A Spectral Algorithm for Ternary Function Classification
Bibliographic record
Abstract
The spectral representation and classification of 2-valued and multiple-valued functions has been previously studied and found to be useful in logic design and testing for conventional circuits. Spectral techniques also have potential application for reversible and quantum circuits. This paper addresses the classification of ternary functions into spectral translation equivalence classes. An efficient algorithm is presented that determines the spectral translations to map a given function to the representative function for the equivalence class containing the given function. Using this algorithm we show that the 2-variable ternary functions partition into 11 equivalence classes. While the number of spectral equivalence classes for ternary functions with 3 or more variables is very large, prohibiting full enumeration, we determine a lower bound of 167,275 classes for 3 variables. The algorithm can be used for a significant number of variables to quickly determine if two functions fall within the same equivalence class and, if they do, to find a sequence of spectral translations to map one to the other. Generalization of the approach to higher radix functions is briefly discussed.
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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".