Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2502.03749

PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport

Di Wu·Ling Liang·Haizhao Yang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the regularization parameter is small, Sinkhorn convergence slows, and the iterates approach an entropic solution that remains separated from the true OT plan by an entropic-bias plateau. We introduce PINS (Proximal Iterations with sparse Newton and Sinkhorn), a two-loop solver designed to move beyond this plateau. The outer loop applies an entropic proximal-point method, solving the original OT problem through a sequence of entropic subproblems with shifted cost matrices. Each inner subproblem is then solved by a Sinkhorn warm-up followed by sparse-Newton refinement. We prove that PINS converges globally to an optimal solution of the unregularized OT problem and that the inner Hessian admits a sparsification at every outer iteration with a structure independent of the cost matrix. On synthetic and augmented-MNIST instances, PINS achieves much lower relative cost errors than Sinkhorn-type baselines, which stall at the entropic-bias plateau, and is $5$--$73\times$ faster than Sinkhorn with the same outer loop at matched accuracy. On large-scale DOTmark instances, a streaming implementation reduces peak memory by $24$--$54\%$ compared with the network-simplex linear programming (LP) solver and remains feasible under per-process memory budgets for which the LP solver fails.

Explore related subjects

cs.LGmath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Di Wu, Ling Liang, Haizhao Yang. 2025-02-06. PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport. https://arxiv.org/abs/2502.03749

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

AUC Maximization from Biased Positive-unlabeled Data with Confidence

Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced binary classification. Although positive and negative data are required for maximizing the AUC, negative data are often difficult to collect in some real-world applications due to privacy concerns or the need for specialized expertise to annotate them. Thus, AUC maximization from positive and unlabeled (PU) data has been attracting attention. Existing methods assume that labeled positive data are unbiased samples from the true positive distribution. However, this ideal assumption is often violated in practice. In this paper, we propose a method to maximize the AUC from biased PU data. To address the bias, our key idea is to exploit {\it confidence}, i.e., the probability that an instance is positive, associated with the small number of labeled positive data. We derive an estimator of the AUC risk using biased PU data with confidence, enabling AUC maximization under such bias. We further show that the rewritten AUC risk induces a Bayes-optimal AUC ranking even when the available confidence is any strictly increasing transformation of the true posterior probability. We experimentally show the effectiveness of our method on eight real-world datasets.

cs.LG↗
arXiv2026

Measuring the Value of World-Model Updates: A Counterfactual Utility Protocol for Continual Adaptation

Continual world models must decide whether new data justify changing the model. Fixed replay schedules and prediction-error triggers specify when to update, but neither reveals the value of an individual update: one deployment run cannot show how the same model would have performed at that moment had it held its parameters. We introduce the fork ledger, which branches a deployment stream at pre-registered decision points into matched update and hold continuations under common random numbers. It evaluates both continuations on the same episodes and records $\Delta R = R_{\mathrm{update}} - R_{\mathrm{hold}}$. Always applying one fixed update mechanism lowers return on all three simulated control tasks: CartPole ($-144.0$; checkpoint-bootstrap $95\%$ CI $[-185.4,-116.1]$, against a converged return near $650$), Walker ($-82.8$; $[-101.1,-61.7]$) and Cheetah ($-18.6$; $[-29.0,-6.6]$). Divergence is an outcome of applying the update, so the estimand counts every attempted fork; restricted to the $693$ of $720$ that did not collapse, CartPole and Walker are unchanged in sign ($-113.4$ and $-82.1$) and Cheetah becomes unresolved ($-3.9$; $[-17.5,+13.0]$). The task is the unit of inference: each contributes $240$ attempted forks over five pretrained checkpoints crossed with two drift directions. The ledger makes counterfactual utility observable for a fixed mechanism, allowing triggers to be judged by the updates they select rather than by surprise detection alone.

cs.LG↗
arXiv2026

When More Is Not Better: Component Anti-Synergy in a P300 Speller

P300 brain-computer interface (BCI) spellers can provide hands-free communication for people with severe motor impairments. Modern pipelines combine multiple individually promising components, often assuming that 'more-is-better'. We tested this assumption using a four-component full-factorial experiment varying the inclusion of Euclidean Alignment (EA), xDAWN spatial filtering, subject calibration, and language model priors on a public P300 dataset. Performance was evaluated using accuracy, repetitions, and information transfer rate (ITR) with mixed-effects models. Results show that the value of components is conditional rather than additive. Calibration was the strongest singular contributor, while EA compensated for its absence in zero-calibration settings. Adding independently useful components could also reduce performance, revealing component anti-synergy. Contrary to conventional wisdom, LM support was not universally beneficial: its effect depends strongly on the strength of the underlying EEG pipeline, while results from a larger LM showed a similar pattern. Together, these findings challenge maximal 'all-on' pipeline design and highlight the value of selecting spatial and language-support components according to the quality of available EEG evidence.

cs.LG↗