DECA: Decentralizing Block-Wise Adam for Efficient LLM Full-Parameter Fine-Tuning on Non-IID Data

Fine-tuning large language models (LLMs) in privacy-sensitive and resource-constrained environments remains challenging. Since training data are often distributed across multiple clients, decentralized fine-tuning offers a natural paradigm for collaborative adaptation without a central server. However, enabling full-parameter fine-tuning (FPFT) in this decentralized setting is difficult: FPFT provides strong adaptation capacity but incurs prohibitive resource consumption for billion-scale models. Existing decentralized LLM fine-tuning methods therefore mainly rely on parameter-efficient updates, which improve efficiency but may restrict downstream performance. Moreover, client data are typically non-IID, making decentralized optimization more vulnerable to client drift and unstable convergence. To address these challenges, we propose DECA, a resource-efficient decentralized FPFT framework for LLMs on non-IID data. DECA partitions model parameters into disjoint blocks and performs sequential block-wise Adam optimization, reducing resource consumption while preserving decentralized full-parameter adaptation. To stabilize training, DECA further introduces first- and second-order block-wise moment estimates with fresh local gradient statistics and consensus-derived discrepancy signals. We provide rigorous theoretical analysis and extensive experiments, showing that DECA achieves fast convergence, strong downstream performance, and significant resource efficiency.