  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 a learnable
aggregation function (LAF) 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, and can be
effectively combined with attention-based architectures.

Machine Learning