提出新方法解决神经最优传输中的虚假解问题，能准确学习分布间最优匹配。
Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan
- 通过平滑优化同时学习传输映射与耦合计划，避免虚假解。
- 在分布满足特定条件时，可完全消除虚假解并正确求解最优传输。
- 适用于图像翻译、着色等一到多传输任务，优于现有方法。
我们解决学习最优传输（OT）映射时的收敛问题，其中OT映射指从一个分布到另一个分布以最小化传输成本的映射。半对偶神经OT是一种广泛用于神经网络学习OT映射的方法，但常产生无法准确传递分布的虚假解。我们识别出半对偶神经OT的极大极小解恢复真实OT映射的充分条件。针对该条件不满足的情况，提出新方法OTP，同时学习OT映射与最优传输计划（即两分布间的最优耦合）。在对分布做出严格假设的前提下，证明该模型可消除虚假解并正确求解OT问题。实验表明，OTP在现有方法失效时仍能恢复最优传输映射，并在图像到图像翻译任务中优于当前基于OT的模型。值得注意的是，当确定性OT映射不存在时，如着色这类一到多任务，该模型仍可学习随机传输映射。
原文摘要 · Abstract (English)
We address the convergence problem in learning the Optimal Transport (OT) map, where the OT Map refers to a map from one distribution to another while minimizing the transport cost. Semi-dual Neural OT, a widely used approach for learning OT Maps with neural networks, often generates fake solutions that fail to transfer one distribution to another accurately. We identify a sufficient condition under which the max-min solution of Semi-dual Neural OT recovers the true OT Map. Moreover, to address cases when this sufficient condition is not satisfied, we propose a novel method, OTP, which learns both the OT Map and the Optimal Transport Plan, representing the optimal coupling between two distributions. Under sharp assumptions on the distributions, we prove that our model eliminates the fake solution issue and correctly solves the OT problem. Our experiments show that the OTP model recovers the optimal transport map where existing methods fail and outperforms current OT-based models in image-to-image translation tasks. Notably, the OTP model can learn stochastic transport maps when deterministic OT Maps do not exist, such as one-to-many tasks like colorization.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。