Teaching Dimensions based on Cooperative Learning.
Bibliographic record
Abstract
The problem of how a teacher and a learner can cooperate in the process of learning concepts from examples in order to minimize the required sample size without “coding tricks ” has been widely addressed, yet without achieving teaching and learning protocols that meet what seems intuitively an optimal choice for selecting samples in teaching. We introduce the model of subset teaching sets, based on the idea that both teacher and learner can exploit the assumption that the partner is cooperative. We show how this can reduce the sample size drastically without using coding tricks. For instance, monomials can be taught with only two examples independent of the number of variables. The corresponding variant of the teaching dimension (STD) turns out to be nonmonotonic with respect to subclasses of concept classes. We discuss why this nonmonotonicity might be inherent in optimal cooperative teaching scenarios. Nevertheless, trying to overcome nonmonotonicity, we introduce a second variant, the recursive teaching dimension (RTD), which is monotonic and yields the same positive results for some concept classes, such as the class of all monomials, yet can be arbitrarily worse than the STD.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".