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This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass frequencies coefficients for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds high-frequency information at different scales. Compared to ReLU, shrinkage activation improves model performance on denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with well-preserved prediction performance.
We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neu
Graph neural networks are emerging as continuation of deep learning success w.r.t. graph data. Tens of different graph neural network variants have been proposed, most following a neighborhood aggregation scheme, where the node features are updated v
While many existing graph neural networks (GNNs) have been proven to perform $ell_2$-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via $ell_1$-based graph smoot
Chemical kinetics consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize feed-forward artificial neural networks
As large-scale graphs become increasingly more prevalent, it poses significant computational challenges to process, extract and analyze large graph data. Graph coarsening is one popular technique to reduce the size of a graph while maintaining essent