  Learning embedding spaces of suitable geometry is critical for representation
learning. In order for learned representations to be effective and efficient,
it is ideal that the geometric inductive bias aligns well with the underlying
structure of the data. In this paper, we propose Switch Spaces, a data-driven
approach for learning representations in product space. Specifically, product
spaces (or manifolds) are spaces of mixed curvature, i.e., a combination of
multiple euclidean and non-euclidean (hyperbolic, spherical) manifolds. To this
end, we introduce sparse gating mechanisms that learn to choose, combine and
switch spaces, allowing them to be switchable depending on the input data with
specialization. Additionally, the proposed method is also efficient and has a
constant computational complexity regardless of the model size. Experiments on
knowledge graph completion and item recommendations show that the proposed
switch space achieves new state-of-the-art performances, outperforming pure
product spaces and recently proposed task-specific models.
