几何增广的潜空间
Geometrically Enriched Latent Spaces
摘要：
生成模型中的一个常见假设是生成器将潜在空间浸入到欧几里得环境空间中。相反，我们认为环境空间是一个黎曼流形，它允许通过相关的黎曼度量编码领域知识。然后，可以在潜在空间中相应地定义最短路径，以遵循学习的流形并尊重周围的几何形状。通过精心设计的环境度量，我们可以确保最短路径是良好的行为，即使是确定性的发电机，否则会表现出误导性的偏见。实验上，我们表明，我们的方法提高了可解释性的学习表示使用随机和确定性的发电机。
英文摘要：
A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through the associated Riemannian metric. Shortest paths can then be defined accordingly in the latent space to both follow the learned manifold and respect the ambient geometry. Through careful design of the ambient metric we can ensure that shortest paths are well-behaved even for deterministic generators that otherwise would exhibit a misleading bias. Experimentally we show that our approach improves interpretability of learned representations both using stochastic and deterministic generators.
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。
