fix(train): serialize GaLore projector state in checkpoints

[MrCapricornLiu]

GaLore stores a GaLoreProjector instance in optimizer state. Consequently, a normal optimizer checkpoint cannot be restored by Trainer's torch.load(..., weights_only=True): it fails with an unsupported-global error before training resumes.

Serialize the projector as a dictionary of configuration values and tensors, then reconstruct it when loading optimizer state. The live optimizer keeps its projector object. Move cached projection bases to the gradient's device/dtype before reuse, so CPU-mapped checkpoints can resume on CUDA without waiting for the next SVD refresh. This applies to the bundled AdamW, Adafactor and AdamW8bit implementations.

Validation:

• Four regression methods pass on CUDA, including five projection modes on CPU, CPU-mapped restoration on CUDA, bitsandbytes 8-bit state, ordinary parameter groups and legacy in-memory projector states.
• A tiny GPT-2 with the real Transformers Trainer fails to resume on main. With the patch, resuming at step 3 produces exactly the same parameters as uninterrupted training through step 6.
• Changed-file pre-commit hooks and git diff --check pass. Base-revision whole-repository lint has an unrelated formatting failure in tests/megatron/test_infonce_ddp_e2e.py.

This makes newly written checkpoints compatible with safe loading. It does not change safe-loading policy for older pickled-object checkpoints, or address the separate per-parameter optimizer wrapper's checkpoint handling. Validation used FP32 parameters; distributed/sharded checkpoints and q-galore were not tested.

[tastelikefeet]

lint the code by:

pre-commit run --all-files

please