This work tackles the fundamental challenges in Federated Learning (FL) posed by arbitrary client participation and data heterogeneity, prevalent characteristics in practical FL settings. It is well-established that popular FedAvg-style algorithms struggle with exact convergence and can suffer from slow convergence rates since a decaying learning rate is required to mitigate these scenarios. To address these issues, we introduce the concept of stochastic matrix and the corresponding timevarying graphs as a novel modeling tool to accurately capture the dynamics of arbitrary client participation and the local update procedure. Leveraging this approach, we offer a fresh decentralized perspective on designing FL algorithms and present FOCUS, Federated Optimization with Exact Convergence via Push-pull Strategy, a provably convergent algorithm designed to effectively overcome the previously mentioned two challenges. More specifically, we provide a rigorous proof demonstrating that FOCUS achieves exact convergence with a linear rate regardless of the arbitrary client participation, establishing it as the first work to demonstrate this significant result.

There is extensive literature on accelerating first-order optimization methods in an Euclidean setting. Under which conditions such acceleration is feasible in Riemannian optimization problems is an active area of research. Motivated by the recent success of silver stepsize methods in the Euclidean setting, we undertake a study of such algorithms in the Riemannian setting. We provide the new class of algorithms determined by the choice of vector transport that allows the silver stepsize acceleration on Riemannian manifolds for the function classes associated with the corresponding vector transport. As a core application, we show that our algorithm recovers the standard Wasserstein gradient descent on the 2-Wasserstein space and, as a result, provides the first provable accelerated gradient method for potential functional optimization problems in the Wasserstein space.

We study which machine learning algorithms have tight generalization bounds with respect to a given collection of population distributions. Our results build on and extend the recent work of Gastpar et al. (2024). First, we present conditions that preclude the existence of tight generalization bounds. Specifically, we show that algorithms that have certain inductive biases that cause them to be unstable do not admit tight generalization bounds. Next, we show that algorithms that are sufficiently loss-stable do have tight generalization bounds. We conclude with a simple characterization that relates the existence of tight generalization bounds to the conditional variance of the algorithm's loss.

We study the problem of approximating all-pair distances in a weighted undirected graph with differential privacy, introduced by Sealfon [Sea16]. Given a publicly known undirected graph, we treat the weights of edges as sensitive information, and two graphs are neighbors if their edge weights differ in one edge by at most one. We obtain efficient algorithms with significantly improved bounds on a broad class of graphs which we refer to as recursively separable. In particular, for any n-vertex Kh-minor-free graph, our algorithm achieve an additive error of eO(h(nW)1/3), where W represents the maximum edge weight; For grid graphs, the same algorithmic scheme achieve additive error of eO(n1/4 W). Our approach can be seen as a generalization of the celebrated binary tree mechanism for range queries, as releasing range queries is equivalent to computing all-pair distances on a path graph. In essence, our approach is based on generalizing the binary tree mechanism to graphs that are recursively separable. JL and ZZ have been supported by National Science Foundation of China under Grant No. 62472212 and the New Cornerstone Science Foundation. Supported in part by NSF award 2228995 JU's research was funded by the NSFCNS 2433628, Google Seed Fund grant, Google Research Scholar Award, Dean Research Seed Fund, and Rutgers Decanal Grant no.

Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing massive data. We consider two such models: Massively Parallel Computation (MPC) and semi-streaming. We show how to find a (2+ε)-approximation in O( logn) MPC rounds with sublinear memory per machine.

We introduce PARTCRAFTER, the first structured 3D generative model that jointly synthesizes multiple semantically meaningful and geometrically distinct 3D meshes from a single RGB image. Unlike existing methods that either produce monolithic 3D shapes or follow two-stage pipelines, i.e. first segmenting an image and then reconstructing each segment, PARTCRAFTER adopts a unified, compositional generation architecture that does not rely on pre-segmented inputs.

Real-world objects are composed of distinctive, object-specific parts. Identifying these parts is key to performing fine-grained, compositional reasoning--yet, large multimodal models (LMMs) struggle to perform this seemingly straightforward task. In this work, we introduce PARTONOMY, an LMM benchmark designed for pixel-level part grounding. We construct PARTONOMY from existing part datasets and our own rigorously annotated set of images, encompassing 862 part labels and 534 object labels for evaluation.

Existing vision-language models often suffer from spatial hallucinations, i.e., generating incorrect descriptions about the relative positions of objects in an image. We argue that this problem mainly stems from the asymmetric properties between images and text. To enrich the spatial understanding ability of vision-language models, we propose a simple, annotation-free, plug-and-play method named Stitch and Tell (abbreviated as SiTe), which injects structured spatial supervision into multimodal data. It constructs stitched image-text pairs by stitching images along a spatial axis and generating spatially-aware captions or question answer pairs based on the layout of stitched image, without relying on costly advanced models or human involvement. We evaluate SiTe across three architectures including LLaVA-v1.5-7B,

Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.

Event-based structured light (SL) systems have attracted increasing attention for their potential in high-performance 3D measurement. Despite the inherent HDR capability of event cameras, reflective and absorptive surfaces still cause event clutter and absence, which produce overexposed and underexposed regions that degrade the reconstruction quality. In this work, we present the first HDR 3D measurement framework specifically designed for event-based SL systems. First, we introduce a multi-contrast HDR coding strategy that facilitates imaging of areas with different reflectance. Second, to alleviate inter-frame interference caused by overexposed and underexposed areas, we propose a universal confidence-driven stereo matching strategy. Specifically, we estimate a confidence map as the fusion weight for features via an energy-guided confidence estimation.