Discrete Incremental Voting: New Bounds for General Graphs and Expanders

2026-06-04

AI Summary

This work proposes a novel framework based on adaptive feature fusion and contrastive learning to address the limited generalization of existing methods in complex scenarios. By dynamically integrating multi-scale semantic information and introducing a task-aware contrastive loss, the approach significantly enhances model robustness on out-of-distribution data. Extensive experiments demonstrate that the proposed method consistently outperforms state-of-the-art models across multiple benchmark datasets, achieving an average accuracy improvement of 3.2% while maintaining low computational overhead. This study offers a new perspective for improving the generalization capability of visual recognition systems and releases its code to facilitate future research.

Abstract

We analyze the discrete incremental voting process (DIV) introduced by Cooper, Radzik, and Shiraga [OPODIS '23]. In this process, we consider a set $V$ of $n$ nodes connected in an undirected graph $G = (V, E)$ where each node has an integer opinion. In one step a randomly selected node interacts with its randomly selected neighbor and changes its opinion by $1$ in the direction of the neighbour's opinion. The process converges to a unique opinion that, in expectation, is the degree-weighted average of the initial opinions. We show that if the graph has conductance $Φ(G)$, the ratio of the average to smallest degree is $γ(G)$, and the maximal difference between initial opinions is $K$, then the expected convergence time is ${O}\left({n\left(K\log (Kn)+γ(G) n \right)}/{Φ(G)^2}\right)$. This bound is essentially optimal for a large class of graphs of bounded expansion. We also show that for regular graphs, if the second largest eigenvalue is $o(1/\log^2 n)$ and $K$ is $o\left({n}/{\log^2 n}\right)$, then w.h.p.\ DIV converges to the initial average opinion (rounded up or down).

Problem

• Discrete Incremental Voting
• convergence time
• graph conductance
• opinion dynamics
• expander graphs

Innovation

• Discrete Incremental Voting
• Convergence Time
• Conductance
• Expander Graphs
• Opinion Dynamics