Bibliographic record
Abstract
In this paper, we consider a new definition of typicality based on the weak* topology that is applicable to Polish alphabets (which includes ℝ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ). This notion is a generalization of strong typicality in the sense that it degenerates to strong typicality in the finite alphabet case, and can also be applied to mixed and continuous distributions. Furthermore, it is strong enough to prove a Markov lemma, and thus can be used to directly prove a more general class of results than entropy (or weak) typicality. We provide two example applications of this technique. First, using the Markov Lemma, we directly prove a coding result for Gel'fand-Pinsker channels with an average input constraint for a large class of alphabets and channels without first proving a finite alphabet result and then resorting to delicate quantization arguments. This class of alphabets includes, for example, real and complex inputs subject to a peak amplitude restriction. While this large class does not directly allow for Gaussian distributions with average power constraints, it is shown to be straightforward to recover this case by considering a sequence of truncated Gaussian distributions. As a second example, we consider a problem of coordinated actions (i.e., empirical distributions) for a two node network, where we derive necessary and sufficient conditions for a given desired coordination.
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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 | 0.000 |
| 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) | 0.000 | 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".