Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks
Bibliographic record
Abstract
Abstract A system of interacting multi-class finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-color nodes. The interactions are local and described through local empirical measures. Two levels of heterogeneity are considered: between and within the blocks where the nodes are labeled into two types. The central nodes are those connected only to nodes from the same block, whereas the peripheral nodes are connected to both nodes from the same block and nodes from other blocks. Limits of such systems as the number of nodes tends to infinity are investigated. In particular, under specific regularity conditions, propagation of chaos and the law of large numbers are established in a multi-population setting. Moreover, it is shown that, as the number of nodes goes to infinity, the behavior of the system can be represented by the solution of a McKean–Vlasov system. Then, we prove large deviations principles for the vectors of empirical measures and the empirical processes, which extends the classical results of Dawson and Gärtner ( Stochastics 20 , 1987) and Léonard ( Ann. Inst. H. Poincaré Prob. Statist. 31 , 1995).
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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 | 0.000 | 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 | 0.000 |
| 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 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".