{"type":"ScholarlyArticle","title":"Learning Aggregation Functions","authors":[{"name":"Giovanni Pellegrini","slug":"giovanni-pellegrini","given":"Giovanni","family":"Pellegrini","affiliation":""},{"name":"Alessandro Tibo","slug":"alessandro-tibo","given":"Alessandro","family":"Tibo","affiliation":""},{"name":"Paolo Frasconi","slug":"paolo-frasconi","given":"Paolo","family":"Frasconi","affiliation":""},{"name":"Andrea Passerini","slug":"andrea-passerini","given":"Andrea","family":"Passerini","affiliation":""},{"name":"Manfred Jaeger","slug":"manfred-jaeger","given":"Manfred","family":"Jaeger","affiliation":""}],"abstract":"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 Function), 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, and can be effectively combined with attention-based architectures.","doi":"10.24963/ijcai.2021/398","url":"https://ijcai.org/proceedings/2021/398","pdf":"https://ijcai.org/proceedings/2021/0398.pdf","markdown":"https://ijcai.org/proceedings/2021/398.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/398","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Machine Learning","track":"Main Track","number":398,"pages":{"first":2892,"last":2898},"keywords":["Machine Learning: Deep Learning","Machine Learning: Relational Learning","Machine Learning: Multi-instance; Multi-label; Multi-view learning"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}