Heterogeneous Decision Diagrams for Applications in Harmonic Analysis on Finite Non-Abelian Groups
Bibliographic record
Abstract
Spectral techniques on Abelian groups are a well-established tool in diverse fields such as signal processing, switching theory, multi-valued logic and logic design. The harmonic analysis on finite non-Abelian groups is an extension of them, which has also found applications for particular tasks in the same fields. It takes advantages of the peculiar features of the domain groups and their dual objects. Representing unitary irreducible representations, that are kernels of Fourier transforms on non-Abelian groups, in a compact manner is a key task in this area. These representations are usually specified in terms of rectangular matrices with matrix entries. Therefore, the problem of their efficient representations can be viewed as handling large rectangular matrices with matrix-valued entries. Quantum Multiple-valued Decision Diagrams (QMDDs) and Heterogeneous Decision Diagrams (HDDs) have been used for representation of matrices with numerical values, under some restrictions to the order of matrices to be represented. In this paper, we present a generalization of this concept for the representation of rectangular matrices with matrix-valued entries. We also demonstrate an implementation of an XML-based software package aimed at handling such data structures.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".