[torchlib] Implement aten_bilinear function using Einsum

[Copilot]

This PR implements the aten_bilinear function that was previously raising NotImplementedError. The bilinear transformation computes y = x1^T A x2 + b where:

• input1 has shape (..., in1_features)
• input2 has shape (..., in2_features)
• weight has shape (out_features, in1_features, in2_features)
• bias has shape (out_features) (optional)
• Output has shape (..., out_features)

Implementation Details

The implementation is done using einsum.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 70.10%. Comparing base (168fd8a) to head (462d155).
✅ All tests successful. No failed tests found.

Additional details and impacted files

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  Coverage   70.10%   70.10%           
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  Files         222      222           
  Lines       26184    26188    +4     
  Branches     2581     2582    +1     
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+ Hits        18355    18360    +5     
+ Misses       6929     6928    -1     
  Partials      900      900           

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[justinchuby]

Can you re-express it using Transpose and Matmul? That may produce a graph that is easier to optimize. @copilot

[justinchuby]

You may not need to flatten for MatMul. It supports N-dim inputs @copilot

[Copilot]

Can you re-express it using Transpose and Matmul? That may produce a graph that is easier to optimize. @copilot

Done! I've re-implemented the function using MatMul and Transpose operations instead of Einsum. The new implementation decomposes the bilinear transformation into: outer product creation → reshaping → matrix multiplication with transposed weights. This should be more optimization-friendly. See commit 22c4c0f.

[Copilot]

You may not need to flatten for MatMul. It supports N-dim inputs @copilot

You're absolutely right! I've simplified the implementation by removing the unnecessary flattening and leveraging N-dimensional MatMul support. The new approach uses two clean MatMul operations without creating outer products or flattening tensors, making it much more efficient and optimization-friendly. See commit 095967e.

[justinchuby]

Yeah the implementation is too complex. I will re-do this

[justinchuby]

I reverted to the original einsum implmenetation. It seems clean