Learning Graph ODE for Continuous-Time Sequential Recommendation

TL;DR

The paper tackles the challenge of sequential recommendation under irregular sampling by modeling continuous-time dynamics of user-item interactions. It introduces GDERec, a principled autoregressive graph ODE framework with two specialized GNNs: an edge-evolving ODE-based module for implicit temporal evolution and a temporal attention network for explicit aggregation, trained alternately on hybrid dynamic graphs. Key contributions include the formulation of a hybrid dynamic interaction system, a trainable time encoding, and an autoregressive propagation scheme that optimizes with BPR loss. Empirical results on five real-world datasets show consistent, significant gains over state-of-the-art baselines, validating the method’s ability to handle irregular sampling and evolving collaborative signals with practical impact for continuous-time recommendations.

Abstract

Sequential recommendation aims at understanding user preference by capturing successive behavior correlations, which are usually represented as the item purchasing sequences based on their past interactions. Existing efforts generally predict the next item via modeling the sequential patterns. Despite effectiveness, there exist two natural deficiencies: (i) user preference is dynamic in nature, and the evolution of collaborative signals is often ignored; and (ii) the observed interactions are often irregularly-sampled, while existing methods model item transitions assuming uniform intervals. Thus, how to effectively model and predict the underlying dynamics for user preference becomes a critical research problem. To tackle the above challenges, in this paper, we focus on continuous-time sequential recommendation and propose a principled graph ordinary differential equation framework named GDERec. Technically, GDERec is characterized by an autoregressive graph ordinary differential equation consisting of two components, which are parameterized by two tailored graph neural networks (GNNs) respectively to capture user preference from the perspective of hybrid dynamical systems. The two customized GNNs are trained alternately in an autoregressive manner to track the evolution of the underlying system from irregular observations, and thus learn effective representations of users and items beneficial to the sequential recommendation. Extensive experiments on five benchmark datasets demonstrate the superiority of our model over various state-of-the-art recommendation methods.

Figures (8)

• Figure 1: A toy example of observations sampled at different time intervals. Different time sampling intervals typically imply different user preferences.
• Figure 2: Illustration of the proposed framework GDERec. We propose an autoregressive framework that propagates on a hybrid dynamic interaction system. A basic unit of our framework is composed of two modules. The fed node representations from previous layers are first processed via an ODE-based edge evolving module to generate $H_{t_k}^+$. Then a temporal attention module aggregates neighborhood information to generate $H_{t_{k+1}}$ to be fed into the next layer.
• Figure 3: Performance comparison w.r.t. different types of temporal encoding functions.
• Figure 4: Performance comparison w.r.t. different settings of the number of pivot timestamps $K$.
• Figure 5: Performance comparison w.r.t. model depth. For our GDERec, we define the depth of the edge evolving module by the number of steps the ODE solver takes to calculate the numerical solution. In other words, the little the step size is, the deeper GDERec is.

Theorems & Definitions (2)

• Proof 4.1
• Proof 4.2