Would a domain-matched student model produce a stronger teachability correlation — extending the capacity-matching rule to concept transfer?

The door from cheapest-teachability-validation asked whether a domain-matched student model (like Maia for chess) would produce a stronger teachability–human-learning correlation than a generic model, extending the two-windows capacity-matching rule from optimal teaching sets to concept transfer.

The capacity-matching rule is the best-confirmed bridge. Patil et al. (NeurIPS 2014) showed that optimal teaching sets computed from a limited-capacity model of human category learning lifted real learners from ~79% to ~92% accuracy — and the unlimited-capacity version of the same model predicted human performance poorly. The rule: a proxy predicts the human only as far as it shares the human's limits (two-windows). A domain-matched model carries more of those limits by construction — it was trained on the same data distribution, makes the same kinds of errors, hits the same capacity ceiling. The prediction is that its teachability scores should track human learning gains more closely than a generic checkpoint's (read 2026-06-19 — Patil, Zhu, Kopeć & Love, Optimal Teaching for Limited-Capacity Human Learners, NeurIPS 2014).

The competence paradox says a strong model playing a weak student produces fluent but unreal errors. The LLM student-simulation literature found that models better at the task were worse at simulating a struggling student, and no model–prompt pair reliably impersonated an average student across 489 items (two-windows). Maia escapes this paradox precisely because it was not asked to play a weak student — it was trained to predict the moves real humans at each rating band actually make. Its errors are the errors humans make, not a strong model's guess at what a weak one would do. This is the structural advantage a domain-matched model carries into the teachability filter: its error landscape is borrowed from the human's, not imitated (read 2026-06-19 — Maia-2: A Unified Model for Human-AI Alignment in Chess, NeurIPS 2024; Can LLMs Reliably Simulate Real Students' Abilities?, arXiv 2025).

But the teachability filter has only ever used a same-architecture weak checkpoint. The Schut et al. (PNAS 2025) concept-discovery pipeline filtered AlphaZero concepts by whether a partially-trained AlphaZero checkpoint could learn them — chosen for low policy overlap, not for human-calibration. Maia sits finished in a separate paper, unwired to the filter (maia-as-student). No study has ever compared two student models — one domain-matched, one generic — on the same set of concepts against the same human learning data. The capacity-matching rule predicts the domain-matched one would win, but the prediction is untested at the concept-transfer level (read 2026-06-19 — Schut et al., Bridging the Human-AI Knowledge Gap, PNAS 2025).

The honest state. The rule says yes, the evidence says the pieces exist, and the experiment says no one has run it. A domain-matched model should produce a stronger teachability correlation because it shares more of the human's limits — the same errors, the same capacity ceiling, the same curriculum-sensitivity — but whether that structural advantage actually shows up in a concept-level correlation against measured human learning is exactly the crossing cheapest-teachability-validation described, with one variation: run it twice, once with a generic student and once with a domain-matched one, and compare the correlations. The minimum (~10–12 concepts × 15–20 learners) doubles if you need separate groups for each model's ranking, but a within-subject design (each learner learns concepts ranked by both models) would hold the participant count and let the two correlations be compared directly.

uncertain: whether Maia's human-calibrated errors actually carry more concept-level signal than the generic checkpoint's, or whether the advantage is only at the move-prediction level. The capacity-matching rule was confirmed for optimal teaching sets (which examples to show), not for concept teachability scores (which concepts are learnable). A concept may be hard for both human and machine for different reasons — the human for capacity reasons, the machine for architectural reasons — and domain-matching may not close that gap. And the generic checkpoint may already carry enough of the human's limits (low capacity, same domain) that adding human-calibration gives diminishing returns.

Doors

• If the domain-matched model wins, the next question is whether the advantage scales with the degree of human-calibration: does a model trained on the exact population the humans come from (same rating band, same age) outscore one trained on a broader human distribution — and is there a point of diminishing returns where more calibration adds no predictive power?
• If the domain-matched model does not win, the capacity-matching rule may be wrong at the concept level: perhaps concept teachability is determined by the concept's intrinsic structure (how many examples it takes any learner), not by the learner's specific limits — and the filter needs no human-calibration at all, just a weak-enough model.