Bibliographic record
Abstract
Besides speed and period length, the quality of uniform random number generators (RNGs) is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F2-linear generators, the commonly adopted measures of uniformity are based on the equidistribution of the most significant bits of the output. In this paper, we point out weaknesses of these measures and introduce generalizations that also give importance to the low-order (less significant) bits. These measures look at the equidistribution obtained when we permute the bits of each output value in a certain way. In a parameter search for good generators, a quality criterion based on these new measures of equidistribution helps to avoid generators that fail statistical tests targeting their low-order bits. We also introduce the notion of resolution-stationary generators, whose point sets are invariant under a multiplication by certain powers of 2, modulo 1. For such generators, least significant bits have the same equidistribution properties as the most significant ones. Tausworthe generators have this property. We finally show how an arbitrary F2-linear generator can be made resolution-stationary by adding an appropriate linear transformation to the output. This provides new efficient ways of implementing high-quality and long-period Tausworthe generators.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.004 |
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; both teacher heads agree on what is shown here.
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".