  Collaborative filtering (CF) is a long-standing problem of recommender
systems. Many novel methods have been proposed, ranging from classical matrix
factorization to recent graph convolutional network-based approaches. After
recent fierce debates, researchers started to focus on linear graph
convolutional networks (GCNs) with a layer combination, which show
state-of-the-art accuracy in many datasets. In this work, we extend them based
on neural ordinary differential equations (NODEs), because the linear GCN
concept can be interpreted as a differential equation, and present the method
of Learnable-Time ODE-based Collaborative Filtering (LT-OCF). The main novelty
in our method is that after redesigning linear GCNs on top of the NODE regime,
i) we learn the optimal architecture rather than relying on manually designed
ones, ii) we learn smooth ODE solutions that are considered suitable for CF,
and iii) we test with various ODE solvers that internally build a diverse set
of neural network connections. We also present a novel training method
specialized to our method. In our experiments with three benchmark datasets,
Gowalla, Yelp2018, and Amazon-Book, our method consistently shows better
accuracy than existing methods, e.g., a recall of 0.0411 by LightGCN vs. 0.0442
by LT-OCF and an NDCG of 0.0315 by LightGCN vs. 0.0341 by LT-OCF in
Amazon-Book. One more important discovery in our experiments that is worth
mentioning is that our best accuracy was achieved by dense connections rather
than linear connections.
