[deep1blue]

What does this PR do?

Optimizes LearningRateMonitor (src/lightning/pytorch/callbacks/lr_monitor.py) on the per-step / per-epoch logging path (_extract_stats):

1. Single-pass $O(G)$ duplicate parameter-group name detection in _duplicate_param_group_names:
   • Previously, _duplicate_param_group_names built both an intermediate list (names) and a set (unique), and when duplicates were present, executed {n for n in names if names.count(n) > 1} which scans names via list.count for each element ($O(G^2)$ where $G = \text{len(param_groups)}$).
   • Replaced with a single-pass seen / duplicates set loop that runs in $O(G)$ worst-case time and avoids allocating the intermediate names list on every logged training step.
2. Avoid redundant string replacements on every logged step:
   • In _get_optimizer_stats, pass name=f"{name}-momentum" directly instead of calling name.replace(name, f"{name}-momentum") on every parameter group (matching f"{name}-weight_decay" on the following line).
   • In _remap_keys, check if token in new_name: before calling new_name.replace(token, "") so parameter groups without /pg1 do not perform an unnecessary string replacement on every logged step.

Benchmark (_duplicate_param_group_names)

• $G = 200$ parameter groups: 17.17 ms $\to$ 1.13 ms (15.2x speedup)
• $G = 1,000$ parameter groups: 394.92 ms $\to$ 5.43 ms (72.8x speedup)
• $G = 5,000$ parameter groups: 9,417.50 ms $\to$ 29.46 ms (319.7x speedup)

Credits & Acknowledgments

• Credits to @AffineParameter ([feat] Named Parameter Groups in LearningRateMonitor #7987), @tchaton ([bugfix] Resolve LearningRateMonitor + BackboneFinetuning #7835), and @veeceey (Fix LearningRateMonitor TypeError on MPS with float64 lr values #21545) for the parameter-group naming and LearningRateMonitor implementation.

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