# Behavioral Validation

This records whether the released stimuli actually elicit the intended space-tracking
behavior in capable open models. It is a check on the stimuli, not a reproduction of any
result in the papers that study these constructions (arXiv:2607.10248, arXiv:2607.11945):
those papers' numbers come from the project experiment scripts, and this corpus is a
companion stimulus suite derived from the same constructions.

## Method

Each row's `prompt` is a completion that ends on a copula, so the answer is the next
token. For every prompt we read the next-token logits and take:

- **forced accuracy** (primary): argmax restricted to the item's in-play values
  (`value_space_map`). This is the minimal-pair question: does the model pick the correct
  space's value over the competing one?
- **open accuracy** (secondary): argmax over the full color vocabulary. The gap between
  open and forced surfaces the model's color prior and any off-vocabulary drift; it is a
  diagnostic, not the headline.

Answers are scored on the first token of ` {color}` using the target model's own
tokenizer; the single-token audit below reports whether each answer is one token.

Scoring is completion-style (no chat template), matching the corpus format. Instruction
models may behave differently under their chat template; verify for your setup.

## Caveats

- **Two architectures, still provisional.** These numbers are Qwen2.5-7B-Instruct and
  OLMo-2-1124-7B-Instruct. Agreement across two models is reassuring but not proof of
  generality. The cross-model pattern matters more than any single cell: a frame weak on
  one model may be fine on another, and only frames weak on both point to the stimulus.
- Accuracy below 1.0 is expected: two-space and nested constructions are genuinely hard,
  and the two-entity control is designed to leak (see below). The bar is that a capable
  model tracks the correct space well above chance, not perfectly.

## Per-construction results

Completion scoring, all splits, forced accuracy (argmax restricted to the item's competing
values). Overall 0.87 (Qwen2.5-7B-Instruct) and 0.90 (OLMo-2-1124-7B-Instruct).

| construction | n | Qwen-7B | OLMo-2-7B |
|---|---:|---:|---:|
| single_space_control | 120 | 1.000 | 1.000 |
| belief_reality | 450 | 0.933 | 0.933 |
| counterfactual_or_alternative_space | 500 | 0.846 | 0.930 |
| nested_depictive | 360 | 0.825 | 0.892 |
| two_entity_selectivity | 240 | 0.858 | 0.854 |
| nested_belief | 240 | 0.821 | 0.817 |

Both models track the correct space well above the two-value chance line (0.50) on every
construction. Forced accuracy is the metric that answers the space-tracking question; the
open six-way argmax deflates the four-color constructions through the model's prior toward
the two unused colors, so it stays a diagnostic rather than the headline.

The two-entity control leaks as designed (swap 0.125 Qwen, 0.142 OLMo-2): it separates
entity-bound space assignment from a global image-versus-reality feature, and a model that
copies the distractor's value scores as swap. Nested belief is the hardest construction on
both models, driven by one frame (see below).

## Per-template results

Forced accuracy per frame. This is the diagnostic for a weak surface realization.

| construction | template | n | Qwen-7B | OLMo-2-7B |
|---|---|---:|---:|---:|
| belief_reality | belief-thinks | 150 | 0.967 | 0.860 |
| belief_reality | belief-convinced | 150 | 0.960 | 0.960 |
| belief_reality | belief-believes | 150 | 0.873 | 0.980 |
| counterfactual | cf-hypothetical | 100 | 0.940 | 0.940 |
| counterfactual | cf-painting | 100 | 0.810 | 0.910 |
| counterfactual | cf-story | 100 | 0.910 | 0.900 |
| counterfactual | cf-dream | 100 | 0.800 | 0.930 |
| counterfactual | cf-movie | 100 | 0.770 | 0.970 |
| nested_belief | nb-imagines-confirms | 80 | 0.975 | 0.900 |
| nested_belief | nb-assumes-sees | 80 | 0.800 | 0.838 |
| nested_belief | nb-thinks-knows | 80 | 0.688 | 0.713 |
| nested_depictive | nd-reflection-portrait | 120 | 0.867 | 0.933 |
| nested_depictive | nd-photo-painting | 120 | 0.825 | 0.900 |
| nested_depictive | nd-snapshot-sketch | 120 | 0.783 | 0.842 |
| single_space_control | single-space-* | 40 each | 1.000 | 1.000 |
| two_entity_selectivity | te-painting | 80 | 0.850 | 0.912 |
| two_entity_selectivity | te-photo | 80 | 0.863 | 0.838 |
| two_entity_selectivity | te-drawing | 80 | 0.863 | 0.812 |

`nb-thinks-knows` is the hardest nested-belief frame (0.69 Qwen, 0.71 OLMo-2) but no longer
near chance. An earlier build read 0.60 / 0.55: the readout then repeated a verb
(`{observer} thinks {believer} thinks ...`), which let the model collapse the two belief
levels. Changing the outer verb to `believes` lifted the frame on both models (+0.09 Qwen,
+0.16 OLMo-2), so the cause was surface phrasing, not a defect in the scenario. It stays the
softest nested-belief frame, consistent with genuine 2-deep difficulty on top of the
phrasing effect.

Frame variance elsewhere is model-specific rather than stimulus-driven: `cf-movie` is Qwen's
softest counterfactual (0.77) but OLMo-2's strongest (0.97).

## Single-token audit

All answer colors are a single token under both models' tokenizers (Qwen2.5-7B-Instruct and
OLMo-2-1124-7B-Instruct), with the leading space: blue, green, red, brown, yellow, purple.
Re-check for any other model before interpreting token-level results.

## Reproduce

The build and validation scripts live in the source repository,
[github.com/osteele/mental-spaces](https://github.com/osteele/mental-spaces). With the
model and a GPU available, the validation script scores every prompt (`uv run` installs
`torch` and `transformers` from the lockfile):

```bash
uv run python scripts/exp_corpus_behavioral_audit.py --model Qwen/Qwen2.5-7B-Instruct
```