# Cable representation analysis — ACT encoder, DG-5F / UR5e cable sorting

What the ACT encoder's internal representation holds about the cable being
handled. All figures come from a forward hook on `policy.model.encoder`: the
transformer tokens are mean-pooled into a single 512-d vector per frame.

**Every split in this directory is episode-level.** Frames inside one episode
are near-duplicates, so a frame-level split leaks the answer and inflates every
number below.

## Model under analysis

| | |
|---|---|
| policy | ACT, action chunk 60 |
| training | 300k steps on `Kaz55/dg5f_ur5e_bluev2_cable170_330_270ep` (270 episodes) |
| cameras | 2× RealSense + 2× GelSight |
| excluded | `observation.velocity`, `observation.effort` |

Cable naming: **1.70 sq → 1.7 mm**, **blue → 2.6 mm**, **3.30 sq → 4.5 mm**
(mm = outer diameter; sq = conductor cross-section).

## Headline results

**The encoder knows which cable it is holding.**

```
full 512-d linear probe, 3 cables       97.9%   (chance 33.3%)
full 512-d linear probe, 4 cable sizes  94.0%   (chance 25.0%)
```

**It encodes thickness as a quantity, not just as a class label.** Ridge
regression onto physical diameter, fitted on training episodes only — the
ordering is never supplied, yet 2.6 mm lands between 1.7 and 4.5:

```
held-out R^2 = 0.88
  true 1.7 mm -> 1.81 +- 0.33 mm
  true 2.6 mm -> 2.66 +- 0.39 mm
  true 4.5 mm -> 4.33 +- 0.43 mm
```

**But the discrimination is visual, not tactile.** Splitting each episode at
contact onset (detected per episode from finger torque) gives almost the same
accuracy before the GelSight has touched anything as after:

```
             probe accuracy   diameter R^2
pre-contact      94.9%            0.72
post-contact     95.6%            0.83
```

This reconciles the training-loss result seen across 4+ datasets: **removing
GelSight entirely leaves training loss unchanged**, and GelSight resolution from
192 tokens down to 0 makes no difference. The policy separates cables by sight.

PCA in each phase, probe accuracy on exactly the axes drawn:

```
             PC1/PC2   PC1-PC3      variance PC1 / PC2 / PC3
pre-contact   46.7%     77.2%          18.9% / 9.2% / 5.8%
post-contact  64.9%     82.8%           9.7% / 7.0% / 6.1%
```

PC1/PC2 is dominated by arm pose, which is why the unsupervised 2-D view looks
messier than the probe numbers suggest. The cable-identity structure lives on
later components (PC3/PC4) and in the 3-D view.

## Four cable sizes — does an intermediate size land in between?

`4sizes/`. Adds **3.00 sq**, an intermediate cross-section, from
`Kaz55/dg5f_ur5e_cable3sizes_180ep`. 900 frames per size (60 episodes × 15
frames), 3600 total.

**Yes — 3.00 sq sits between blue and 3.30 sq.** On the regressed size axis:

```
size axis held-out R^2 = 0.86
  1.70 sq        true 1.70 -> 1.83 +- 0.22
  blue (2.6 mm)  true 2.30 -> 2.36 +- 0.22
  3.00 sq        true 3.00 -> 2.94 +- 0.22
  3.30 sq        true 3.30 -> 3.21 +- 0.20
```

and in raw 512-d centroid distances, where blue↔3.30 is the largest of the three
— exactly what it must be if 3.00 lies between them:

```
  blue <-> 3.00   4.59
  3.00 <-> 3.30   3.33
  blue <-> 3.30   5.27   <- largest
```

**Caveat.** 3.00 sq comes from a different dataset, so session-level confounds
(lighting, gel condition, recording day) travel with that label. The ordering
result is what guards against over-reading it: a session artefact has no reason
to land *between* two other sizes — it would sit off to one side.

`blue` was entered as 2.30 sq for the ordering test; the ordering itself does not
depend on that value.

## Directory map

| path | contents |
|---|---|
| `4sizes/` | t-SNE and size axis over 4 cable sizes, `results_4sizes.txt` |
| `contact/` | pre/post-contact PCA (2-D, 3-D, rotating GIFs), phase analysis, `results_contact.txt` |
| `diameter/` | diameter-ordered clusters, `results_diameter.txt` |
| `pca2d/` | PC1/PC2 views, informative-component views |
| `pca3d/` | PC1-PC3, rotating GIF |
| `tsne/` | t-SNE over the 3 original cables |
| `pptx/` | `cable_representation.pptx` — the figures as PowerPoint slides |
| `cache/` | extracted encoder features (`.npz`) — every figure replots from these without a GPU |
| `scripts/` | extraction (`collect_*.py`) and plotting (`plot_*.py`) |
| `results_probe.txt` | full-512-d probe accuracies |

## Reproducing

Replot from the cached features (no GPU, no model download):

```bash
python scripts/plot_4sizes_tsne.py --cache cache/cache_4sizes.npz --outdir 4sizes/
python scripts/plot_contact_pca.py --cache cache/cache_cable_contact.npz --out contact/cable_contact_pca.png
python scripts/summarize_from_cache.py --cache cache/cache_cable_feats.npz
```

Re-extract features from the trained policy (needs the checkpoint and a GPU):

```bash
python scripts/collect_4sizes.py --policy-path <checkpoint>
python scripts/collect_contact_feats.py --policy-path <checkpoint>
```