We propose a unified approach to obtain structured sparse optimal paths in the latent space of a variational autoencoder (VAE) using dynamic programming and Gumbel propagation. We solve the classical optimal path problem by a probability softening solution, called the stochastic optimal path, and transform a wide range of DP problems into directed acyclic graphs in which all possible paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference. Our approach obtaining latent optimal paths enables end-to-end training for generative tasks in which models rely on the information of unobserved structural features. We validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis.

翻译：我们提出一种统一的方法，通过动态规划和Gumbel传播在变分自编码器（VAE）的隐空间中获取结构化稀疏最优路径。采用概率软化解法（称为随机最优路径）求解经典最优路径问题，并将广泛动态规划问题转化为有向无环图，其中所有可能路径服从吉布斯分布。通过Gumbel分布的性质证明了吉布斯分布与消息传递算法的等价性，并给出变分贝叶斯推断所需的所有要素。本方法获取隐式最优路径的能力，使依赖未观测结构特征信息的生成任务能够实现端到端训练。我们验证了该方法的行为特性，并在两个实际应用场景中展示其可行性：语音合成与歌声合成。