Fixed-Point Neural Optimal Transport without Implicit Differentiation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916001240580096 |
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| author | Park, Yesom Gelphman, Eric Osher, Stanley Fung, Samy Wu |
| author_facet | Park, Yesom Gelphman, Eric Osher, Stanley Fung, Samy Wu |
| contents | We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the Kantorovich dual and reformulate the associated c-transform as a proximal fixed-point problem. This yields a stable single-network framework in which dual feasibility is enforced exactly through proximal optimality conditions rather than adversarial training. Despite the inner fixed-point computation, gradients can be computed without differentiating through the fixed-point iterations, enabling efficient training without requiring implicit differentiation. We further establish convergence of stochastic gradient descent. The resulting framework is efficient, scalable, and broadly applicable: it simultaneously recovers forward and backward transport maps and naturally extends to class-conditional settings. Experiments on high-dimensional Gaussian benchmarks, physical datasets, and image translation tasks demonstrate strong transport accuracy together with improved training stability and favorable computational and memory efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10792 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fixed-Point Neural Optimal Transport without Implicit Differentiation Park, Yesom Gelphman, Eric Osher, Stanley Fung, Samy Wu Optimization and Control Machine Learning 49Q22, 68T07, 65K10 We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the Kantorovich dual and reformulate the associated c-transform as a proximal fixed-point problem. This yields a stable single-network framework in which dual feasibility is enforced exactly through proximal optimality conditions rather than adversarial training. Despite the inner fixed-point computation, gradients can be computed without differentiating through the fixed-point iterations, enabling efficient training without requiring implicit differentiation. We further establish convergence of stochastic gradient descent. The resulting framework is efficient, scalable, and broadly applicable: it simultaneously recovers forward and backward transport maps and naturally extends to class-conditional settings. Experiments on high-dimensional Gaussian benchmarks, physical datasets, and image translation tasks demonstrate strong transport accuracy together with improved training stability and favorable computational and memory efficiency. |
| title | Fixed-Point Neural Optimal Transport without Implicit Differentiation |
| topic | Optimization and Control Machine Learning 49Q22, 68T07, 65K10 |
| url | https://arxiv.org/abs/2605.10792 |