Multiscale Gossip for Efficient Decentralized Averaging in Wireless Packet Networks
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Bibliographic record
Abstract
This paper describes and analyzes a hierarchical gossip algorithm for solving the distributed average consensus problem in wireless sensor networks. The network is recursively partitioned into subnetworks. Initially, nodes at the finest scale gossip to compute local averages. Then, using geographic routing to enable gossip between nodes that are not directly connected, these local averages are progressively fused up the hierarchy until the global average is computed. We show that the proposed hierarchical scheme with $k$ levels of hierarchy is competitive with state-of-the-art randomized gossip algorithms, in terms of message complexity, achieving $ε$-accuracy with high probability after $O\big(n \log \log n \log \frac{kn}ε \big)$ messages. Key to our analysis is the way in which the network is recursively partitioned. We find that the optimal scaling law is achieved when subnetworks at scale $j$ contain $O(n^{(2/3)^j})$ nodes; then the message complexity at any individual scale is $O(n \log \frac{kn}ε)$, and the total number of scales in the hierarchy grows slowly, as $Θ(\log \log n)$. Another important consequence of hierarchical construction is that the longest distance over which messages are exchanged is $O(n^{1/3})$ hops (at the highest scale), and most messages (at lower scales) travel shorter distances. In networks that use link-level acknowledgements, this results in less congestion and resource usage by reducing message retransmissions. Simulations illustrate that the proposed scheme is more message-efficient than existing state-of-the-art randomized gossip algorithms based on averaging along paths.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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