LightCCN: Light Cell Complex Networks for Collaborative Filtering

Abstract

Graph-based collaborative filtering models achieve strong performance by propagating user and item embeddings over the bipartite interaction graph, but they represent only pairwise relations. Any pattern among three or more items has to be recovered through multi-hop propagation rather than modelled directly. Topological deep learning extends graphs with group-level cells, arranged in a hierarchy that connects a group to the pairs and items it is composed of, yet the framework is almost unexplored in recommendation. This thesis introduces LightCCN, a model that gives frequently co-consumed item triples their own learned representation, linked to the pairs and items they contain. Formally, it lifts the user-item interaction data to a cell complex of order 2, propagates embeddings at every order of the complex, and injects the pooled higher-order signal into user representations through a user-side readout. The design is challenging because the structure is not given in advance. Which groups deserve representation and how much structure a dataset supports are modelling choices. On the top-ranked metrics, LightCCN is significantly better than its graph-based counterpart on four of the six datasets and statistically tied on the rest, at almost no additional capacity. Controlled ablations attribute the gains to the readout rather than to higher-order propagation. Depth experiments show maintained or improved accuracy against the same-depth counterpart and no over-smoothing. The amount of admitted structure matters and differs per dataset, so it is exposed as a single control selected on validation data. The selection also removes the structure on the dataset where it hurts. Overall, the results show that higher-order structures improve collaborative filtering when given an explicit path to the user representations, with gains that concentrate at the top of the ranking, and that topological deep learning is an effective and interpretable framework for capturing them.