Worked on the pytorch/xla repository to address a critical issue affecting BatchNorm behavior under automatic mixed precision (AMP) on TPUs and GPUs. Focused on deep learning and performance optimization, the developer implemented a fix to ensure correct normalization when lower-precision inputs such as FP16 or BF16 are used alongside FP32 weights. This adjustment prevents incorrect results during mixed-precision training and enhances stability for XLA backends. The solution was developed using C++ and Python, and included the addition of an automated regression test to validate the fix and safeguard against future issues in mixed-precision BatchNorm scenarios.