Bridging structural and statistical heterogeneity: a unified DFL framework via column-wise aggregation and consensus-aware topology

Decentralized Federated Learning (DFL) is an emerging paradigm that enables collaborative model training across distributed clients without relying on a central parameter server. However, deploying DFL in realistic edge environments faces two critical limitations: structural heterogeneity among local models due to varying computational capabilities of client nodes, and model divergence caused by statistical heterogeneity (non-IID data) within static or inefficient communication topologies. While prior works have tackled these challenges individually, a unified perspective on their synergistic optimization is still lacking. In this paper, we introduce ColADTM-DFL framework, which jointly addresses structural and statistical heterogeneity in a single system workflow. First, ColADTM-DFL enables each node to train a width-adaptive submodel while ensuring semantically aligned parameter fusion. Then, considering the model divergence exacerbated by statistical heterogeneity, our framework defines Consensus Distance to quantify inter-node model discrepancy. Leveraging this metric, we present a consensus-aware topology algorithm, which dynamically restructures the communication graph to minimize global divergence while reducing redundant communication cost. Extensive experiments across heterogeneous edge settings demonstrate that our method significantly accelerates time-to-target accuracy, as well as reduces communication cost by up to 46.3% under the same resource budget compared to baselines.