[WebGPU EP] Add EINSUM implementation

[feich-ms]

Description

This PR added the native implementation of einsum operator, based and expanded on existing einsum.ts. All the test cases in einsum_test.cc have been passed.

The equation attribute value of einsum op is a string which consists of left hand side (LHS) and optionally right hand side (RHS) separated by '->'. Ex.

• "ij->ji" matrix transpose
• "ii->i" diagonal elements of a square matrix
• "ij->" sum over all elements of a matrix
• "ij,jk->ik" explicit matrix multiplication
• "ij,jk" implicit matrix multiplication
• "ij,jk->" matrix multiplication and sum over all elements
• "ij,jk,kl->il" three matrix multiplication
• "...ij,...jk->...ik" batched matmul with broadcasting
• ",...i->...i" matrix element multiplication with one scalar
• "abc,cd->abc" keep the original abc matrix shape but matmul and sum over along d

LHS consists of a sequence of terms separated by commas. Each term corresponds to an input variable.
Each symbol corresponds to a dimension in the input variable. The symbol can be either a letter, 'a' to 'z' or 'A' to
'Z' or '...' to represent arbitrary dimensions or empty to represent a scalar.

Empty RHS are handleed differently for implicit vs explicit modes.

• Implicit mode - arrow is not in the equation where the equation "ij,jk" equals to "ij,jk->ik" which is actually a matrix multiplication.
• Explicit mode - arrow is in the equation where the equation "ij,jk->" contains two steps, first step is a matrix multiplication just like the implicit mode, and the second step is to sum up the matrix produced by the first step to a scalar.

For all the test cases, pls refer to einsum_test.cc

[feich-ms]

@satyajandhyala @xiaofeihan1 @qjia7 @guschmue @fs-eire, pls help to reiview, thanks.

[fs-eire]

/azp run Linux QNN CI Pipeline, Win_TRT_Minimal_CUDA_Test_CI, Windows ARM64 QNN CI Pipeline, Windows GPU Doc Gen CI Pipeline, Windows x64 QNN CI Pipeline

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[Copilot]

Pull Request Overview

This PR adds the native Einsum implementation for the WebGPU provider, enhancing operator support by integrating a new kernel alongside its corresponding tests. Key changes include:

• Adding a new test case in onnxruntime/test/providers/cpu/math/einsum_test.cc for explicit Einsum reduction with multi-input.
• Enabling the Einsum kernel registration in onnxruntime/core/providers/webgpu/webgpu_execution_provider.cc.
• Introducing the Einsum operator implementation in onnxruntime/core/providers/webgpu/math/einsum.h.

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated no comments.

File	Description
onnxruntime/test/providers/cpu/math/einsum_test.cc	Added a test case for explicit Einsum reduction to scalar with multi-input.
onnxruntime/core/providers/webgpu/webgpu_execution_provider.cc	Enabled the Einsum kernel by uncommenting the registration entry.
onnxruntime/core/providers/webgpu/math/einsum.h	Introduced the new Einsum operator abstraction and related utility classes.

[fs-eire]

lgtm