  Tensor, an extension of the vector and matrix to the multi-dimensional case,
is a natural way to describe the N-ary relational data. Recently, tensor
decomposition methods have been introduced into N-ary relational data and
become state-of-the-art on embedding learning. However, the performance of
existing tensor decomposition methods is not as good as desired. First, they
suffer from the data-sparsity issue since they can only learn from the N-ary
relational data with a specific arity, i.e., parts of common N-ary relational
data. Besides, they are neither effective nor efficient enough to be trained
due to the over-parameterization problem. In this paper, we propose a novel
method, i.e., S2S, for effectively and efficiently learning from the N-ary
relational data. Specifically, we propose a new tensor decomposition framework,
which allows embedding sharing to learn from facts with mixed arity. Since the
core tensors may still suffer from the over-parameterization, we propose to
reduce parameters by sparsifying the core tensors while retaining their
expressive power using neural architecture search (NAS) techniques, which can
search for data-dependent architectures. As a result, the proposed S2S not only
guarantees to be expressive but also efficiently learns from mixed arity.
Finally, empirical results have demonstrated that S2S is efficient to train and
achieves state-of-the-art performance.
