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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
An Accelerated Stochastic Variance-Reduced Algorithm for ...
[Submitted on 2 Mar 2022 (v1), last revised 3 Jul 2026 (this ver · 2022-03-02 · via stat updates on arXiv.org

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Abstract:Fixed-support Wasserstein barycenters average probability distributions while accounting for the geometry of the support. We study the entropically regularized Wasserstein barycenter problem with a fixed regularization parameter and propose an accelerated stochastic variance-reduced primal-dual algorithm. The proposed algorithm uses a semi-dual finite-sum structure in which each stochastic gradient requires only one softmax over the barycenter support. The resulting finite-sum components have dimension-free smoothness bounds, which lead to a complexity result showing that the method improves the support-size dependence of deterministic accelerated gradient by a square-root factor while preserving accelerated dependence on the target accuracy. Experiments on synthetic data, DOTmark images, shape aggregation, and digit-averaging instances are consistent with the theoretical dependence on support size and accuracy and show lower arithmetic costs than the tested first-order baselines.

Submission history

From: Yiling Xie [view email]
[v1] Wed, 2 Mar 2022 01:16:10 UTC (105 KB)
[v2] Tue, 22 Mar 2022 21:01:28 UTC (106 KB)
[v3] Tue, 30 May 2023 00:15:35 UTC (82 KB)
[v4] Fri, 3 Jul 2026 09:56:12 UTC (533 KB)