fix: model weight updates with automatic_optimization=False in mixed precision training

[iamarunbrahma]

What does this PR do?

Fixes an issue where model weights were not being properly updated when using automatic_optimization=False with mixed precision training (16-mixed precision). The core issues were:

1. Improper gradient scaling/unscaling in the AMP plugin
2. Missing validation of gradient values before optimizer steps
3. Lack of proper error handling for repeated unscale operations

The changes include:

• Enhanced AMP plugin implementation with proper gradient scaling workflow
• Added explicit gradient unscaling before optimizer steps
• Improved error handling for edge cases
• Added warning when gradients become NaN/inf during training

Fixes #20215

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📚 Documentation preview 📚: https://pytorch-lightning--20460.org.readthedocs.build/en/20460/

[lantiga]

Thank you for the contribution, will review today

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 79%. Comparing base (be608fa) to head (4e6faf5).
Report is 47 commits behind head on master.

❗ There is a different number of reports uploaded between BASE (be608fa) and HEAD (4e6faf5). Click for more details.

HEAD has 1182 uploads less than BASE

Flag	BASE (be608fa)	HEAD (4e6faf5)
cpu	288	24
lightning_fabric	39	0
pytest	146	0
python3.9	72	6
lightning	215	18
python3.11	72	6
python3.10	36	3
gpu	2	0
python3.12	108	9
pytorch2.1	54	9
pytest-full	144	24
pytorch_lightning	36	6
pytorch2.2.2	18	3
pytorch2.3	18	3
pytorch2.5.1	36	6
pytorch2.4.1	18	3

Additional details and impacted files

@@            Coverage Diff            @@
##           master   #20460     +/-   ##
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- Coverage      88%      79%     -9%     
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  Files         267      265      -2     
  Lines       23276    23288     +12     
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- Hits        20383    18322   -2061     
- Misses       2893     4966   +2073     

[lantiga]

something must have happened when submitting the PR, changes need to go in here
https://github.com/Lightning-AI/pytorch-lightning/blob/master/src/lightning/pytorch/plugins/precision/amp.py#L67

but they appear as a stand-alone file https://github.com/Lightning-AI/pytorch-lightning/pull/20460/files#diff-77ef63a4f3cecc394dba6f10386a36ba11362b5e4086b71fca4a4561caf8b0c8, with the method outside the class

[lantiga]

@iamarunbrahma looking at the signature for optimizer_step from, are you working off a pre-2.0 version of PyTorch Lightning? optimizer_idx was removed before 2.0.0 in #16539

[lantiga]

ok the more I look at this the more puzzled I am, can you clarify the code in the PR @iamarunbrahma, how it fits with the plugin optimizer_step and how it solves the original issue?

[lantiga]

BTW the title is contradicting the issue: the issue describes something happening with automatic_optimization=True, not False. I'm closing this one.