Federated learning (FL) is now recognized as a key framework for communicationefficient collaborative learning. Most theoretical and empirical studies, however, rely on the assumption that clients have access to pre-collected data sets, with limited investigation into scenarios where clients continuously collect data. In many real-world applications, particularly when data is generated by physical or biological processes, client data streams are often modeled by non-stationary Markov processes.

Dynamic functional brain networks (DFBNs) are powerful tools in neuroscience research. Recent studies reveal that DFBNs contain heterogeneous neural nodes with more extensive connections and more drastic temporal changes, which play pivotal roles in coordinating the reorganization of the brain. Moreover, the spatiotemporal patterns of these nodes are modulated by the brain's historical states. However, existing methods not only ignore the spatio-temporal heterogeneity of neural nodes, but also fail to effectively encode the temporal propagation mechanism of heterogeneous activities. These limitations hinder the deep exploration of spatio-temporal relationships within DFBNs, preventing the capture of abnormal neural heterogeneity caused by brain diseases.

Fine-tuning large language models (LLMs) poses significant computational burdens, especially in federated learning (FL) settings. We introduce Layer-wise Efficient Federated Fine-tuning (LEFF), a novel method designed to enhance the efficiency of FL fine-tuning while preserving model performance and minimizing client-side computational overhead. LEFF strategically selects layers for finetuning based on client computational capacity, thereby mitigating the straggler effect prevalent in heterogeneous environments. Furthermore, LEFF incorporates an importance-driven layer sampling mechanism, prioritizing layers with greater influence on model performance. Theoretical analysis demonstrates that LEFF achieves a convergence rate of O(1/ T). Extensive experiments on diverse datasets demonstrate that LEFF attains superior computational efficiency and model performance compared to existing federated fine-tuning methods, particularly under heterogeneous conditions.

Federated Multi-Task Learning (FL-MTL) enables clients with heterogeneous data to collaboratively train models capable of handling multiple downstream tasks. However, FL-MTL faces key challenges, including statistical heterogeneity, task interference, and the need to balance local learning with global knowledge sharing. Traditional methods like FedAvg struggle in such settings due to the lack of explicit mechanisms to address these issues. In this paper, we propose FedRAM, a threestep framework that progressively updates two scalar hyperparameters: the task importance weight and the client aggregation coefficient. FedRAM introduces a reference-proxy-agent strategy, where the proxy model serves as an intermediate between the local reference model and the global agent model. This design reduces the need for repeated local training while preserving local performance. Extensive experiments on six real-world FL-MTL benchmarks show that FedRAM improves performance by at least 3% over the most baseline on both in-domain and outof-domain tasks, while reducing computational cost by 15 . These results make FedRAM a robust and practical solution for large-scale FL-MTL applications. The code is available at https://github.com/wwffvv/FedRAM.

Personalized federated learning addresses data heterogeneity across distributed agents but lacks uncertainty quantification that is both agent-specific and instancespecific, which is a critical requirement for risk-sensitive applications. We propose personalized federated conformal prediction (PFCP), a novel framework that combines personalized federated learning with conformal prediction to provide statistically valid agent-personalized prediction sets with instance-localization. By leveraging privacy-preserving knowledge transfer from other source agents, PFCP ensures marginal coverage guarantees for target agents while significantly improving conditional coverage performance on individual test instances, which has been validated by extensive experiments.

Federated Learning (FL) confronts a significant challenge known as data heterogeneity, which impairs model performance and convergence. Existing methods have made notable progress in addressing this issue. However, improving performance in certain heterogeneity scenarios remains an overlooked question: How robust are these methods to deploy under diverse heterogeneity scenarios? To answer this, we conduct comprehensive evaluations across varied heterogeneity scenarios, showing that most existing methods exhibit limited robustness. Meanwhile, insights from these experiments highlight that sharing statistical information can mitigate heterogeneity by enabling clients to update with a global perspective. Motivated by this, we propose FedGPS (Federated Goal-Path Synergy), a novel framework that seamlessly integrates statistical distribution and gradient information from others. Specifically, FedGPS statically modifies each client's learning objective to implicitly model the global data distribution using surrogate information, while dynamically adjusting local update directions with gradient information from other clients at each round. Extensive experiments show that FedGPS outperforms state-of-the-art methods across diverse heterogeneity scenarios, validating its effectiveness and robustness.

