Implement Single-Head Multi-Track Finder

[dhshin04]

Summary

Implements single-run, single-head multi-track loss and data pipeline improvements for MultiTrackFinder.

• models/losses.py: Add min_perm_multi_track_loss — pure-TensorFlow min-over-permutations matching. Evaluates all P! GT reorderings, minimizes masked sparse CE + focal presence per permutation, and adds an inter-pair diversity penalty outside the min. Supports max_pairs 1–5 (hard cap at 5). Old multi_track_loss kept for A/B comparison.
• data/multi_track/gen_training_random.py: Canonical GT pair ordering (sort by μ⁺ element ID sum) and --pair_dist skewed option (exponentially decaying pair-count distribution).
• models/MultiTrackFinder.py: Wire min_perm_multi_track_loss(max_pairs=...); add --focal_gamma and --lambda_diversity CLI args; fix --lambda_presence default to 1.0.
• scripts/train_multi_v2.slurm: New training script with updated hyperparameters (lambda_presence=1.0, focal_gamma=2.0, lambda_diversity=0.05), outputs multi_track_finder_v2.keras.
• scripts/preprocess_multitrack.slurm: Add --pair_dist skewed --at_least_one_pair to train and val data generation.
• eval_multi_track.py: Apply canonical GT sort before residual computation so eval ordering matches training.
• docs/plan/: Updated Plan 01, 03, and 00_EXECUTION_ORDER.md.

Before Running train_multi_v2.slurm

Reprocess training data first (canonical ordering + skewed pair distribution):

sbatch scripts/preprocess_multitrack.slurm

Recommended: 1-epoch multi-GPU smoke test on the cluster before the full 72h run:

# Temporarily add --epochs 1 to the python3 call in train_multi_v2.slurm
sbatch scripts/train_multi_v2.slurm

Verify finite loss on epoch 1, then restore --epochs 60 for the full run.

Test plan

• Single-device smoke test: min_perm_multi_track_loss() returns finite value for (4, 5, 2, 62) batch
• Pre-commit hooks (ruff lint + format) pass on changed files
• Code review: shape/broadcast fix for gather+transpose; max_pairs parameterized with P<=5 guard
• Multi-GPU smoke test on HPC cluster before full training run
• After merge: rerun preprocessing, then sbatch scripts/train_multi_v2.slurm