Explicit engagement state (latent engaged/disengaged) — break the ignore-recall ceiling from study 02

[hanhou]

Follow-up to #23 (closed). That issue delivered the 3-action output (L/R/ignore) — 02-gru-scaling-law-ignore, grid complete 48/48. It did not deliver the engagement state its title also promised: there is no latent engaged/disengaged state variable in the model. Ignore is predicted as a third output class, not as the emission of an inferred internal state.

Why it's worth doing — the recall ceiling

r2 — ignore detection found:

• Ignore-class PR-AUC scales with D (~0.61 → 0.64, D=10→614; no-skill base rate ~0.05–0.10). Real, sustained signal — this was the headroom-ier target the study was chasing, and it delivered.
• But recall is capped near 0.47 regardless of scale. More mice sharpen the ranking of ignore-likelihood without moving the model off a conservative operating point. The report calls this a genuine detection ceiling, not a data-scarcity artifact — i.e. more data will not fix it.

A pure 3-way softmax has to explain ignore trials from trial-level features alone. But disengagement is session-structured and temporally autocorrelated (motivation, satiation, drift) — mice go into and out of disengaged bouts. That structure is a latent state, and a model with no state variable to carry it is a plausible cause of exactly this ranking-good / recall-capped signature.

Scope

• Add an explicit engagement state — e.g. a 2-state (engaged / disengaged) latent with learned transition dynamics (HMM-style, or a gated latent in the RNN), where ignore is the emission of the disengaged state rather than a bare third class.
• Test whether it breaks the 0.47 recall ceiling (the concrete falsifiable target).
• Check whether the engagement state is session-structured and predictable from the session latent — this is a natural consumer of the content-inferred session latent in Hierarchical (mixed-effects) foundation model via amortized VI — VAE-style arm of the hierarchical-Bayes comparison #57, and a good test case for it.
• Keep the arm-for-arm comparability of 02: hold GRU H, session conditioning, λ-forward schedule, lr, batch, held-out cohort, and snapshot pin identical so the new variant drops into the existing N×D grid.

Metric caveat (inherited from 02, must carry into any report)

3-way NL has a different chance baseline (uniform 1/3 vs 1/2) over a different trial support than the 2-way study. It is not comparable to 01's L/R numbers by subtraction. Score conditional L/R likelihood on the shared engaged trials and the ignore class separately.

Done when

• A trainable engagement-state variant exists and is evaluated on the same held-out cohort.
• A clear verdict on the recall ceiling: does an explicit latent state move recall off ~0.47, or is the ceiling intrinsic to the behavior (i.e. ignore trials are genuinely unpredictable beyond a certain point)? A negative result here is a real result — it would say disengagement is not predictable from behavior alone and needs an exogenous signal (video, photometry → Neural correlation with learned cognitive variables #30).

Related: #23 (closed, parent work) · #57 (session latent) · #30 (exogenous engagement signals) · parent #33