Implement Ensemble-Based Multi-Track Finder

[dhshin04]

Summary

Implements a fixed-N ensemble approach to multi-track dimuon pair finding, decomposing the problem into two independently trainable components:

• Track counter (models/TrackCounter.py): classifies how many ground-truth pairs (0..N) are in each event, using the denoiser U-Net++ backbone with a GlobalAveragePooling → Dense head and sparse-CE loss
• Fixed-N finders (models/MultiTrackFinder.py): unified code path for all N (1–3); output always (B, N, 2, 62, 201); trained with the new min_perm_loss — a brute-force permutation-invariant loss (N! ≤ 6) that finds the minimum-cost assignment of predicted pair slots to ground-truth slots

Key changes

File	Change
data/multi_track/gen_fixed_pairs.py	New: fixed-pair data generator (fork of gen_training_random.py)
models/losses.py	Add min_perm_loss(n_pairs) — permutation-invariant loss; exact match to custom_loss at N=1
models/data_loader.py	Add load_data_counter() — returns (X, counts) for counter training
models/MultiTrackFinder.py	Rewrite: unified N path, --n_pairs replaces --max_pairs / presence loss args
models/TrackCounter.py	New: classification model with curriculum learning and sklearn confusion report
eval_multi_track.py	Rewrite: permutation-matched metrics per pair, no chi-squared, --n_pairs arg
scripts/preprocess_fixed.slurm	New: generates fixed-N and random training data for all N
scripts/train_counter.slurm	New: counter training job (1× A100)
scripts/train_finder.slurm	New: parameterized finder training + eval (4× A100, N_PAIRS env var)

Design decisions

• N=1 exact equivalence: min_perm_loss(1) is mathematically identical to the original custom_loss (same CE + overlap penalty scalar), so N=1 can be retrained through the new code without regressions
• Orchestrator deferred: counter and finders are trained and evaluated independently; the routing orchestrator is out of scope for this PR
• Brute-force permutations: N ≤ 3 gives at most 3! = 6 permutations, making Hungarian matching unnecessary

Test plan

• Run gen_fixed_pairs.py on a small sample; verify HitArray_mup has length N*62 and nPairs == N every event
• Confirm min_perm_loss(1) value matches custom_loss on identical input (after squeezing the N=1 pair axis)
• Smoke-train MultiTrackFinder.py --n_pairs 1 and --n_pairs 2 for 1 epoch; confirm output shapes (B,1,2,62,201) and (B,2,2,62,201)
• Smoke-train TrackCounter.py for 1 epoch; confirm confusion matrix prints at end
• Run eval_multi_track.py --n_pairs 2 on a checkpoint; confirm per-pair tables print and no chi-squared appears
• Submit train_finder.slurm with N_PAIRS=1, N_PAIRS=2, N_PAIRS=3 on HPC