Add challenge 120: Fused AdamW (Medium)

[adityasharmaaaaa]

Adds a new challenge implementing a fused AdamW optimizer step (decoupled weight decay + bias-corrected first/second moment updates), covering params/m/v as in-place stateful tensors, a gap in the existing challenge set, which has no optimizer-related content despite covering PPO/DPO/GRPO/GAE losses. Includes starters for all 6 supported frameworks (CUDA, Mojo, CuTe, PyTorch, Triton, JAX), an example/functional/performance test suite (11 functional cases covering zero-grad, warm/cold optimizer state, extreme step counts, non-default betas, etc.), and a challenge.html writeup with two hand-verified worked examples. Verified pre-commit run --all-files passes (mojo-format excluded locally, no mojo binary installed) and ran reference_impl against every generated test case to confirm finite, valid output.

[kunal-mansukhani]

Review notes — not merging (challenge ID collision)

114 is already taken on main as challenges/hard/114_multi_head_latent_attention.

Challenge quality looks solid (decoupled AdamW reference, good edge cases, all 6 starters, CI green), but please renumber to a free ID (120+ after today's merges of 115/117/119) and update challenges/medium/114_fused_adamw → new path before we can squash-merge.

Thanks for the contribution — happy to merge once the ID is unique.

[adityasharmaaaaa]

@kunal-mansukhani Renumbered to 120 (folder is now challenges/medium/120_fused_adamw) and rebased on latest main. Ready for another look.