# FPRM — Maze-Hard 30×30 (single-z, conv1d)

Fixed-Point Tiny Recursive Model (FPRM / FPTRM single-z) trained on **Maze-Hard 30×30**.
Under test-time scaling it reaches **87.0% test exact-match** (full-path sequence accuracy),
the best of our maze runs.

Original run name: `fptrm_singlez_maze_isolrev_repro_warmup2000` (step_78120 = final).

## Results

| metric | value |
|---|---|
| **test exact-match (sequence acc)** | **87.0%** (best of 6 eval-restart seeds; mean 86.6%) |
| token accuracy | 99.57% |
| eval budget | `max_iter=35000`, `stepsize_decay=0.996`, `patience=10` |

Per-seed scaling-eval results are in [`eval_results/`](eval_results) (seeds 0–5:
86.6 / 86.5 / 86.4 / 86.6 / **87.0** / 86.6 %). The conv1d variant here and a no-conv variant
both peak at 87.0%; a conv2d variant reaches 84.5% — i.e. the conv branch is not the deciding
factor on maze.

## ⚠️ Data note (read before reproducing)

This model was trained on the **non-augmented** Maze-Hard set (1000 mazes, single orientation).
The training config records `data_paths: [data/maze-30x30-hard-1k]`, but in our pipeline that
path later became the **8× dihedral-augmented** build, which collapses maze training to ~5%
(augmentation breaks this task for a non-equivariant model). **To reproduce, train on the
non-augmented 1000-maze build.** The test split is identical (single orientation) either way.

## Architecture

| | value |
|---|---|
| model | FPTRM single-z (`fp_trm_singlez`) |
| hidden size / heads / expansion | 512 / 8 / 4 |
| H-cycles / L-cycles | 0 / 0 |
| H-layers / L-layers | 0 / 2 |
| n_backwards_L | 6 |
| positional enc / puzzle-emb len | RoPE / 16 |
| halting | fixed-point |
| max_iter (train) | 24 (deterministic) |
| max_iter (eval) | 1000 default; **35000** for the scaling result |
| stepsize-decay / patience (eval) | 0.996 / 10 (train-time default 0.9 / 5) |
| fp_thresh | 0.1 |
| norm type / placement | pre-norm / output |
| residual scaling | input-independent (α₁, α₂ init = 0.75, 0.25) |
| conv branch | conv1d (kernel 4) |
| init_std | 1.0 |

## Optimizer

| | value |
|---|---|
| optimizer | AdamW (β = 0.9, 0.95) |
| learning rate | 1e-4 (constant after 2000-step warm-up) |
| weight decay | 1.0 |
| **puzzle-emb LR** | **1e-2 (decoupled)** |
| puzzle-emb WD | 1.0 |
| batch size | 768 |
| epochs | 60000 |
| EMA | enabled (rate 0.999) |
| seed | 0 |

> Note: the optimizer is **AdamW** (`adam_atan2` was not used for this checkpoint).

## Files

- `step_<N>` — EMA-averaged eval checkpoints (53 MB each), N = 6510 … **78120** (final).
  Because `ema=True`, `step_<N>` is the EMA copy — **these are the weights to load for
  inference/eval**.
- `step_<N>_train_state.pt` — full training state (live weights + optimizer + EMA), for
  resuming training.
- `all_config.yaml` — the exact training configuration.
- `fp_trm_singlez.py`, `losses.py` — model and loss source for this checkpoint.
- `reproduce/` — training SLURM script (`submit_fptrm_maze_87pct_repro_8gpu.sh`) and the
  eval script (`singlez_eval_sweep.py`).
- `eval_results/` — the per-seed scaling-eval JSONs that produced the 87%.

## Reproduce the 87%

1. **Train** with `reproduce/submit_fptrm_maze_87pct_repro_8gpu.sh` (FPTRM single-z, conv1d/k4,
   pre-norm/output, input-independent residual scaling, decoupled puzzle-emb LR=1e-2, 60000
   epochs, **non-augmented** maze). Produces `step_78120`.
2. **Eval at the 35k budget** on the resulting checkpoint:
   ```
   python singlez_eval_sweep.py --ckpt-dir <CKPT_DIR> \
       --data-dir <maze-hard-test> \
       --stepsize-decay 0.996 --decay-patience 10 --max-iter 35000 --seed 4
   ```
   `87.0%` is the best of restart seeds 0–5 (mean ≈ 86.6%).