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Gregory Burnham

Publications and source records attributed to Gregory Burnham.

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To Test Machine Comprehension, Start by Defining Comprehension

Many tasks aim to measure machine reading comprehension (MRC), often focusing on question types presumed to be difficult. Rarely, however, do task designers start by considering what systems should in fact comprehend. In this paper we make two key contributions. First, we argue that existing approaches do not adequately define comprehension; they are too unsystematic about what content is tested. Second, we present a detailed definition of comprehension -- a "Template of Understanding" -- for a widely useful class of texts, namely short narratives. We then conduct an experiment that strongly suggests existing systems are not up to the task of narrative understanding as we define it.

cs.CL

Line arrangements modeling curves of high degree: equations, syzygies and secants

We study curves consisting of unions of projective lines whose intersections are given by graphs. Under suitable hypotheses on the graph, these so-called \emph{graph curves} can be embedded in projective space as line arrangements. We discuss property $N_p$ for these embeddings and are able to produce products of linear forms that generate the ideal in certain cases. We also briefly discuss questions regarding the higher-dimensional subspace arrangements obtained by taking the secant varieties of graph curves.

math.AG