We consider nonconvex stochastic optimization problems in the asynchronous centralized distributed setup where the communication times from workers to a server can not be ignored, and the computation and communication times are potentially different for all workers.

Designing algorithms that can explore multimodal target distributions accurately across successive refinements of an underlying high-dimensional problem is a central challenge in sampling. Annealed Langevin dynamics (ALD) is a widely used alternative to classical Langevin since it often yields much faster mixing on multimodal targets, but there is still a gap between this empirical success and existing theory: when, and under which design choices, can ALD be guaranteed to remain stable as dimension increases? In this paper, we help bridge this gap by providing a uniform-in-dimension analysis of continuous-time ALD for multimodal targets that can be well-approximated by Gaussian mixture models. Along an explicit annealing path obtained by progressively removing Gaussian smoothing of the target, we identify sufficient spectral conditions - linking smoothing covariance and the covariances of the Gaussian components of the mixture - under which ALD achieves a prescribed accuracy within a single, dimension-uniform time horizon. We then establish dimension-robustness to imperfect initialization and score approximation: under a misspecified-mixture score model, we derive explicit conditions showing that preconditioning the ALD algorithm with a sufficiently decaying spectrum is necessary to prevent error terms from accumulating across coordinates and destroying dimension-uniform control. Finally, numerical experiments illustrate and validate the theory.

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously recover a sequence of graph Laplacian matrices while reconstructing the unobserved signal entries. Unlike conventional decoupled methods, our integrated approach facilitates a bidirectional flow of information between the graph and signal domains, yielding superior robustness, particularly in high missing-data regimes. To capture realistic network dynamics, we introduce a fused-lasso type regularizer on the sequence of Laplacians. This penalty promotes temporal smoothness by penalizing large successive changes, thereby preventing spurious variations induced by noise while still permitting gradual topological evolution. For solving the joint optimization problem, we develop an efficient Alternating Direction Method of Multipliers (ADMM) algorithm, which leverages the problem's structure to yield closed-form solutions for both the graph and signal subproblems. This design ensures scalability to large-scale networks and long time horizons. On the theoretical front, despite the inherent non-convexity, we establish a convergence guarantee, proving that the proposed ADMM scheme converges to a stationary point. Furthermore, we derive non-asymptotic statistical guarantees, providing high-probability error bounds for the graph estimator as a function of sample size, signal smoothness, and the intrinsic temporal variability of the graph. Extensive numerical experiments validate the approach, demonstrating that it significantly outperforms state-of-the-art baselines in both convergence speed and the joint accuracy of graph learning and signal recovery.

We consider nonconvex stochastic optimization problems in the asynchronous centralized distributed setup where the communication times from workers to a server can not be ignored, and the computation and communication times are potentially different for all workers.

We present a generalised Hanson-Wright inequality and use it to establish new statistical insights into the geometry of data point-clouds. In the setting of a general random function model of data, we clarify the roles played by three notions of dimensionality: ambient intrinsic dimension $p_{\mathrm{int}}$, which measures total variability across orthogonal feature directions; correlation rank, which measures functional complexity across samples; and latent intrinsic dimension, which is the dimension of manifold structure hidden in data. Our analysis shows that in order for persistence diagrams to reveal latent homology and for manifold structure to emerge it is sufficient that $p_{\mathrm{int}}\gg \log n$, where $n$ is the sample size. Informed by these theoretical perspectives, we revisit the ground-breaking neuroscience discovery of toroidal structure in grid-cell activity made by Gardner et al. (Nature, 2022): our findings reveal, for the first time, evidence that this structure is in fact isometric to physical space, meaning that grid cell activity conveys a geometrically faithful representation of the real world.

We propose an efficient and robust iterative solution to the multi-object matching problem. We first clarify serious limitations of current methods as well as the inappropriateness of the standard iteratively reweighted least squares procedure. In view of these limitations, we suggest a novel and more reliable iterative reweighting strategy that incorporates information from higher-order neighborhoods by exploiting the graph connection Laplacian. We demonstrate the superior performance of our procedure over state-of-the-art methods using both synthetic and real datasets.

Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation from the others, i.e., edge class, which occurs frequently in multi-class classification. First, the existence of edge classes often makes the total mean biased in the calculation of between-class scatter matrix. Second, the exploitation of l2-norm based between-class distance criterion magnifies the extremely large distance corresponding to edge class. In this regard, a novel self-weighted robust LDA with l21-norm based pairwise between-class distance criterion, called SWRLDA, is proposed for multi-class classification especially with edge classes. SWRLDA can automatically avoid the optimal mean calculation and simultaneously learn adaptive weights for each class pair without setting any additional parameter. An efficient re-weighted algorithm is exploited to derive the global optimum of the challenging l21-norm maximization problem. The proposed SWRLDA is easy to implement, and converges fast in practice. Extensive experiments demonstrate that SWRLDA performs favorably against other compared methods on both synthetic and real-world datasets, while presenting superior computational efficiency in comparison with other techniques.