TL;DR

The bug can be potentially fixed by re-examining the changes introduced in pull request #81316 and ensuring that the potrf implementations do not use other parts of the matrix as scratch space.

Guidance

• Review the code changes in https://github.com/pytorch/pytorch/pull/81316 to understand the reasoning behind the introduction of the bug.
• Investigate the documentation of potrf implementations, such as MAGMA, cuBLAS, and Apple's Accelerate, to determine if they use other parts of the matrix as scratch space.
• Verify that the elements marked as "not referenced" in the LAPACK documentation are indeed not accessed by the potrf implementations.
• Consider adding additional checks or modifications to the code to ensure that the potrf implementations do not access other parts of the matrix.

Example

No code snippet is provided as the issue does not contain sufficient information to create a minimal example.

Notes

The fix may require a deep understanding of the LAPACK library and the specific implementations of potrf. Additionally, the issue may be specific to certain versions of PyTorch or the underlying libraries.

Recommendation

Apply workaround: The issue is likely related to a specific change in the code, and applying a workaround to revert or modify this change may be the most straightforward solution.