  Learning on sets is increasingly gaining attention in the machine learning
community, due to its widespread applicability. Typically, representations over
sets are computed by using fixed aggregation functions such as sum or maximum.
However, recent results showed that universal function representation by sum-
(or max-) decomposition requires either highly discontinuous (and thus poorly
learnable) mappings, or a latent dimension equal to the maximum number of
elements in the set. To mitigate this problem, we introduce LAF (Learning
Aggregation Functions), a learnable aggregator for sets of arbitrary
cardinality. LAF can approximate several extensively used aggregators (such as
average, sum, maximum) as well as more complex functions (e.g. variance and
skewness). We report experiments on semi-synthetic and real data showing that
LAF outperforms state-of-the-art sum- (max-) decomposition architectures such
as DeepSets and library-based architectures like Principal Neighborhood
Aggregation.
