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arxiv: 2605.08793 · v1 · submitted 2026-05-09 · 💻 cs.MS · cs.AI· cs.LG· stat.CO· stat.ML

Recognition: no theorem link

cuRegOT: A GPU-Accelerated Solver for Entropic-Regularized Optimal Transport

Yixuan Qiu
Authors on Pith no claims yet

Pith reviewed 2026-05-12 01:19 UTC · model grok-4.3

classification 💻 cs.MS cs.AIcs.LGstat.COstat.ML
keywords optimal transportentropic regularizationGPU solverSinkhorn algorithmquasi-Newtonparallel computing
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The pith

cuRegOT provides a GPU solver for entropic regularized optimal transport that delivers significant speedups over state-of-the-art methods with preserved convergence guarantees.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces cuRegOT as a specialized GPU implementation for solving entropic regularized optimal transport problems more efficiently. It addresses the slow convergence of the standard Sinkhorn algorithm and the GPU inefficiencies of quasi-Newton methods by adding amortized symbolic analysis, asynchronous iteration generation, and fused gradient kernels. These changes come with proofs that the algorithm still converges correctly. If true, this would make large-scale optimal transport computations much faster on modern hardware, enabling bigger applications in machine learning without sacrificing reliability. The work focuses on practical performance gains backed by theory.

Core claim

cuRegOT is a GPU-accelerated solver for entropic-regularized optimal transport that combines an amortized symbolic analysis strategy to reduce CPU overhead, an asynchronous mechanism for generating Sinkhorn iterates, and a fused kernel for efficient gradient computation. These optimizations are supported by theoretical guarantees of convergence, and experiments show substantial speedups compared to prior GPU solvers on various benchmark tasks.

What carries the argument

Amortized symbolic analysis combined with asynchronous Sinkhorn iterate generation and fused gradient kernels, addressing CPU bottlenecks and irregular memory patterns in GPU-based OT solving.

Load-bearing premise

The GPU-specific optimizations do not alter the convergence behavior or numerical accuracy of the entropic OT solver through changes in execution or floating-point operations.

What would settle it

Reproducing the benchmark experiments and finding either insufficient speedups or failures in convergence guarantees would disprove the paper's main results.

Figures

Figures reproduced from arXiv: 2605.08793 by Yixuan Qiu.

Figure 1
Figure 1. Figure 1: An overview of the cuRegOT pipeline. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Visualization of GPU kernel occupancy. the symbolic analysis part that merely utilizes CPU. Recall that the Sinkhorn algorithm solves the same dual problem (3). While generally slower to converge than Newton-type methods, its iterations are computationally inexpensive and highly parallelizable on the GPU. Therefore, when the host CPU begins the serial symbolic analysis task, we propose to simultaneously tr… view at source ↗
Figure 3
Figure 3. Figure 3: Benchmark result for synthetic datasets. The horizontal axis represents the [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Benchmark result for the CIFAR-10 dataset. [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: , in which “-A” means removing the amortized symbolic analysis strategy, “-S” means removing the candidate Sinkhorn iterate generation, and “-A-S” means removing both. Clearly, the plots show that removing either of the algorithmic improvement may slow down the solver. This suggests that both the amortized symbolic analysis and the Sinkhorn iteration generation contribute to the performance of the cuRegOT … view at source ↗
Figure 6
Figure 6. Figure 6: Evolution of the transport plan during Sinkhorn iterations, based on the [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Benchmark result for the CIFAR-10 dataset with additional class pairs. [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Benchmark result that uses the duality gap (on a logarithmic scale) as the [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Benchmark result for different solvers under the regularization parameter [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Benchmark result for different solvers under the regularization parameter [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Benchmark result for the hyperparameter S in the cuRegOT solver. The regularization parameter is set to η = 0.001. B Theoretical Analysis Details B.1 Complexity Analysis for [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
read the original abstract

