Bibliographic record
Abstract
AbstractWe study sequences of functions of the form F np → {0,1} for varying n, and define a notionof convergence based on the induced distributions from restricting the functions to a randomaffine subspace. Using a decomposition theorem and a recently proven equi-distribution theoremfrom higher order Fourier analysis, we prove that the limits of such convergent sequences canbe represented by certain measurable functions. We are also able to show that every suchlimit object arises as the limit of some sequence of functions. These results are in the spirit ofsimilar results which have been developed for limits of graph sequences. A more general, albeitsubstantially more sophisticated, limit object was recently constructed by Szegedy in [Sze10]. 1 Introduction In limit theories of discrete structures, one often studies a large object by studying its “localstatistics”. More precisely, there is a sampling rulethat allows one to sample a randomsubstructure,and this induces a probability measure on the set of possible small substructures. For example givena graph G and a positive integer k, one can select k random vertices in G and look at the subgraphinduced by G on these k vertices. This introduces a probability distribution on k-vertex graphs.Every such sampling rule leads to a notion of convergence. Namely a sequence of structures iscalled convergent if these probability distributions converge. So in the above example, a sequenceof graphs is called convergent [LS06] if for every k, the corresponding probability distributions onthe k-vertex graphs converges.Let p be a fixed prime, and denote F= F
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".