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We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with static GNN models and is extended to dynamic and stochastic settings through hybrid dynamical system theory. Here, Neural GDEs improve performance by exploiting the underlying dynamics geometry, further introducing the ability to accommodate irregularly sampled data. Results prove the effectiveness of the proposed models across applications, such as traffic forecasting or prediction in genetic regulatory networks.
Continuous-depth neural models, where the derivative of the models hidden state is defined by a neural network, have enabled strong sequential data processing capabilities. However, these models rely on advanced numerical differential equation (DE) s
Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete dynamical int
Time-continuous emotion prediction has become an increasingly compelling task in machine learning. Considerable efforts have been made to advance the performance of these systems. Nonetheless, the main focus has been the development of more sophistic
Continuous deep learning architectures enable learning of flexible probabilistic models for predictive modeling as neural ordinary differential equations (ODEs), and for generative modeling as continuous normalizing flows. In this work, we design a f
Existing graph neural networks (GNNs) largely rely on node embeddings, which represent a node as a vector by its identity, type, or content. However, graphs with unlabeled nodes widely exist in real-world applications (e.g., anonymized social network