Bibliographic record
Abstract
This paper considers a massive random access scenario in which a small set of k users out of a large number of n potential users are active at any given time, and a central base-station wishes to send a common message to the active users in order to label them into a finite number of categories. Specifically, given c possible categories, the base-station wishes to send label ℓ to a set of k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ℓ</inf> users, where ℓ ∈ {1, …, c} and $\sum\nolimits_{\ell = 1}^c {{k_\ell } = k} $. Assuming that n, k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , …, k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> are fixed, we ask: what is the minimum rate of the common message that the base-station needs to send so that the correct label is received at each of the k active users? This paper shows that instead of a conventional scheme of listing the indices of the users followed by their labels, which requires a common message rate of $k\left( {\log (n) + H\left( {\frac{{{k_1}}}{k}, \ldots ,\frac{{{k_c}}}{k}} \right)} \right)$ bits, it is possible to construct a fixed-length common message code with a rate of just $kH\left( {\frac{{{k_1}}}{k}, \ldots ,\frac{{{k_c}}}{k}} \right)$ bits plus a term that scales in n as O(log log(n)) for fixed k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , …, k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , where H(•) is the entropy of a probability distribution. If a variable-length code is permitted, the minimum common message rate is characterized as $kH\left( {\frac{{{k_1}}}{k}, \ldots ,\frac{{{k_c}}}{k}} \right) + O(1)$ bits, with no dependence on n. Finally, if k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , …, k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> deviate from the values for which the common message is designed, an additional cost per user equal to a Kullback-Leibler divergence term would be incurred.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".