On learning discretized geometric concepts
Why this work is in the frame
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Bibliographic record
Abstract
We present a polynomial time online learning algorithm that learns any discretized geometric concept generated from any number of halfspaces with any number of known (to the learner) slopes in a constant dimensional space. In particular, our algorithm learns (from equivalence queries only) unions of discretized axis-parallel rectangles in a constant dimensional space in polynomial time. The algorithm also runs in polynomial time in l if the teacher lies on l counterexamples. We then show a PAC-learning algorithm for the above discretized geometric concept when the example oracle lies on the labels of the examples with a fixed probability p/spl les/ 1/2 -1/r that runs in polynomial time also with r. We use these methods, as well as a bounded version of the finite injury priority method, to construct algorithms for learning several classes of rectangles. In particular we design efficient algorithms for learning several classes of unions of discretized axis-parallel rectangles in either arbitrary dimensional spaces or constant dimensional spaces.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it