论文标题
几何丰富的潜在空间
Geometrically Enriched Latent Spaces
论文作者
论文摘要
生成模型中的一个常见假设是，发电机将潜在空间浸入欧几里得环境空间中。取而代之的是，我们将环境空间视为Riemannian歧管，它允许通过相关的Riemannian指标编码域知识。然后可以在潜在空间中相应地定义最短路径，以遵循学习的歧管并尊重环境几何形状。通过仔细设计环境指标，我们可以确保最短的路径即使对于确定性发电机，否则就会表现出误导性偏见。在实验上，我们表明我们的方法可以使用随机和确定性发生器来提高学习表示的解释性。
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.
