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

Researchers introduce cuRegOT, a GPU-accelerated solver that significantly improves the speed of entropic-regularized optimal transport computations through algorithmic optimizations like amortized symbolic analysis and fused kernels. The breakthrough addresses a critical computational bottleneck in machine learning by outperforming existing GPU-based solvers while maintaining theoretical convergence guarantees.

Optimal transport has become central to modern machine learning applications, from generative modeling to domain adaptation, but computational constraints have limited its practical deployment at scale. The Sinkhorn algorithm, the industry standard, parallelizes easily but converges slowly on difficult problems. Recent quasi-Newton approaches improve convergence rates but struggle on GPUs due to irregular memory access patterns and CPU bottlenecks in symbolic analysis. cuRegOT addresses this fundamental tension through careful architectural design. The amortized symbolic analysis strategy reduces CPU overhead by batching and deferring computation, while asynchronous Sinkhorn generation decouples iteration creation from the main solver loop. The fused gradient evaluation kernel minimizes memory bandwidth requirements, a critical constraint on accelerators. These innovations represent not merely incremental engineering but strategic algorithmic-hardware codesign that exploits GPU strengths while mitigating known weaknesses. The theoretical convergence guarantees ensure the optimizations don't sacrifice mathematical soundness. For the broader AI and scientific computing ecosystem, faster optimal transport solvers enable real-time applications in machine learning pipelines that previously required prohibitive computational resources. This particularly impacts fields like generative AI, where optimal transport underpins certain diffusion and flow-matching approaches. The work demonstrates how GPU computing evolves beyond naive parallelization toward sophisticated problem-specific optimization, setting precedent for similar codesign efforts across numerical algorithms.

• →cuRegOT combines algorithmic innovations with GPU-specific optimizations to dramatically accelerate entropic-regularized optimal transport computations
• →Amortized symbolic analysis and fused kernels eliminate CPU bottlenecks that previously hindered quasi-Newton methods on GPUs
• →Theoretical convergence guarantees ensure algorithmic soundness despite aggressive performance optimizations
• →Faster OT solvers enable new real-time machine learning applications previously limited by computational constraints
• →The work exemplifies strategic hardware-algorithm codesign increasingly necessary for unlocking GPU potential in scientific computing