Subspace Optimization for Efficient Federated Learning under Heterogeneous Data

Federated learning increasingly operates in a large-model regime where communication, memory, and computation are all scarce. Typically, non-IID client data induce drift that degrades the stability and performance of local training. Existing remedies such as SCAFFOLD introduce heterogeneity-correction mechanisms to address this challenge, but they incur substantial extra communication and memory overhead. This paper proposes a subspace optimization method for federated learning (SSF), which performs heterogeneity-corrected optimization in a low-dimensional subspace using only projected quantities, while preserving full-dimensional control information through a backfill-style update that retains residual components whenever the active subspace changes. Under standard smoothness and bounded-variance assumptions, SSF attains a non-asymptotic rate of order $\widetilde{\mathcal{O}}(1/T+1/\sqrt{NKT})$. Experiments show favorable accuracy--efficiency trade-offs under heterogeneous data.

FedSLoP: Memory-Efficient Federated Learning with Low-Rank Gradient Projection

Federated learning enables a population of clients to collaboratively train machine learning models without exchanging their raw data, but standard algorithms such as FedAvg suffer from slow convergence and high communication and memory costs in heterogeneous, resource-constrained environments. We introduce FedSLoP, a federated optimization algorithm that combines stochastic low-rank subspace projections of gradients, thereby reducing the dimension of communicated and stored updates while preserving optimization progress. On the theoretical side, we develop a detailed nonconvex convergence analysis under standard smoothness and bounded-variance assumptions, showing that FedSLoP is guaranteed to converge to a first-order stationary point at a rate of $O(1/\sqrt{NT})$. On the empirical side, we conduct extensive experiments on federated MNIST classification with heterogeneous data partitions, showing that FedSLoP substantially reduces communication volume and client-side memory while achieving competitive or better accuracy compared with FedAvg and representative sparse or low-rank baselines. Together, our results demonstrate that random subspace momentum methods such as FedSLoP provide a principled and effective approach to communication- and memory-efficient federated learning. Codes are available at: https://github.com/pkumelon/FedSLoP.git.

Moaw: Unleashing Motion Awareness for Video Diffusion Models

Video diffusion models, trained on large-scale datasets, naturally capture correspondences of shared features across frames. Recent works have exploited this property for tasks such as optical flow prediction and tracking in a zero-shot setting. Motivated by these findings, we investigate whether supervised training can more fully harness the tracking capability of video diffusion models. To this end, we propose Moaw, a framework that unleashes motion awareness for video diffusion models and leverages it to facilitate motion transfer. Specifically, we train a diffusion model for motion perception, shifting its modality from image-to-video generation to video-to-dense-tracking. We then construct a motion-labeled dataset to identify features that encode the strongest motion information, and inject them into a structurally identical video generation model. Owing to the homogeneity between the two networks, these features can be naturally adapted in a zero-shot manner, enabling motion transfer without additional adapters. Our work provides a new paradigm for bridging generative modeling and motion understanding, paving the way for more unified and controllable video learning frameworks.