# Dimension/noise sweep (2026-02-22)

This page summarizes a small sweep exploring how the steepest-descent global-hit probability depends on:

- feature dimension `d`
- noise magnitude (`noise_k0`; larger means p-adically smaller noise)

Sweep command (example):

```bash
python3 code/run_experiments.py \
  --out-base outputs/2026-02-22 \
  --ps 3 --ds 1,2,3,4 --noise-models haar --noise-k0s 0,2,4,6 \
  --n 20 --trials 10 --policies steepest
python3 code/make_experiment_report.py --base outputs/2026-02-22
```

Result:

![heatmap](padic_lr_global_hit_heatmap.png)

## Quick readout (this run)

This particular sweep used `p=3`, `noise_model=haar`, `n=20`, `trials=10` per cell.

Mean global-hit probability (steepest descent):

| d \\ noise_k0 | 0 | 2 | 4 | 6 |
|---:|---:|---:|---:|---:|
| 1 | 0.784 | 0.641 | 0.762 | 0.801 |
| 2 | 0.453 | 0.470 | 0.544 | 0.520 |
| 3 | 0.323 | 0.452 | 0.342 | 0.243 |
| 4 | 0.264 | 0.192 | 0.273 | 0.224 |

Pooled over `noise_k0`, the mean global-hit drops with `d`:

- `d=1`: 0.747
- `d=2`: 0.497
- `d=3`: 0.340
- `d=4`: 0.238

Practical note: runtime grows quickly with `d` (for fixed `n`) because hyperplanes are enumerated from all `(d+1)`-subsets.