Rates of convergence for greedy gossip with eavesdropping
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Bibliographic record
Abstract
Greedy gossip with eavesdropping (GGE) is a randomized gossip algorithm that exploits the broadcast nature of wireless communications to converge rapidly on grid-like network topologies without requiring that nodes know their geographic locations. When a node decides to gossip, rather than choosing one of its neighbors randomly, it greedily chooses to gossip with the neighbor whose values are most different from its own. We assume that all transmissions are wireless broadcasts so that nodes can keep track of their neighbors' values by eavesdropping on their communications. We have previously proved that GGE converges to the average consensus on connected network topologies. In this paper we study the rate of convergence of GGE, a non-trivial task due to the greedy, data-driven nature of the algorithm. We demonstrate that GGE outperforms standard randomized gossip, and we characterize the rate of convergence in terms of a topology-dependent constant analogous to the second-largest eigenvalue characterization for previous randomized gossip algorithms. Simulations demonstrate that the convergence rate of GGE is superior to existing average consensus algorithms such as geographic gossip.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it