Probabilistic Word Embeddings in Kinematic Space

In this paper, we propose a method for learning representations in the space of Gaussian-like distribution defined on a novel geometrical space called Kinematic space. The utility of non-Euclidean geometry for deep representation learning has recently been in vogue, specifically models of hyperbolic geometry such as Poincaré and Lorentz models have proven useful for learning hierarchical representations. Going beyond manifolds with constant curvature, albeit has better representation capacity might lead to unhanding of computationally tractable tools like Riemannian optimization methods. Here, we explore a pseudo-Riemannian auxiliary Lorentzian space called Kinematic space and provide a principled approach for constructing a Gaussian-like distribution, which is compatible with gradient-based learning methods, to formulate a probabilistic word embedding framework. Contrary to, mapping lexically distributed representations to a single point vector in Euclidean space, we advocate for mapping entities to density-based representations, as it provides explicit control over the uncertainty in representations. We test our framework by embedding WordNet-Noun hierarchy, a large lexical database, our experiments report strong consistent improvements in Mean Rank and Mean Average Precision (MAP) values compared to probabilistic word embedding frameworks defined on Euclidean and hyperbolic spaces. We show an average improvement of 72.68% in MAP and 82.60% in Rank compared to the hyperbolic version. Our work serves as evidence for the utility of novel geometrical spaces for learning hierarchical representations.