论文标题
通过可区分的镶嵌的半分化归一流流量
Semi-Discrete Normalizing Flows through Differentiable Tessellation
论文作者
论文摘要
离散和连续分布之间的映射是一项艰巨的任务，许多人不得不求助于启发式方法。我们提出了一种基于镶嵌的方法，该方法可以直接学习连续空间中的量化边界，并具有精确的可能性评估。这是通过使用具有有效的对数决定性雅各布式的简单同态形态来构建凸多属的归一化流程来完成的。我们在两个应用程序设置中探索了这种方法，从离散到连续的映射，反之亦然。首先，Voronoi的消除化允许在多维空间中自动学习量化边界。边界的位置和区域之间的距离可以编码量化离散值之间有用的结构关系。其次，无论混合组件的数量如何，Voronoi混合模型的可能性评估的近恒定计算成本。从经验上讲，我们显示了对一系列结构化数据模式的现有方法的改进。
Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space, complete with exact likelihood evaluations. This is done through constructing normalizing flows on convex polytopes parameterized using a simple homeomorphism with an efficient log determinant Jacobian. We explore this approach in two application settings, mapping from discrete to continuous and vice versa. Firstly, a Voronoi dequantization allows automatically learning quantization boundaries in a multidimensional space. The location of boundaries and distances between regions can encode useful structural relations between the quantized discrete values. Secondly, a Voronoi mixture model has near-constant computation cost for likelihood evaluation regardless of the number of mixture components. Empirically, we show improvements over existing methods across a range of structured data modalities.
