Daily Papers

Federated fine-tuning of foundation models with Low-Rank Adaptation (LoRA) provides an efficient solution for reducing communication and computation costs while preserving data locality. However, the direct combination of FedAvg and LoRA suffers from three key issues: limited update space, which restricts the model's effective learning capacity; inter-round state mismatch, which disrupts cross-round local optimization continuity; and a client-agnostic starting state, which slows local convergence on clients. Although recent methods mitigate the limited update space issue by merging LoRA updates into the backbone across communication rounds, inter-round state mismatch and the client-agnostic starting state remain insufficiently addressed. To address these issues, we propose FedSmoothLoRA, a federated LoRA tuning framework that preserves the enlarged update space, improves cross-round local optimization continuity, and provides a client-aware starting state for local training. At each communication round, FedSmoothLoRA constructs the local LoRA initialization using two matrices: a Round-Matching matrix that preserves cross-round local state continuity, and a Gradient-Aligned matrix that provides client-specific optimization guidance from gradient signals estimated on local data. Together, these designs enable smoother and faster convergence. Extensive experiments on image classification and natural language generation tasks demonstrate that FedSmoothLoRA consistently outperforms existing federated LoRA tuning methods. Code: https://github.com/wangzehao0704/FedSmoothLoRA

We study estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance σ^2, while the component means are estimated using a likelihood with variance τ^2, yielding a family of mismatched likelihood functions parameterized by the ratio ρ=τ/σ. We show that the interplay between ρ and the signal-to-noise ratio (SNR) induces a sharp phase diagram. Under correct specification (ρ=1), maximum likelihood recovers the true means, independently of the SNR. However, once the model is misspecified, two different regimes emerge. Under under-smoothing (ρ<1), the estimated Gaussian means are displaced from the truth, and in low SNR this discrepancy grows as the SNR decreases: for every fixed ρ<1, the squared error scales as SNR^{-1}. Under over-smoothing (ρ>1), the fitted likelihood blurs the cluster separation, causing distinct component means to collapse towards the overall mixture center once ρ^2 exceeds a threshold of the form 1 + λ,SNR, where λ depends on the geometry of the true means. We further show that the hard assignment objective arises as the limit τto 0 of the same mismatched likelihood family, and derive corresponding low- and high-SNR results for hard-assignment mean estimation and latent-label recovery. Furthermore, in low SNR, Bayes-optimal clustering is close to random guessing, and the hard-assignment target remains far from the true means. These results show that in low-SNR applications, even mild variance misspecification or hard-assignment procedures can induce substantial bias, whereas in high SNR these effects are largely absent.