  Recently, it has been shown that many functions on sets can be represented by
sum decompositions. These decompositons easily lend themselves to neural
approximations, extending the applicability of neural nets to set-valued
inputs---Deep Set learning. This work investigates a core component of Deep Set
architecture: aggregation functions. We suggest and examine alternatives to
commonly used aggregation functions, including learnable recurrent aggregation
functions. Empirically, we show that the Deep Set networks are highly sensitive
to the choice of aggregation functions: beyond improved performance, we find
that learnable aggregations lower hyper-parameter sensitivity and generalize
better to out-of-distribution input size.
