Learning Matrix Functions over Rings (Extended Abstract)
Bibliographic record
Abstract
) Nader H. Bshouty 1 and Christino Tamon ?2 and David K. Wilson 1 1 Dept. Computer Science, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4 Canada 2 Dept. Mathematics and Computer Science, Clarkson University, P.O. Box 5815, Potsdam, NY 13699-5815, U.S.A. Abstract. Let R be a commutative Artinian ring with identity and let X be a finite subset of R. We present an exact learning algorithm with a polynomial query complexity for the class of functions representable as f(x) = n Y i=1 A i (x i ) where for each 1 i n, A i is a matrix-valued mapping A i : X ! R m i \\Thetam i+1 and m1 = mn+1 = 1. These functions are referred to as matrix functions. Our algorithm uses a decision tree based hypothesis class called decision programs that takes advantage of linear dependencies. We also show that the class of matrix functions is equivalent to the class of decision programs. Our learning algorithm implies the following results. 1. Multivariate p...
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".