# State tracking (A5 / S5)

FPRM (FPTRM-singlez) trained on permutation-group state tracking over the alternating
group **A5** and the symmetric group **S5**. Trained at sequence length 32, evaluated for
length generalisation up to k = 128. Three seeds per group.

## Results at k = 128 (mean ± sample std over 3 seeds)

| group | accuracy | best | worst | mean L-level calls / sample |
|---|---|---|---|---|
| A5 | **98.1 ± 2.2** | 99.9 | 95.5 | 60 ± 9 |
| S5 | **98.8 ± 0.9** | 99.7 | 97.9 | 70 ± 7 |

Eval uses fixed-point halting with `max_iter_eval=160` (per-sample compute ceiling),
`stepsize_decay=0.95`, and `decay_patience=5` (A5) / `10` (S5). For comparison, a TRM
baseline under the same 160-call budget reaches 45.8 ± 3.9 (A5) and 39.4 ± 1.9 (S5).

## Layout

```
state_tracking/
├── {a5,s5}_seed{1,2,3}/
│   ├── step_97656           # final model weights (load these)
│   ├── all_config.yaml      # exact training config
│   ├── fp_trm_singlez.py    # model source at training time
│   └── losses.py
├── eval_results/            # per-k CSVs (k = 1..128), one per run
└── reproduce/               # per-k eval driver, sbatch scripts, eval-only patches
```

Unlike the other folders, these runs were trained with `ema: false`, so `step_97656`
holds the raw (non-EMA) weights, and no `*_train_state.pt` is included.

`eval_results/*.csv` columns: `family, group, seed, k, acc_halt, mean_halt_steps,
never_halted_frac, l_level`.

## Reproducing the eval

From the repo root (branch `dev/vera/fptrm_new` or a descendant):

```bash
git apply state_tracking/reproduce/*.patch
cp state_tracking/reproduce/eval_fp_per_k.py scripts/
```

The patches are eval-only and default to no-ops. `per_k_node.sbatch` and
`submit_per_k.sh` show the exact per-k eval invocation used for the CSVs.