Optimal transport (OT) has emerged as a fundamental tool in modern machine learning, yet its computational cost remains a significant bottleneck for large-scale applications. While harnessing the massive parallelism of modern GPU hardware is critical for efficiency, the de facto standard Sinkhorn algorithm, despite its ease of parallelization, often suffers from slow convergence in challenging problems. More recently, the sparse-plus-low-rank quasi-Newton method offers a balance between convergence rate and per-iteration complexity; however, its efficiency on GPUs is severely hindered by the serial nature of sparse matrix symbolic analysis and irregular memory access patterns. To bridge this gap, we present cuRegOT, a high-performance GPU solver tailored for entropic-regularized OT. We introduce a suite of algorithmic and architectural optimizations, including an amortized symbolic analysis strategy to mitigate CPU bottlenecks, an asynchronous Sinkhorn iterates generation mechanism, and a fused kernel for bandwidth-efficient gradient evaluation. These strategies are backed by rigorous theoretical guarantees ensuring algorithmic convergence. Extensive numerical experiments demonstrate that cuRegOT achieves significant speedups over state-of-the-art GPU-based solvers across a variety of benchmark tasks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces cuRegOT, a GPU-accelerated solver for entropic-regularized optimal transport. It targets the sparse-plus-low-rank quasi-Newton method by adding an amortized symbolic analysis pass to reduce CPU bottlenecks, an asynchronous mechanism for Sinkhorn iterate generation, and fused kernels for bandwidth-efficient gradient evaluation. The work asserts that these changes are accompanied by rigorous theoretical convergence guarantees and reports substantial empirical speedups over prior GPU OT solvers on benchmark tasks.

Significance. If the claimed convergence guarantees are shown to hold under asynchrony and kernel fusion, and if the speedups are reproducible while preserving numerical accuracy, the solver could meaningfully accelerate large-scale OT computations in machine learning pipelines such as generative modeling and domain adaptation.

major comments (1)
  1. Abstract: the assertion of 'rigorous theoretical guarantees ensuring algorithmic convergence' for the asynchronous Sinkhorn iterates generation mechanism is load-bearing for the central claim. The provided description gives no indication that the analysis accounts for relaxed synchronization, non-deterministic iteration ordering, or altered floating-point accumulation from kernel fusion; if the proof assumes synchronous updates, the guarantees do not automatically transfer to the delivered GPU code.
minor comments (1)
  1. §4 (Experiments): the speed-up tables would benefit from explicit reporting of the number of independent runs, standard deviations, and any data-exclusion rules to allow readers to assess robustness.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on the manuscript. We address the major comment below and will incorporate revisions to improve clarity.

read point-by-point responses

  1. Referee: Abstract: the assertion of 'rigorous theoretical guarantees ensuring algorithmic convergence' for the asynchronous Sinkhorn iterates generation mechanism is load-bearing for the central claim. The provided description gives no indication that the analysis accounts for relaxed synchronization, non-deterministic iteration ordering, or altered floating-point accumulation from kernel fusion; if the proof assumes synchronous updates, the guarantees do not automatically transfer to the delivered GPU code.

    Authors: We agree that the abstract statement requires more precise scoping to avoid ambiguity. The convergence analysis establishes guarantees for the underlying sparse-plus-low-rank quasi-Newton method and the associated Sinkhorn iterations under standard synchronous assumptions. The asynchronous mechanism reorders the generation of iterates on the GPU for improved throughput but computes identical mathematical updates to the synchronous version; each new iterate is produced from the preceding state without changing the fixed-point equations or the sequence of operations. Kernel fusion is applied only to the gradient evaluation step and preserves the exact arithmetic result up to standard floating-point associativity, which does not affect the convergence conditions. We will revise the abstract to state that the guarantees apply to the core algorithmic framework, and we will add a short paragraph in the methods section explaining the equivalence of the asynchronous implementation to its synchronous counterpart together with additional numerical checks confirming identical convergence behavior. revision: yes

Circularity Check

0 steps flagged

No circularity: algorithmic implementation with independent convergence claims

full rationale

The paper describes a GPU-accelerated implementation of the Sinkhorn algorithm for entropic OT, introducing practical optimizations (amortized analysis, asynchronous iteration, kernel fusion) and stating that these are supported by standard theoretical convergence guarantees. No equations, fitted parameters, or predictions are presented that reduce by construction to quantities defined on the same data or via self-referential definitions. The central claims concern engineering speedups and preservation of existing theory under implementation changes; these do not form a closed derivation loop. The work is self-contained as a software contribution without load-bearing self-citations or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of entropic optimal transport and GPU memory models; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (2)
  • domain assumption Entropic regularization yields a strictly convex problem whose unique solution can be recovered by Sinkhorn-type iterations
    Invoked when the authors state that the optimizations preserve algorithmic convergence.
  • domain assumption Sparse matrix symbolic analysis can be amortized across multiple right-hand sides without changing the nonzero pattern
    Basis for the claimed CPU-bottleneck mitigation.

pith-pipeline@v0.9.0 · 5497 in / 1452 out tokens · 42305 ms · 2026-05-12T01:19:20.942350+00:00 · methodology

discussion (0)

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Reference graph

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