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Large, pre-trained transformer language models, which are pervasive in natural language processing tasks, are notoriously expensive to train. To reduce the cost of training such large models, prior work has developed smaller, more compact models which achieves a significant speedup in training time while maintaining competitive accuracy to the original model on downstream tasks. Though these smaller pre-trained models have been widely adopted by the community, it is not known how well are they calibrated compared to their larger counterparts. In this paper, focusing on a wide range of tasks, we thoroughly investigate the calibration properties of pre-trained transformers, as a function of their size. We demonstrate that when evaluated in-domain, smaller models are able to achieve competitive, and often better, calibration compared to larger models, while achieving significant speedup in training time. Post-hoc calibration techniques further reduce calibration error for all models in-domain. However, when evaluated out-ofdomain, larger models tend to be better calibrated, and label-smoothing instead is an effective strategy to calibrate models in this setting. .

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Agents that communicate back and forth with humans to help them execute nonlinguistic tasks are a long sought goal of AI. These agents need to translate between utterances and actionable meaning representations that can be interpreted by task-specific problem solvers in a contextdependent manner. They should also be able to learn such actionable interpretations for new predicates on the fly. We define an agent architecture for this scenario and present a series of experiments in the Blocks World domain that illustrate how our architecture supports language learning and problem solving in this domain.

Stochastic Gradient Descent has been widely studied with classification accuracy as a performance measure. However, these stochastic algorithms cannot be directly used when nondecomposable pairwise performance measures are used such as Area under the ROC curve (AUC) which is a common performance metric when the classes are imbalanced. There have been several algorithms proposed for optimizing AUC as a performance metric, and one of the recent being a stochastic proximal gradient algorithm (SPAM). But the downside of the stochastic methods is that they suffer from high variance leading to slower convergence. To combat this issue, several variance reduced methods have been proposed with faster convergence guarantees than vanilla stochastic gradient descent. Again, these variance reduced methods are not directly applicable when non-decomposable performance measures are used. In this paper, we develop a Variance Reduced Stochastic Proximal algorithm for AUC Maximization (VRSPAM) and perform a theoretical analysis as well as empirical analysis to show that our algorithm converges faster than SPAM which is the previous state-of-the-art for the AUC maximization problem.