matmul_naive_texture3d_float                                                    {29, 115, 32}            {4, 2, 8}                                      712
```

for matrix multiplication shaders. This behaviour was introduced in D64418632 / pytorch#6409.

However, through experimental testing a "square" work group size of `{8, 8, 1}` works a lot better for matrix multiplication shaders. The theoretical analysis for this behaviour is that the local work group size determines the memory locations that need to be loaded to compute the overall work group. For a work group with size `{W, H, 1}` the data required to compute the output would be `W * OUTPUT_TILE_W` columns of the weight tensor and `H * OUTPUT_TILE_H` rows of the input tensor. Note that all work group items in the same W index will be requesting the same columns from the weight tensor, and all work group items in the same H index will be requesting the same rows from the input tensor.

If `H==W`, then that "balances" the amount of data needed to loaded from each input tensor and may result in better data sharing behaviour among all work group items. Assuming `OUTPUT_TILE_W == OUTPUT_TILE_H == 1`, a local work group of size `{64, 1, 1}` would require 1 unique row from the input tensor an 64 unique columns to be loaded from the weight tensor, resulting in `(1 + 64) * K = 65K` elements to be loaded in total, where K is the size of the shared reduction dim. Conversely, a local work group of size `{8, 8, 1}` would require 8 unique rows / 8 unique columns resulting in only `(8 + 8) * K = 16K` unique elements to be loaded.

This highlights the need to use dedicated logic to compute work group sizes for matrix multiplication shaders.

## Changes

* Introduce `pick_hw_square_wg_size`
* Use the new local work group size determination function for Quantized Linear, Matmul, and Linear

Differential Revision: [D79813236](https://our.internmc.facebook.com/intern/diff/D79813236/)
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