Papers › Improving Local Identifiability in Probabilistic Box Embeddings

Improving Local Identifiability in Probabilistic Box Embeddings

9 Oct 2020NeurIPS 2020 12arXiv:2010.04831archive 2025-07-28

Shib Sankar Dasgupta, Michael Boratko, Dongxu Zhang, Luke Vilnis, Xiang Lorraine Li, Andrew McCallum

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly promising example of such an embedding as they are closed under intersection and their volume can be calculated easily, allowing them to naturally represent calibrated probability distributions. The benefits of geometric embeddings also introduce a problem of local identifiability, however, where whole neighborhoods of parameters result in equivalent loss which impedes learning. Prior work addressed some of these issues by using an approximation to Gaussian convolution over the box parameters, however, this intersection operation also increases the sparsity of the gradient. In this work, we model the box parameters with min and max Gumbel distributions, which were chosen such that space is still closed under the operation of the intersection. The calculation of the expected intersection volume involves all parameters, and we demonstrate experimentally that this drastically improves the ability of such models to learn.

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