  Graph Neural Network (GNN) architectures are defined by their implementations
of update and aggregation modules. While many works focus on new ways to
parametrise the update modules, the aggregation modules receive comparatively
little attention. Because it is difficult to parametrise aggregation functions,
currently most methods select a ``standard aggregator'' such as
$\mathrm{mean}$, $\mathrm{sum}$, or $\mathrm{max}$. While this selection is
often made without any reasoning, it has been shown that the choice in
aggregator has a significant impact on performance, and the best choice in
aggregator is problem-dependent. Since aggregation is a lossy operation, it is
crucial to select the most appropriate aggregator in order to minimise
information loss. In this paper, we present GenAgg, a generalised aggregation
operator, which parametrises a function space that includes all standard
aggregators. In our experiments, we show that GenAgg is able to represent the
standard aggregators with much higher accuracy than baseline methods. We also
show that using GenAgg as a drop-in replacement for an existing aggregator in a
GNN often leads to a significant boost in performance across various tasks.
