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基于正向-后向SDEs理论的薛定谔桥(Schrödinger Bridge)似然训练
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Paper: "Likelihood Training of Schrödinger Bridge Using Forward-Backward SDEs Theory" https://www.semanticscholar.org/paper/Likelihood-Training-of-Schr%C3%B6dinger-Bridge-using-Chen-Liu/509e166d5e66df10675a0e15063daad518dcc5ad 摘要:Schrödinger Bridge(SB)是一个熵正则的最优运输问题,与基于评分的生成性模型(SGM)相比,由于其数学上的灵活性,在深度生成性建模中受到了越来越多的关注。 然而,SB的最优化原则是否与深度生成模型的现代训练有关尚不清楚,这通常依赖于构造对数似然对象,这就提出了SB模型作为原则性选择是否适合于生成性应用的问题。 在这项工作中,我们提出了一种新的基于正倒向随机微分方程理论的SB模型似然训练的计算框架--一种出现在随机最优控制中的数学方法,它将SB的最优性条件转化为一组SDE。 重要的是,这些随机微分方程可以用来为某人构建可能性目标,令人惊讶的是,这些目标将特殊情况下的可能性目标概括为特殊情况。 这导致了一种新的优化原则,它继承了相同的SB最优性,但又不损失现代生成性训练技术的应用,我们表明,所产生的训练算法在MNIST、CelebA和CIFAR10上生成逼真的图像时取得了类似的结果。 Abstract: Schrödinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However, it remains unclear whether the optimization principle of SB relates to the modern training of deep generative models, which often rely on constructing log-likelihood objectives.This raises questions on the suitability of SB models as a principled alternative for generative applications. In this work, we present a novel computational framework for likelihood training of SB models grounded on Forward-Backward Stochastic Differential Equations Theory - a mathematical methodology appeared in stochastic optimal control that transforms the optimality condition of SB into a set of SDEs. Crucially, these SDEs can be used to construct the likelihood objectives for SB that, surprisingly, generalizes the ones for SGM as special cases. This leads to a new optimization principle that inherits the same SB optimality yet without losing applications of modern generative training techniques, and we show that the resulting training algorithm achieves comparable results on generating realistic images on MNIST, CelebA, and CIFAR10.
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