A Relative Fractal Dimension Spectrum as a Complexity Measure
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Bibliographic record
Abstract
This paper presents a derivation of a new relative fractal dimension spectrum, D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rq</sub> to measure the dissimilarity between two finite probability distributions originating from various signals. This measure is an extension of the Kullback-Leibler (KL) distance and the Renyi fractal dimension spectrum, D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> . Like the KL distance, D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rq</sub> determines the dissimilarity between two probability distributions X and Y of the same size, but does it at different scales, while the scalar KL distance is a single-scale measure. Like the Renyi fractal dimension spectrum, the D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rq</sub> is also a bounded vectorial measure obtained at different scales and for different moment orders, q. However, unlike the D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q'</sub> , all the elements of the new D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rq</sub> become zero when X and Y are the same. Experimental results show that this objective measure is consistent with the subjective mean-opinion-score (MOS) when evaluating the perceptual quality of images reconstructed after their compression. Thus, it could also be used in other areas of cognitive informatics
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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 | 0.000 | 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 it