Abstract
To cope with the challenges posed by high-concurrency training tasks involving large models and big data, Directed Acyclic Graph (DAG) and shard were proposed as alternatives to blockchain-based federated learning, aiming to enhance training concurrency. However, there is insufficient research on the specific consensus designs and the effects of varying shard sizes on federated learning. In this paper, we combine DAG and shard by designing three tip selection consensus algorithms and propose an adaptive algorithm to improve training performance. Additionally, we achieve concurrent control over the scale of the directed acyclic graph's structure through shard and algorithm adjustments. Finally, we validate the fairness of our model with an incentive mechanism and its robustness under different real-world conditions and demonstrate DAG-Shard-based Federated Learning (DSFL)'s advantages in high concurrency and fairness while adjusting the DAG size through concurrency control. In concurrency, DSFL improves accuracy by 8.19-12.21% and F1 score by 7.27-11.73% compared to DAG-FL. Compared to Blockchain-FL, DSFL shows an accuracy gain of 7.82-11.86% and an F1 score improvement of 8.89-13.27%. Additionally, DSFL outperforms DAG-FL and Chains-FL on both balanced and imbalanced datasets.