Hi rwightman,

This PR aims to add a cautious optimizer to AdamP.

Motivation / Principle
You are already familiar with the cautious optimizer and have integrated it into most optimizers. Our goal is to extend this idea to AdamP. AdamP separates parameters into two parts: one part lies on a sphere and is updated along tangent directions, while the other part is updated in the standard way. When applying a cautious optimizer to spherical parameters, the update should preserve the feature-learning direction (i.e., alignment of tangent-direction signs). Other parameters can use the standard cautious mask. This is the core idea behind our modification. We also wrote a short document explaining why this design is reasonable [1].

Changes

1. We added an optional caution parameter to the adamp file. When set to True, the cautious mask is applied.
2. We added the optimizer name cadamp to _optim_factory.py.
3. We added tests for cadamp in test_optim.py.

Test Results
We tested the PR and obtained the following results:

tests/test_optim.py::test_optim_factory[cadamp] PASSED
tests/test_optim.py::test_cadamp[cadamp] PASSED

That is, all tests pass successfully.

Recent work [2,3] has shown that constraining parameters to lie on a sphere can significantly improve performance. We believe that the spherical cautious optimizer can serve as a useful plugin for spherical-constrained optimization. We hope you can review this PR at your convenience.

References:
[1] https://openreview.net/forum?id=4lTJbNpWr3
[2] https://psychedelic-sunstone-851.notion.site/Fantastic-Pretraining-Optimizers-and-Where-to-Find-Them-2-1-Hyperball-Optimization-2e924306e6f280e7a5ffee00eb40a0dd
[3] https://arxiv.org/abs/2601.08393

Best regards,
Jinghui