Efficiently reaching consensus on the largest entries of a vector
Bibliographic record
Abstract
We consider a problem where agents gossip on a d-dimensional state vector. The goal is to achieve a consensus on the average. However, instead of computing the average of the entire d-dimensional state, the goal is to have all agents reach a consensus on the largest k entries of the average initial state vector. For example, the value in each entry could correspond to the agents' opinions about a different item, in which case the goal is to determine which are the k most popular items, on average. A primary challenge is that the indices of the k largest entries are not known a priori, and so the agents must adaptively identify which entries are the largest while also computing their values. We consider an asynchronous gossip-style algorithm where pairs of agents interact, communicate, and update only those state entries which either agent currently believes to be one of the largest k. We show that, as long as the underlying communication graph is connected, the algorithm converges to a state where all agents reach a consensus on the indices and values of the largest k entries of the initial average. We study, via numerical simulation, the convergence rate of the algorithm in terms of the total number of scalar values transmitted to reach a desired level of accuracy.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".