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

Fine-tuning large language models (LLMs) on domain-specific data is essential for downstream adaptation. In many deployments, a participant cannot hold the complete model locally. This happens because the model owner keeps the full model proprietary, or because the participant lacks sufficient compute resources. Split Learning (SL) addresses this by partitioning the model between the participant and a server so that only a small portion runs locally. When the underlying data is additionally distributed across multiple institutions with privacy requirements, Federated Learning (FL) further enables collaborative training across participants by sharing only model updates instead of raw data. In this combined setting, each client transmits intermediate activations to the server, and for LLM fine-tuning, this exchange poses an inherent privacy paradox. The autoregressive nature of LLMs causes the transmitted activations to leak the input, and existing perturbation-based defenses are fundamentally ineffective in this setting. We address this leakage through a learned obfuscate-and-recover scheme that protects participants' private datasets while still allowing an independently deployable model to be trained on the server side. Experiments demonstrate that our approach achieves strong privacy protection with modest utility loss and system overhead, making split-based federated LLM fine-tuning practically viable.

Fine-tuning large language models (LLMs) has become a central application of modern optimization, enabling pretrained models to adapt to diverse downstream tasks and domain-specific data. A major obstacle in large-scale fine-tuning is the memory overhead of backpropagation, which requires storing activations, gradients, and optimizer states. Zeroth-order (ZO) optimization offers a memory-efficient alternative, but its performance is highly sensitive to the stepsize and smoothing parameter, often requiring costly task-specific tuning. Parameter-free (PF) optimization addresses this issue by adapting algorithmic parameters without prior knowledge of problem-dependent constants. Moreover, large-scale fine-tuning can benefit from geometry-aware updates that account for the heterogeneous structure of parameter blocks, which can be modeled through methods that exploit linear minimization oracle (LMO). In this work, we study PF adaptation for LMO-based ZO optimization and introduce $\texttt{AdaNAGED}$, a method that unifies gradient-free training, adaptive tuning, and non-Euclidean update geometry. We establish convergence guarantees and validate the method on large-scale LLM fine-tuning task with $\texttt{OPT}-1.3\mathrm{B}$ model.

Low-rank adaptation (LoRA) has emerged as a powerful tool for parameter-efficient fine-tuning of large language models (LLMs). This paper studies LoRA under a federated learning setting, enabling collaborative fine-tuning across clients while preserving parameter efficiency. We focus on a highly heterogeneous regime in which clients share only partial structure and a substantial subset may be contaminated. We propose Collaborative Low-rank Alignment and Identifiable Recovery (CLAIR), a contamination-aware framework that relies only on preliminary local estimators. Its formulation applies broadly, from linear regression to neural network and LLM modules, whenever local adaptation can be represented by matrix-valued updates. CLAIR recovers the shared LoRA subspace and detects contaminated clients via a structured low-rank plus block-sparse decomposition. We prove exact recovery of the shared LoRA subspace in the noiseless case, stable recovery under preliminary estimation error, and consistent collaborative-set recovery under mild separation conditions. We further quantify the gain from CLAIR refinement: it reduces off-subspace estimation error through cross-client averaging while preserving client-specific variation within the shared LoRA subspace, thus improves over local fine-tuning whenever this oracle gain outweighs the costs of subspace estimation and benign-client heterogeneity. Empirically, we demonstrate the benefits of CLAIR by fine-tuning a Transformer architecture on a text-copying task. The results show accurate contamination detection and improved benign-client performance compared with local fine-tuning and non-robust federated averaging.