We study the problem of learning a hypergraph via edge detecting queries. In this problem, a learner queries subsets of vertices of a hidden hypergraph and observes whether these subsets contain an edge or not. In general, learning a hypergraph with $m$ edges of maximum size $d$ requires $\Omega((2m/d)^{d/2})$ queries. In this paper, we aim to identify families of hypergraphs that can be learned without suffering from a query complexity that grows exponentially in the size of the edges. We show that hypermatchings and low-degree near-uniform hypergraphs with $n$ vertices are learnable with poly$(n)$ queries. For learning hypermatchings (hypergraphs of maximum degree $ 1$), we give an $O(\log^3 n)$-round algorithm with $O(n \log^5 n)$ queries. We complement this upper bound by showing that there are no algorithms with poly$(n)$ queries that learn hypermatchings in $o(\log \log n)$ adaptive rounds. For hypergraphs with maximum degree $\Delta$ and edge size ratio $\rho$, we give a non-adaptive algorithm with $O((2n)^{\rho \Delta+1}\log^2 n)$ queries. To the best of our knowledge, these are the first algorithms with poly$(n, m)$ query complexity for learning non-trivial families of hypergraphs that have a super-constant number of edges of super-constant size.

翻译：我们研究通过边检测查询学习超图的问题。在此问题中，学习者查询隐藏超图的顶点子集，并观察这些子集是否包含边。一般而言，学习具有$m$条边且最大规模为$d$的超图需要$\Omega((2m/d)^{d/2})$次查询。本文旨在识别能够以不随边规模指数增长的查询复杂度进行学习的超图族。我们证明具有$n$个顶点的超匹配与低度近均匀超图可通过多项式$(n)$次查询学习。对于超匹配（最大度为$ 1$的超图）的学习，我们给出一个$O(\log^3 n)$轮算法，其查询次数为$O(n \log^5 n)$。我们通过证明不存在能以多项式$(n)$次查询在$o(\log \log n)$自适应轮内学习超匹配的算法，对此上界进行了补充。对于最大度为$\Delta$且边规模比为$\rho$的超图，我们给出一个非自适应算法，其查询次数为$O((2n)^{\rho \Delta+1}\log^2 n)$。据我们所知，这是首个能以多项式$(n, m)$查询复杂度学习具有超常数规模边且边数为超常数的非平凡超图族的算法。