Done

How about enhancing the current TransposeProgram with shared path instead of adding a new one?
You are doing transpose from perm [0, 1, 2, 3] to perm [0, 2, 3, 1]. It equals that we are transposing from [o, i, hw] to [o, hw, i]. You can simply extend the DoTranspose with shared path to support any shape that only transpose the last two dimensions and keep the previous dimensions unchanged. Currently, the shared path only supports 2d transpose from new shape from perm [0, 1] to new shape with perm [1, 0]. We can extend it to transpose from [0, 1, 2] to [0, 2, 1] if the transpose meets the requirement that only transpose the last two dimensions by reshape it into 3d tensor [d0 * d1*...*dn-3, dn-2, dn-1]

Understood.
I intend to improve the current Transpose path discussed in the previous PR #26501.
Could I handle this as a separate task for a following PR?

What if the sg_size is larger than or less than TILE_M_SIZE?

Currently, Lunar Lake devices support a subgroup size of 32.
We must carefully add support for devices with different subgroup sizes, passing this value as a parameter to the template.

BTW, using subgroupShuffle improves the performance 5%~10%, comparing no subgroupShuffle.

If you only want to support sg_size = 32, I prefer you write it like blow. Otherwise, you can't make sure the sg_size must be 32 unless your check the supported subgroup range with subgroupMinSize = subgroupMaxSize = 32.

if (sg_size == 32) {
      let src_data = src_tile[inner_k_idx][sg_id];
      for (var m_idx = 0u; m_idx < TILE_M_SIZE; m_idx++) {
        results[m_idx] += output_element_t(dot(weight_data, subgroupShuffle(src_data, m_idx)));
      }
}
else {
      for (var m_idx = 0u; m_idx < TILE_M_SIZE; m_idx++) {
        results[m_idx] += output_element_t(dot(weight_data, src_tile[inner_k_idx][m_idx]));
      }
}

My understanding is that most modern GPUs typically support a subgroup size of 32 or greater, which this shader is designed to support.

The code's purpose is to mitigate potential performance penalties associated with the runtime conditional check (if (sg_size == 32)) within the shader.

if (sg_size == 32) {
  // do somethings
}

Testing on Lunar Lake showed these penalties to be high.

Add comment in the code about it. Or I can simply make use_subgroup=false by default.