Abstract. Large numeric matrices and multidimensional data arrays appear in many science domains, as well as in applications of financial and business warehousing. Common applications include eigenvalue determination of large matrices, which decompose into a set of linear algebra operations. With the rise of in-memory databases it is now feasible to execute these complex analytical queries directly in the database without being restricted by hard disc latencies for random accesses. In this paper, we present a way to integrate linear algebra operations and large matrices as first class citizens into an in-memory database following a two-layered architectural model. The architecture consists of a logical component receiving manipulation statements and linear algebra expressions, and of a physical layer, which autonomously administrates multiple matrix storage representations. A cost-based hybrid storage representation is presented and an experimental implementation is evaluated for matrix-vector multiplications.
Since out-of-distribution generalization is a generally ill-posed problem, various proxy targets (e.g., calibration, adversarial robustness, algorithmic corruptions, invariance across shifts) were studied across different research programs resulting in different recommendations. While sharing the same aspirational goal, these approaches have never been tested under the same experimental conditions on real data. In this paper, we take a unified view of previous work, highlighting message discrepancies that we address empirically, and providing recommendations on how to measure the robustness of a model and how to improve it. To this end, we collect 172 publicly available dataset pairs for training and out-of-distribution evaluation of accuracy, calibration error, adversarial attacks, environment invariance, and synthetic corruptions. We fine-tune over 31k networks, from nine different architectures in the many-and few-shot setting. Our findings confirm that in-and out-of-distribution accuracies tend to increase jointly, but show that their relation is largely dataset-dependent, and in general more nuanced and more complex than posited by previous, smaller scale studies.
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