  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.
