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Graph neural networks (GNNs) are a powerful inductive bias for modelling algorithmic reasoning procedures and data structures. Their prowess was mainly demonstrated on tasks featuring Markovian dynamics, where querying any associated data structure depends only on its latest state. For many tasks of interest, however, it may be highly beneficial to support efficient data structure queries dependent on previous states. This requires tracking the data structures evolution through time, placing significant pressure on the GNNs latent representations. We introduce Persistent Message Passing (PMP), a mechanism which endows GNNs with capability of querying past state by explicitly persisting it: rather than overwriting node representations, it creates new nodes whenever required. PMP generalises out-of-distribution to more than 2x larger test inputs on dynamic temporal range queries, significantly outperforming GNNs which overwrite states.
The principal submatrix localization problem deals with recovering a $Ktimes K$ principal submatrix of elevated mean $mu$ in a large $ntimes n$ symmetric matrix subject to additive standard Gaussian noise. This problem serves as a prototypical exampl
This paper aims to unify spatial dependency and temporal dependency in a non-Euclidean space while capturing the inner spatial-temporal dependencies for spatial-temporal graph data. For spatial-temporal attribute entities with topological structure,
Graph neural networks (GNNs) emerged recently as a standard toolkit for learning from data on graphs. Current GNN designing works depend on immense human expertise to explore different message-passing mechanisms, and require manual enumeration to det
Constructing appropriate representations of molecules lies at the core of numerous tasks such as material science, chemistry and drug designs. Recent researches abstract molecules as attributed graphs and employ graph neural networks (GNN) for molecu
Graph Neural Network (GNN) has been demonstrated its effectiveness in dealing with non-Euclidean structural data. Both spatial-based and spectral-based GNNs are relying on adjacency matrix to guide message passing among neighbors during feature aggre