[ExecuTorch][WebGPU] Add q4gsw training kernels (backward, weight-grad, requant) to the WebGPU backend

[JCNTH]

Stack from ghstack (oldest at bottom):

• [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_q4gsw_dw #20940
• [ExecuTorch][Vulkan] Add et_vk.linear_q4gsw_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

Add the 4-bit fine-tuning weight-path custom ops — et_vk.linear_q4gsw_backward (input grad dX), et_vk.linear_q4gsw_dw (weight grad dW), and et_vk.q4gsw_requant (STE re-quant of fp32 latents → 4-bit codes) — that close the on-device training loop through a frozen 4-bit base.

Key changes:

• runtime/ops/quantized_linear/{QuantizedLinearBackward,QuantizedLinearDw,QuantizedLinearRequant}.cpp + q4gsw_{backward,dw,requant}.wgsl — the three training kernels
• custom_ops_lib.py — 3 custom-op defs (linear_q4gsw_backward + register_autograd on linear_q4gsw, linear_q4gsw_dw, q4gsw_requant)
• op_registry.py — 3 OpFeatures
• CMakeLists.txt WEBGPU_SRCS — wire the sources

Training-only, WebGPU-only custom ops registered under the shared Vulkan partitioner; Vulkan has no kernels for them yet (a separate Vulkan-kernel track covers that). Guards mirror the sibling Dw/Requant ops (scales-rank + K==0).

Co-authored-with: Claude Code.
@exported-using-ghexport

Differential Revision: D111755130

Differential Revision: D111755130

[pytorch-bot]

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