We now extend the definitions to tests that can produce one of r different values rather than just 2 values. In this case, the learning problem can be expressed by learning matrix M:A×X→{ωj∣j∈{0,1,…,r−1}} where ω=e2πi/r is a primitive r-th root of u…

Several possibilities remain open for future work. First, more attributes could be collected and evaluated, possibly integrating other linguistic theories about verbs. Second, future work could move beyond using attributes as a pivot between languag…

In this section, we study lower-bounds on the approximation ratio and size of the composable core-sets for the k-determinant maximization and the experimental design problem. In particular, we prove Theorem 1.2.We also prove the bound given by 6.7 i…

We have thoroughly examined data-driven models for automatically solving algebra word problems, including retrieval, classification, and generation techniques. We find that a well-tuned classifier outperforms generation and retrieval on several data…

In this paper, we considered the problem of finding second order stationary points with a stochastic gradient oracle, and presented the first result with linear dependence on dimension. In the special case where the stochastic gradients are Lipschit…