Learning representations of entities and relations in structured knowledge bases is an active area of research, with much emphasis placed on choosing the appropriate geometry to capture the hierarchical structures exploited in, for example, isa or ha
spart relations. Box embeddings (Vilnis et al., 2018; Li et al., 2019; Dasgupta et al., 2020), which represent concepts as n-dimensional hyperrectangles, are capable of embedding hierarchies when training on a subset of the transitive closure. In Patel et al., (2020), the authors demonstrate that only the transitive reduction is required and further extend box embeddings to capture joint hierarchies by augmenting the graph with new nodes. While it is possible to represent joint hierarchies with this method, the parameters for each hierarchy are decoupled, making generalization between hierarchies infeasible. In this work, we introduce a learned box-to-box transformation that respects the structure of each hierarchy. We demonstrate that this not only improves the capability of modeling cross-hierarchy compositional edges but is also capable of generalizing from a subset of the transitive reduction.
Recent advances in NLP systems, notably the pretraining-and-finetuning paradigm, have achieved great success in predictive accuracy. However, these systems are usually not well calibrated for uncertainty out-of-the-box. Many recalibration methods hav
e been proposed in the literature for quantifying predictive uncertainty and calibrating model outputs, with varying degrees of complexity. In this work, we present a systematic study of a few of these methods. Focusing on the text classification task and finetuned large pretrained language models, we first show that many of the finetuned models are not well calibrated out-of-the-box, especially when the data come from out-of-domain settings. Next, we compare the effectiveness of a few widely-used recalibration methods (such as ensembles, temperature scaling). Then, we empirically illustrate a connection between distillation and calibration. We view distillation as a regularization term encouraging the student model to output uncertainties that match those of a teacher model. With this insight, we develop simple recalibration methods based on distillation with no additional inference-time cost. We show on the GLUE benchmark that our simple methods can achieve competitive out-of-domain (OOD) calibration performance w.r.t. more expensive approaches. Finally, we include ablations to understand the usefulness of components of our proposed method and examine the transferability of calibration via distillation.