Heterogeneous Federated Learning (HtFL) enables collaborative learning across clients with diverse model architectures and non-IID data distributions, which are prevalent in real-world edge computing applications. Existing HtFL approaches typically employ proxy datasets to facilitate knowledge sharing or implement coarse-grained model-level knowledge transfer. However, such approaches not only elevate risks of user privacy leakage but also lead to the loss of fine-grained model-specific knowledge, ultimately creating barriers to effective knowledge sharing. To address these challenges, we propose FedFree, a novel proxy-datafree and model-free HtFL framework featuring two key innovations. First, FedFree introduces a reverse layer-wise knowledge transfer mechanism that aggregates heterogeneous client models into a global model solely using Gaussianbased pseudo-data, eliminating reliance on proxy datasets. Second, it leverages Knowledge Gain Entropy (KGE) to guide targeted layer-wise knowledge alignment, ensuring that each client receives the most relevant global updates tailored to its specific architecture. We provide rigorous theoretical convergence guarantees for FedFree and conduct extensive experiments on CIFAR-10 and CIFAR100. Results demonstrate that FedFree achieves substantial performance gains, with relative accuracy improving up to 46.3% over state-of-the-art baselines.

Federated learning (FL) is an effective and widely used approach to training deep learning models on decentralized datasets held by distinct clients. FL also strengthens both security and privacy protections for training data. Common challenges associated with statistical heterogeneity between distributed datasets have spurred significant interest in personalized FL (pFL) methods, where models combine aspects of global learning with local modeling specific to each client's unique characteristics. This work investigates the efficacy of theoretically supported, adaptive MMD measures in pFL, primarily focusing on the Ditto framework, a state-ofthe-art technique for distributed data heterogeneity. The use of such measures significantly improves model performance across a variety of tasks, especially those with pronounced feature heterogeneity. Additional experiments demonstrate that such measures are directly applicable to other pFL techniques and yield similar improvements across a number of datasets. Finally, the results motivate the use of constraints tailored to the various kinds of heterogeneity expected in FL systems.

Cryo-EM is a transformational paradigm in molecular biology where computa-1 tional methods are used to infer 3D molecular structure at atomic resolution from2 extremely noisy 2D electron microscope images. At the forefront of research is3 how to model the structure when the imaged particles exhibit non-rigid conforma-4 tional flexibility and compositional variation where parts are sometimes missing.5 We introduce a novel 3D reconstruction framework with a hierarchical Gaussian6 mixture model, inspired in part by Gaussian Splatting for 4D scene reconstruction.7 In particular, the structure of the model is grounded in an initial process that infers8 a part-based segmentation of the particle, providing essential inductive bias in9 order to handle both conformational and compositional variability. The framework,10 called CryoSPIRE, is shown to reveal biologically meaningful structures on com-11 plex experimental datasets, and establishes a new state-of-the-art on CryoBench, a12 benchmark for cryo-EM heterogeneity methods.

Federated Graph Learning (FGL) has been shown to be particularly effective in enabling collaborative training of Graph Neural Networks (GNNs) in decentralized settings. Model-heterogeneous FGL further enhances practical applicability by accommodating client preferences for diverse model architectures. However, existing model-heterogeneous approaches primarily target Euclidean data and fail to account for a crucial aspect of graph-structured data: topological relationships. To address this limitation, we propose TRUST, a novel knowledge distillation-based modelheterogeneous FGL framework. Specifically, we propose Progressive Curriculum Node Scheduler to progressively introduce challenging nodes based on learning difficulty. In Adaptive Curriculum Distillation Modulator, we propose an adaptive temperature modulator that dynamically adjusts knowledge distillation temperature to accommodate varying client capabilities and graph complexity. Moreover, we leverage Wasserstein-Driven Affinity Distillation to enable models to capture crossclass structural relationships through optimal transport. Extensive experiments on multiple graph benchmarks and model-heterogeneous settings show that TRUST outperforms existing methods, achieving an average 3.6% performance gain, particularly under moderate heterogeneity conditions.