The current paradigm of training large language models (LLMs) on publicly available Web data is becoming unsustainable, with high-quality data sources in specialized domains nearing exhaustion. Federated Learning (FL) emerges as a practical solution for the next generation of AI on a decentralized Web, enabling privacy-preserving collaborative fine-tuning by leveraging private data distributed across a global client base. While Low-Rank Adaptation (LoRA) is the standard for efficient fine-tuning, its application in federated settings presents a critical challenge: communication overhead remains a significant bottleneck across the Web's heterogeneous network conditions. The structural redundancy within LoRA parameters not only incurs a heavy communication burden but also introduces conflicts when aggregating client updates. To address this, we propose FedSRD, a Sparsify-Reconstruct-Decompose framework designed for communication-efficient FL. We first introduce an importance-aware sparsification method that preserves the structural integrity of LoRA updates to reduce the uploaded parameter count. The server then reconstructs and aggregates these updates in a full-rank space to mitigate conflicts. Finally, it decomposes the global update into a sparse low-rank format for broadcast, ensuring a symmetrically efficient cycle. We also propose an efficient variant, FedSRD-e, to reduce computational overhead. Experimental results on 10 benchmarks demonstrate that our framework significantly reduces communication costs by up to 90\% while even improving model performance on heterogeneous client data.

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