# Representation batteries: content projection and model-layer readout

Run date: 2026-07-29

## Question

Every energy tested before today failed the basin audit: descent from any
start found configurations below the true one. The manifold gate located
the cause in the node states, and `STRUCTURE_DESIGN.md` distilled it into
requirement batteries. This report covers the first two batteries -- R6
(content-subspace projection) and R3 (model-layer relational readout) --
and the full assignment gate on the resulting states. Both batteries
change the states only; the energy, the gate machinery, and the hidden
evaluation protocol are unchanged.

## R6: within-scene noise whitening lifts the ceiling

Views of the same scene share content and differ in style. Directions
maximizing between-scene over within-scene variance are the solution of a
generalized eigenproblem fitted per modality on unpaired orbit structure:
Flickr directions on the 12,000 text-only training orbits, VG directions
only on nodes outside the evaluated subset. The contrast with population
whitening carries the entire lesson: population whitening equalizes the
total covariance and collapsed the cross-modal signal to 0.03; whitening
the within-scene covariance instead amplifies exactly the directions where
independent redescriptions agree.

| Condition | Baseline rho / improving swaps | Projected best |
|---|---|---|
| Flickr orbit mean | 0.298 / 7.8% | 0.358 / 0.5% (k=32) |
| Flickr single caption | 0.189 / 15.6% | 0.326 (k=16) |
| VG region_closed, both sides | 0.213 / 23.5% | 0.614 (k=8); 0.25% swaps (k=128) |

A single projected caption carries more shared relational signal than the
five-caption orbit mean of the raw states. On VG the cross-modal Spearman
nearly triples.

## R3: the model layer shares its states, not its attention

For each VG node the sixteen phrases were encoded jointly in one Qwen
context (four phrase orders, cross-phrase attention pooled per layer
group, in-context phrase states from the final layer), and each image was
encoded once with DINO patch attention pooled over region-box pairs. At
the replayed true view correspondence, on all 5,000 nodes:

| Relation source | Matched rho | Gap z |
|---|---:|---:|
| Isolated-encoding cosine (baseline) | 0.128 | 46.6 |
| Attention x attention, best layer pair | 0.076 | 6.8 |
| In-context cosine x in-context cosine | **0.216** | **69.6** |

Attention weights are modality-specialized -- DINO's spatial attention and
Qwen's causal attention share almost nothing directly. What the model
layer shares is the result of context mixing: **in-context states carry
1.7 times the cross-modal relational signal of isolated encodings.** The
"relations live in the model layer" hypothesis holds with that
refinement: the readout is the mixed states, not the mixing weights.

## The assignment gate passes on Visual Genome

Full gate on content-projected states (`content_gate.py`), with ten
random-restart quenches per run and subset seeds 0--2. "Margin" is how far
the best quench ends above the true energy; positive margin with near-zero
accuracy quenches means descent found nothing below the truth.

| Condition | z | Improving swaps | Kept | Margin | Passes |
|---|---:|---:|---:|---:|---|
| VG isolated states, k=128, seeds 0/1/2 | 207--219 | 0.25--0.28% | 52--54% | +5.1--10.8% | yes, 3/3 |
| VG isolated states, k=256, seeds 0/1/2 | 199--212 | 0.19--0.23% | 54--59% | +7.8--15.8% | yes, 3/3 |
| VG in-context + projection, k=64/128/256 | 209--213 | 0.17--0.23% | 52--59% | +11.6--18.5% | yes, 3/3 |
| Flickr text-side projection, k=128/256 | 141--147 | 0.23--0.25% | 56--57% | -0.9---0.6% | no |

Nine of nine VG conditions pass: for the first time in the project, no
descent trajectory from any start reaches an energy below the true
configuration. The in-context composite widens the margin over isolated
states by roughly a factor of two at matched k. Flickr fails by under one
percent: with a single visual view there is no within-scene visual orbit
to whiten, so the visual side's private fine structure stays in the
energy. The pass is therefore attributable to two-sided multi-view
structure, which is a data-protocol requirement, not a dataset accident.

## What did not pass

- The true assignment is still not a strict local minimum anywhere:
  0.17--0.28% of transpositions improve it (roughly 200--350 swaps of
  131k), and exact descent from the truth keeps 52--59% of nodes. The
  passed gate licenses soft-coupling recovery, not exact hard matching.
- Flickr at node level, per the single-view limitation above.
- Blind recovery is untested: everything here evaluates orderings around
  the hidden truth. Nothing yet demonstrates that unpaired optimization
  finds this basin from scratch.

## Conclusion

The information ceiling diagnosed by the manifold gate was real and was
liftable by two purely unimodal operations: whiten the within-scene view
noise, and read states after the model's own context mixing. On
two-sided multi-view data the resulting energies order the true
configuration below everything descent can reach, with margins of 5--19%
replicated over three subset seeds and ten restarts.

The next phase is the alignment process under the P-requirements of
`STRUCTURE_DESIGN.md`: soft-coupling recovery (Sinkhorn over real states,
which preserves the decodable path back to the frozen LLM), scored by
coupling mass on the hidden truth and by calibrated seed precision, then
the coarse-to-fine recursion onto view level. The passed node-level gate
is the license for that phase, not a claim of usable multimodal ability.

## Main artifacts

- `artifacts/manifold_gate/content_projection.json`
- `artifacts/manifold_gate/content_gate_{flickr,vg}_k{16,32,128}.json`
- `artifacts/manifold_gate/confirm_vg_k{128,256}_seed{0,1,2}.json`
- `artifacts/manifold_gate/confirm_vg_ctx_k{64,128,256}.json`
- `artifacts/manifold_gate/confirm_flickr_k256.json`
- `artifacts/manifold_gate/attn_{text,vision}_full.pt`
- `artifacts/manifold_gate/attention_probe_full.json`