Learning Aggregation Functions
This work provides a more flexible and powerful aggregation mechanism for machine learning practitioners working with set-structured data, improving performance over existing methods.
The paper introduces a learnable aggregation function (LAF) for sets of arbitrary cardinality to address limitations of fixed aggregation functions like sum or maximum. LAF can approximate various aggregators and complex functions, outperforming state-of-the-art sum- and max-decomposition architectures and combining effectively with attention-based architectures.
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.