克服半对偶神经最优传输中的虚假解：一种平滑方法用于学习最优传输计划
Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan
AI总结：
OTP模型通过平滑方法克服半对偶神经OT中的虚假解问题，准确学习最优传输计划并提升图像到图像翻译性能。
摘要：
我们解决了学习最优传输（OT）映射中的收敛问题，其中OT映射指的是从一种分布到另一种分布的过程中最小化传输成本的映射。半对偶神经OT是一种广泛用于通过神经网络学习OT映射的方法，但常常生成虚假解，这些解无法准确地将一种分布转换为另一种分布。我们确定了一个充分条件，使得半对偶神经OT的max-min解能够恢复真实的OT映射。此外，为了处理这种充分条件不满足的情况，我们提出了一种新的方法OTP，该方法同时学习OT映射和最优传输计划，代表两种分布之间的最优耦合。在对分布施加尖锐假设的情况下，我们证明了我们的模型消除了虚假解问题，并正确解决了OT问题。我们的实验表明，OTP模型恢复了现有方法无法恢复的最优传输映射，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，OTP模型可以在确定性OT映射不存在的情况下学习随机传输映射，例如颜色化等一对一多的任务。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
