On Invoking Transitivity to Enhance the <italic>Pursuit</italic>-Oriented Object Migration Automata
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Bibliographic record
Abstract
From the earliest studies in graph theory, the phenomenon of transitivity has been used to design and analyze problems that can be mapped onto graphs. Some of the practical examples of this phenomenon are the “Transitive Closure”algorithm, the multiplication of Boolean matrices, the determination of communicating states in Markov chains, and so on. The use of transitivity, however, to catalyze the partitioning problems is, to our knowledge, unreported, and it is by no means trivial considering the pairwise occurrences of the queries in the query stream. This paper pioneers such a mechanism. In particular, we consider the object migrating automaton (OMA) that has been used for decades to solve the Equi-Partitioning Problem where W objects are placed in R partitions of equal sizes so that objects accessed together fall in to the same partition. The OMA, which encountered certain deadlock configurations, was enhanced by Gale et al. to yield the enhanced OMA (EOMA). Both the OMA and the EOMA were significantly improved by incorporating into them, the recently-introduced “Pursuit”phenomenon from the field of learning automata (LA). In this paper <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> , we shall show that the Pursuit matrix that consists of the estimates of the probabilities of the pairs presented to the LA, possesses the property of transitivity akin to the property found in graph-related problems. By making use of this observation, transitive-closure-like arguments can be made to invoke reward and penalty operations on the Pursuit OMA and the PEOMA. This implies that objects can be moved toward their correct partitions even when the system is dormant, i.e., when the environment does not present any queries or partitioning information to the learning algorithm. The results that we present demonstrate that the newly designed transitive-based algorithms are about 20% faster than their non-transitive versions. As far as we know, these are the fastest partitioning algorithms to-date.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 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 it