Recent advances in open-domain QA have led to strong models based on dense retrieval, but only focused on retrieving textual passages. In this work, we tackle open-domain QA over tables for the first time, and show that retrieval can be improved by a retriever designed to handle tabular context. We present an effective pre-training procedure for our retriever and improve retrieval quality with mined hard negatives. As relevant datasets are missing, we extract a subset of NATURAL QUESTIONS (Kwiatkowski et al., 2019) into a Table QA dataset. We find that our retriever improves retrieval results from 72.0 to 81.1 recall@10 and end-to-end QA results from 33.8 to 37.7 exact match, over a BERT based retriever.

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Recent advances in open-domain QA have led to strong models based on dense retrieval, but only focused on retrieving textual passages. In this work, we tackle open-domain QA over tables for the first time, and show that retrieval can be improved by a retriever designed to handle tabular context. We present an effective pre-training procedure for our retriever and improve retrieval quality with mined hard negatives. As relevant datasets are missing, we extract a subset of NATURAL QUESTIONS (Kwiatkowski et al., 2019) into a Table QA dataset. We find that our retriever improves retrieval results from 72.0 to 81.1 recall@10 and end-to-end QA results from 33.8 to 37.7 exact match, over a BERT based retriever. * Work completed while interning at Google. S read ("Chlorine") S read (...) S read ("Latin")which element is named for the greek word for green? TAPAS q (q)List of chemical element name etymologies Element Origin Meaning ... Fluorine Latin a flowing ...

We consider the problem of projecting a vector onto the simplex ∆ = {x ∈ R d + : d i=1 xi = 1}, using a Bregman projection. This is a common problem in firstorder methods for convex optimization and online-learning algorithms, such as mirror descent. We derive the KKT conditions of the projection problem, and show that for Bregman divergences induced by ω-potentials, one can efficiently compute the solution using a bisection method. More precisely, anapproximate projection can be obtained in O(d log 1 ). We also consider a class of exponential potentials for which the exact solution can be computed efficiently, and give a O(d log d) deterministic algorithm and O(d) randomized algorithm to compute the projection. In particular, we show that one can generalize the KL divergence to a Bregman divergence which is bounded on the simplex (unlike the KL divergence), strongly convex with respect to the 1 norm, and for which one can still solve the projection in expected linear time.

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