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 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 | 0.000 |
| 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) | 0.000 | 0.000 |
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 teacher head, 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".