arXiv:2509.16902v1 Announce Type: cross Abstract: Federated learning (FL) enables distributed devices to collaboratively train machine learning models while maintaining data privacy. However, the heterogeneous hardware capabilities of devices often result in significant training delays, as straggler clients with limited resources prolong the aggregation process. Existing solutions such as client selection, asynchronous FL, and partial training partially address these challenges but encounter issues such as reduced accuracy, stale updates, and compromised model performance due to inconsistent training contributions. To overcome these limitations, we propose FedEL, a federated elastic learning framework that enhances training efficiency while maintaining model accuracy. FedEL introduces a novel window-based training process, sliding the window to locate the training part of the model and dynamically selecting important tensors for training within a coordinated runtime budget. This approach ensures progressive and balanced training across all clients, including stragglers. Additionally, FedEL employs a tensor importance adjustment module, harmonizing local and global tensor importance to mitigate biases caused by data heterogeneity. The experiment results show that FedEL achieves up to 3.87x improvement in time-to-accuracy compared to baselines while maintaining or exceeding final test accuracy.