Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the target distribution. Parallel Tempering (PT) serves as the gold standard, while recent diffusion-based approaches offer a continuous alternative at the cost of neural training. In this work, we introduce Conditional Diffusion Sampling (CDS), a framework that combines these two paradigms. To this end, we derive Conditional Interpolants, a class of stochastic processes whose transport dynamics are governed by an exact, closed-form stochastic differential equation (SDE), requiring no neural approximation. Although these dynamics require sampling from a non-trivial initialization distribution, we show both theoretically and empirically that the cost of this initialization diminishes for sufficiently short diffusion times. CDS leverages this by a two-stage procedure: (1) PT is used to efficiently sample the initial distribution, and then (2) samples are transported via the transport SDE. This combination couples the robust global exploration of PT with efficient local transport. Experiments suggest that CDS has the potential to achieve a superior trade-off between sample quality and density evaluation cost compared to state-of-the-art samplers.

In this paper, we study a large-scale multi-agent minimax optimization problem, which models many interesting applications in statistical learning and game theory, including Generative Adversarial Networks (GANs). The overall objective is a sum of agents' private local objective functions. We focus on the federated setting, where agents can perform local computation and communicate with a central server. Most existing federated minimax algorithms either require communication per iteration or lack performance guarantees with the exception of Local Stochastic Gradient Descent Ascent (SGDA), a multiple-local-update descent ascent algorithm which guarantees convergence under a diminishing stepsize. By analyzing Local SGDA under the ideal condition of no gradient noise, we show that generally it cannot guarantee exact convergence with constant stepsizes and thus suffers from slow rates of convergence. To tackle this issue, we propose FedGDA-GT, an improved Federated (Fed) Gradient Descent Ascent (GDA) method based on Gradient Tracking (GT).

Distributed stochastic gradient descent is an important subroutine in distributed learning. A setting of particular interest is when the clients are mobile devices, where two important concerns are communication efficiency and the privacy of the clients. Several recent works have focused on reducing the communication cost or introducing privacy guarantees, but none of the proposed communication efficient methods are known to be privacy preserving and none of the known privacy mechanisms are known to be communication efficient. To this end, we study algorithms that achieve both communication efficiency and differential privacy. For $d$ variables and $n \approx d$ clients, the proposed method uses $\cO(\log \log(nd))$ bits of communication per client per coordinate and ensures constant privacy. We also improve previous analysis of the \emph{Binomial mechanism} showing that it achieves nearly the same utility as the Gaussian mechanism, while requiring fewer representation bits, which can be of independent interest.

Personalized Federated Learning faces many challenges such as expensive communication costs, training-time adversarial attacks, and performance unfairness across devices. Recent developments witness a trade-off between a reference model and local models to achieve personalization. We follow the avenue and propose a personalized FL method towards the three goals. When it is time to communicate, our method projects local models into a shared-and-fixed low-dimensional random subspace and uses infimal convolution to control the deviation between the reference model and projected local models. We theoretically show our method converges for smooth objectives with square regularizers and the convergence dependence on the projection dimension is mild. We also illustrate the benefits of robustness and fairness on a class of linear problems. Finally, we conduct a large number of experiments to show the empirical superiority of our method over several state-of-the-art methods on the three aspects.

We present the design and results of the MICCAI Federated Tumor Segmentation (FeTS) Challenge 2024, which focuses on federated learning (FL) for glioma sub-region segmentation in multi-parametric MRI and evaluates new weight aggregation methods aimed at improving robustness and efficiency. Six participating teams were evaluated using a standardized FL setup and a multi-institutional dataset derived from the BraTS glioma benchmark, consisting of 1,251 training cases, 219 validation cases, and 570 hidden test cases with segmentations for enhancing tumor (ET), tumor core (TC), and whole tumor (WT). Teams were ranked using a cumulative scoring system that considered both segmentation performance, measured by Dice Similarity Coefficient (DSC) and the 95th percentile Hausdorff Distance (HD95), and communication efficiency assessed through the convergence score. A PID-controller-based method achieved the top overall ranking, obtaining mean DSC values of 0.733, 0.761, and 0.751 for ET, TC, and WT, respectively, with corresponding HD95 values of 33.922 mm, 33.623 mm, and 32.309 mm, while also demonstrating the highest communication efficiency with a convergence score of 0.764. These findings advance the state of federated learning for medical imaging, surpassing top-performing methods from previous challenge iterations and highlighting PID controllers as effective mechanisms for stabilizing and optimizing weight aggregation in FL. The challenge code is available at https://github.com/FeTS-AI/Challenge.

The convergence of next-generation wireless systems and distributed Machine Learning (ML) demands Federated Learning (FL) methods that remain efficient and robust with wireless connected peers and under network churn. Peer-to-peer (P2P) FL removes the bottleneck of a central coordinator, but existing approaches suffer from excessive communication complexity, limiting their scalability in practice. We introduce MAR-FL, a novel P2P FL system that leverages iterative group-based aggregation to substantially reduce communication overhead while retaining resilience to churn. MAR-FL achieves communication costs that scale as O(N log N), contrasting with the O(N^2) complexity of previously existing baselines, and thereby maintains effectiveness especially as the number of peers in an aggregation round grows. The system is robust towards unreliable FL clients and can integrate private computing.

Satellite constellations in low-Earth orbit are now widespread, enabling positioning, Earth imaging, and communications. In this paper we address the solution of learning problems using these satellite constellations. In particular, we focus on a federated approach, where satellites collect and locally process data, with the ground station aggregating local models. We focus on designing a novel, communication-efficient algorithm that still yields accurate trained models. To this end, we employ several mechanisms to reduce the number of communications with the ground station (local training) and their size (compression). We then propose an error feedback mechanism that enhances accuracy, which yields, as a byproduct, an algorithm-agnostic error feedback scheme that can be more broadly applied. We analyze the convergence of the resulting algorithm, and compare it with the state of the art through simulations in a realistic space scenario, showcasing superior performance.

Federated learning (FL) has been extensively studied as a privacy-preserving training paradigm. Recently, federated block coordinate descent scheme has become a popular option in training large-scale models, as it allows clients to train only a subset of the model locally instead of the entire model. However, in the era of large language models (LLMs), even a single block can contain a significant number of parameters, posing substantial communication latency, particularly for resource-constrained clients. To address this challenge in federated training/fine-tuning LLMs, we propose ParaBlock, a novel approach that establishes two parallel threads for communication and computation to enhance communication efficiency. We theoretically prove that the proposed ParaBlock achieves the same convergence rate as the standard federated block coordinate descent methods. Empirical evaluations on fine-tuning LLMs on general instruction following and mathematical reasoning confirm that ParaBlock not only maintains strong performance but also significantly improves communication efficiency.

Distributed stochastic gradient descent is an important subroutine in distributed learning. A setting of particular interest is when the clients are mobile devices, where two important concerns are communication efficiency and the privacy of the clients. Several recent works have focused on reducing the communication cost or introducing privacy guarantees, but none of the proposed communication efficient methods are known to be privacy preserving and none of the known privacy mechanisms are known to be communication efficient. To this end, we study algorithms that achieve both communication efficiency and differential privacy. For $d$ variables and $n \approx d$ clients, the proposed method uses $\cO(\log \log(nd))$ bits of communication per client per coordinate and ensures constant privacy. We also improve previous analysis of the \emph{Binomial mechanism} showing that it achieves nearly the same utility as the Gaussian mechanism, while requiring fewer representation bits, which can be of independent interest.