Rethinking Factor Sharing in Federated LoRA: A Rank-Aware Adaptive Approach

Low-rank adaptation (LoRA) represents large language model (LLM) updates with two compact matrix factors, i.e., $A$ and $B$, providing an efficient way to fine-tune large models in federated learning paradigm. Inspired by the asymmetric roles of the LoRA factors, we study whether $A$ should be shared across clients while $B$ remains client-specific (Share-A/Local-B), or whether $B$ should instead be shared while $A$ remains client-specific (Share-B/Local-A). With a least-squares surrogate, we reveal that Share-A/Local-B requires the client-specific LoRA update matrices to use a common rank-$r$ input-side space, whereas Share-B/Local-A requires a common rank-$r$ output-side space. The two strategies therefore incur different projection residuals, indicating that the preferred strategy is the one with the smaller aggregate residual across clients. With this insight, we propose Federated Adaptive Factor Sharing Low-Rank Adaptation (FedAS-LoRA), which selects the sharing side before training to enhance fine-tuning performance. To enable adaptive factor selection before training, we design a Rank-Aware Shared-Subspace Sufficiency (RSS) metric, which effectively assesses whether a shared rank-$r$ input subspace is sufficient for the local data distributions using representations extracted from a frozen LLM backbone. Experiments across different tasks, data distributions, LoRA ranks, and participation settings confirm the effectiveness of RSS and the superior performance of FedAS-LoRA.

SoftSignSGD(S3): An Enhanced Optimizer for Practical DNN Training and Loss Spikes Minimization Beyond Adam

Adam has proven remarkable successful in training deep neural networks, but the mechanisms underlying its empirical successes and limitations remain underexplored. In this study, we demonstrate that the effectiveness of Adam stems largely from its similarity to SignSGD in robustly handling large gradient fluctuations, yet it is also vulnerable to destabilizing loss spikes due to its uncontrolled update scaling. To enhance the advantage of Adam and mitigate its limitation, we propose SignSoftSGD (S3), a novel optimizer with three key innovations. \emph{First}, S3 generalizes the sign-like update by employing a flexible $p$-th order momentum ($p \geq 1$) in the denominator, departing from the conventional second-order momentum (variance) preconditioning. This design enables enhanced performance while achieving stable training even with aggressive learning rates. \emph{Second}, S3 minimizes the occurrences of loss spikes through unified exponential moving average coefficients for numerator and denominator momenta, which inherently bound updates to $[-1, 1]$ and simplify hyperparameter tuning. \emph{Third}, S3 incorporates an equivalent Nesterov's accelerated gradient(NAG) module, accelerating convergence without memory overhead. Theoretically, we prove that S3 achieves the optimal convergence rate of $O\left(\frac{1}{T^{\sfrac{1}{4}}}\right)$ for general nonconvex stochastic optimization under weak assumptions. Extensive experiments across a range of vision and language tasks show that \textsf{\small S3} not only converges more rapidly and improves performance but also rarely experiences loss spikes, even with a \textbf{$\bm{10 \times}$} larger learning rate. In fact, S3 delivers performance comparable to or better than AdamW with \textbf{$2 \times$} the training steps, establishing its efficacy in both efficiency and final task performance.

Practical Privacy-Preserving Gaussian Process Regression via Secret Sharing

Gaussian process regression (GPR) is a non-parametric model that has been used in many real-world applications that involve sensitive personal data (e.g., healthcare, finance, etc.) from multiple data owners. To fully and securely exploit the value of different data sources, this paper proposes a privacy-preserving GPR method based on secret sharing (SS), a secure multi-party computation (SMPC) technique. In contrast to existing studies that protect the data privacy of GPR via homomorphic encryption, differential privacy, or federated learning, our proposed method is more practical and can be used to preserve the data privacy of both the model inputs and outputs for various data-sharing scenarios (e.g., horizontally/vertically-partitioned data). However, it is non-trivial to directly apply SS on the conventional GPR algorithm, as it includes some operations whose accuracy and/or efficiency have not been well-enhanced in the current SMPC protocol. To address this issue, we derive a new SS-based exponentiation operation through the idea of 'confusion-correction' and construct an SS-based matrix inversion algorithm based on Cholesky decomposition. More importantly, we theoretically analyze the communication cost and the security of the proposed SS-based operations. Empirical results show that our proposed method can achieve reasonable accuracy and efficiency under the premise of preserving data privacy.