[ExecuTorch][Vulkan] Add et_vk.linear_q4gsw_backward kernel (4-bit input-grad)

[JCNTH]

Stack from ghstack (oldest at bottom):

• [ExecuTorch][WebGPU] Glob runtime/ops sources in CMakeLists #21005
• [ExecuTorch][Vulkan] Tests for et_vk.q4gsw_requant #20946
• [ExecuTorch][Vulkan] Add et_vk.q4gsw_requant kernel (STE re-quant to W_4X8) #20945
• [ExecuTorch][Vulkan] Tests for et_vk.linear_q4gsw_backward #20944
• -> [ExecuTorch][Vulkan] Add et_vk.linear_q4gsw_backward kernel (4-bit input-grad) #20943
• [ExecuTorch][Vulkan] Tests for et_vk.fused_ce #20942
• [ExecuTorch][Vulkan] Add et_vk.fused_ce kernels (fused cross-entropy loss + dlogits) #20941
• [ExecuTorch][Vulkan] Tests for et_vk.linear_dW #20940
• [ExecuTorch][Vulkan] Add et_vk.linear_dW kernel (dense fp32 weight-grad GEMM) #20939
• [ExecuTorch][Vulkan] Tests for et_vk.adamw_step #20938
• [ExecuTorch][Vulkan] Add et_vk.adamw_step kernel (on-GPU AdamW optimizer step) #20937
• [ExecuTorch][WebGPU] Tests for the adamw WebGPU ops #20936
• [ExecuTorch][WebGPU] Add et_vk.adamw_step (on-GPU AdamW optimizer step) to the WebGPU backend #20935
• [ExecuTorch][WebGPU] Tests for the fused_ce WebGPU ops #20934
• [ExecuTorch][WebGPU] Add et_vk.fused_ce (fused cross-entropy) to the WebGPU backend #20933
• [ExecuTorch][WebGPU] Tests for the q4gsw_train WebGPU ops #20932
• [ExecuTorch][WebGPU] Add q4gsw training kernels (backward, weight-grad, requant) to the WebGPU backend #20931
• [ExecuTorch][WebGPU] Tests for the shape_copy WebGPU ops #20930
• [ExecuTorch][WebGPU] Add shape/copy ops (dim_order, expand_copy, fill) to the WebGPU backend #20929
• [ExecuTorch][WebGPU] Tests for the gather WebGPU ops #20928
• [ExecuTorch][WebGPU] Add gather and embedding ops to the WebGPU backend #20927
• [ExecuTorch][WebGPU] Tests for the select_bool WebGPU ops #20926
• [ExecuTorch][WebGPU] Add select/boolean ops (where, scalar compares, logical_not) to the WebGPU backend #20925
• [ExecuTorch][WebGPU] Tests for the reduce WebGPU ops #20924
• [ExecuTorch][WebGPU] Add reduce op (sum/mean) to the WebGPU backend #20923
• [ExecuTorch][WebGPU] Tests for the binary WebGPU ops #20922
• [ExecuTorch][WebGPU] Add elementwise binary ops (div, sub) to the WebGPU backend #20921
• [ExecuTorch][WebGPU] Tests for the softmax WebGPU ops #20920
• [ExecuTorch][WebGPU] Add softmax ops (_softmax, _log_softmax) to the WebGPU backend #20919
• [ExecuTorch][WebGPU] Tests for the matmul WebGPU ops #20918
• [ExecuTorch][WebGPU] Add fp32 matmul ops (mm, bmm, linear) to the WebGPU backend #20917

Adds the Vulkan et_vk.linear_q4gsw_backward kernel — the input-gradient of the frozen 4-bit linear_q4gsw base, for on-device adapter training. Computes d_x[M, K] = d_out[M, N] @ dequant(W)[N, K], contracting over N.

Problem: et_vk.linear_q4gsw_backward is registered in the shared Vulkan partitioner (custom_ops_lib.py + op_registry.py) but Vulkan had no runtime kernel, so the op could not run.

Solution: a 4M x 4K register-tiled GLSL kernel that reads the SAME W_4X8 block-packed weight the forward reads, re-deriving the nibble/scale addressing so the training loop stays consistent with the forward with no re-pack. dequant(W[n, k]) = (code - 8) * scale.

Key changes:

• glsl/q4gsw_backward.{glsl,yaml} — buffer x float; W_4X8 nibble unpack mirroring glsl/q4gsw_linear_gemm__w_4x8.glsl (even-N low nibble, odd-N high, N4_padded ivec4 stride, [num_groups, N] scales).
• impl/QuantizedLinearBackward.cpp — reuses prepack_q4_w_4x8_nc_buffer + prepack_q4_scales from the forward; 1D tile dispatch ceil(M/4) * ceil(K/4) with a workgroup-count guard; group_size specialization constant.

Constraints: buffer storage, fp32; N % 4 == 0, K % 4 == 0, group_size % 4 == 0 (matches the forward prepack). Weight/scale layout identical to the forward.
@exported-using-ghexport

Differential Revision: D111797529

Differential Revision: D111797529

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✅ You can merge normally! (1 Unrelated Failure)

As of commit a6c5bf5 with merge base 21554e5 ():

BROKEN TRUNK - The following job failed but were present on the merge base:

👉 Rebase onto the `viable/strict` branch to avoid these failures

• pull / test-arm-backend-no-driver (test_pytest_models_tosa) / linux-job (gh) (trunk failure)

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