ITSPACE: Monotone Gaussian Optimal Transport Updates

• URL: http://arxiv.org/abs/2606.30523v1
• Date: Mon, 29 Jun 2026 16:29:19 GMT
• Title: ITSPACE: Monotone Gaussian Optimal Transport Updates
• Abstract summary: Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings.<n>We propose ITSPACE, a majorization-minimization method that directly optimize this exact BW objective through closed-form updates in a square-root factorization.<n>In exact arithmetic, each satisfies a sufficient-decrease inequality for the BW objective; under inexact polar computations, we provide an explicit certificate-gap bound controlling deviations from exact descent.
• Score: 0.04687712818521871
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings. Under a centered Gaussian approximation, the unregularized Wasserstein-2 optimal-transport (OT) discrepancy admits a closed form on covariances given by the Bures-Wasserstein (BW) objective on the symmetric positive definite (SPD) cone. We propose ITSPACE (Iterative Transport for Stable Proximal Alignment of Covariance Embeddings), a proximal majorization-minimization method that directly optimizes this exact BW objective through closed-form updates in a square-root factorization. In exact arithmetic, each iteration satisfies a sufficient-decrease inequality for the BW objective; under inexact polar computations, we provide an explicit certificate-gap bound controlling deviations from exact descent. The resulting iterations preserve PSD structure by construction and naturally support rank-restricted factors, making ITSPACE well-suited as a lightweight inner-loop primitive in settings where adaptation must be performed from unlabeled target batches under strict step and compute budgets. Across real-world covariance-alignment benchmarks, ITSPACE reaches low-BW-gap solutions substantially faster than BW-gradient descent, methods based on other covariance geometries, and entropically regularized sample-OT baselines.

Related papers

• Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size [43.46286813814826]
  Bregman finite proximal ergo gradient (BPSG) methods bring variance-reduced composite size to objectives whose geometry is poorly captured by Euclidean smoothness.<n>Their performance remains sensitive to stepwise: raw curvature estimates can fluctuate, whereas line searches add repeated searches.<n>We introduce AdaBPSG, a line-search method that combines sparse values and a non-negative matrix factorization rate.
  arXiv  Detail & Related papers  (2026-08-12T12:46:05Z)
• Multimodal Alignment Through Joint Kernel Entropic Gromov--Wasserstein Optimal Transport [4.633342231489067]
  We propose a structure-preserving alignment framework, joint kernel entropic Gromov--Wasserstein Optimal Transport (JK-EGW)<n>JK-EGW maps multiple modalities into a common latent space by minimizing a quadratic optimal transport objective.<n>We show that our proposed method achieves improved multimodal retrieval performance compared to existing alignment baselines.
  arXiv  Detail & Related papers  (2026-08-04T21:21:09Z)
• Expanding SPHERE-JEPA: A Family of Statistical Regularizers for the Hypersphere [11.087393998848254]
  In Self-Supervised Learning (SSL), preventing representation collapse by explicitly enforcing a uniform distribution on the unit hypersphere has proven to be effective.<n>Current frameworks typically rely on sliced statistical regularizers such as SIGReg (used in LeJEPA) and SUSReg (used in SPHEREJEPA)<n>This injects projection variance into the training gradients, destabilizing optimization, and hindering convergence.<n>In this work, we first show that analytically integrating out these random projections yields a deterministic Maximum Mean Discrepancy (MMD), bypassing the variance of sliced methods.
  arXiv  Detail & Related papers  (2026-06-16T07:10:05Z)
• SPHERE-JEPA: Spherical Prediction with Homogeneous Embeddings [11.087393998848254]
  Recently, LeJEPA identified isotropic Gaussian embeddings as optimal for minimizing downstream prediction risk in Euclidean spaces.<n>We show that under a worst-case formulation, both k-nearest neighbors and kernel ridge regression induce hyperspherical uniformity.<n>We introduce SPHERE-JEPA, a theoretically grounded SSL framework.
  arXiv  Detail & Related papers  (2026-05-26T12:00:40Z)
• Curvature-Aware PCA with Geodesic Tangent Space Aggregation for Semi-Supervised Learning [52.452902154360565]
  GTSA-PCA is a geometric extension of Principal Component Analysis.<n>It integrates curvature awareness and geodesic consistency within a unified spectral framework.<n>Our results position GTSA-PCA as a principled bridge between statistical and geometric approaches to dimensionality reduction.
  arXiv  Detail & Related papers  (2026-04-20T20:36:36Z)
• Diversity-Aware Adaptive Collocation for Physics-Informed Neural Networks via Sparse QUBO Optimization and Hybrid Coresets [0.0]
  PINNs enforce governing equations by penalizing PDE residuals at interior collocation points.<n>Standard collocation strategies can oversample smooth regions, produce highly correlated point sets, and incur unnecessary training cost.<n>We propose a sparse graph-based BQM built on a kNN similarity graph and an efficient repair procedure that enforces an exact collocation budget.
  arXiv  Detail & Related papers  (2026-03-06T14:26:34Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations [121.39938773554523]
  The Area Under the ROC Curve (AUC) is a pivotal evaluation metric in real-world scenarios with both class imbalance and decision constraints.<n>We present two simple instance-wise minimax reformulations to close the approximation gap of PAUC optimization.<n>The resulting algorithms enjoy a linear per-iteration computational complexity w.r.t. the sample size and a convergence rate of $O(-2/3)$ for typical one-way and two-way PAUCs.
  arXiv  Detail & Related papers  (2025-12-01T02:52:33Z)
• Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion [55.95767828747407]
  In domains such as molecular and protein generation, physical systems exhibit inherent symmetries that are critical to model.<n>We present a framework that reduces training variance and provides a provably lower-variance gradient estimator.<n>We also present a practical implementation of this estimator incorporating the loss and sampling procedure through a method we call Orbit Diffusion.
  arXiv  Detail & Related papers  (2025-02-14T03:26:57Z)
• Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Bandits [12.674929126684528]
  We address the problem of semi-bandits, where a player selects among P actions from the power set of a set containing d base items. We show that our approach efficiently leverages the semi-bandit feedback and outperforms bandit feedback approaches.
  arXiv  Detail & Related papers  (2024-02-23T08:07:54Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Optimal Scaling for Locally Balanced Proposals in Discrete Spaces [65.14092237705476]
  We show that efficiency of Metropolis-Hastings (M-H) algorithms in discrete spaces can be characterized by an acceptance rate that is independent of the target distribution. Knowledge of the optimal acceptance rate allows one to automatically tune the neighborhood size of a proposal distribution in a discrete space, directly analogous to step-size control in continuous spaces.
  arXiv  Detail & Related papers  (2022-09-16T22:09:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.