text: 114,59,1407247333499285510,62044012,Michael Bronstein,"#GNNs are related to PDEs governing information diffusion on graphs. In a new paper with @b_p_chamberlain James Rowbottom @migorinova @stefan_webb @emaros96 we study a new class of Neural Graph Diffusion PDEs Blog post: <LINK> Paper: <LINK> <LINK> Thinking of GNNs as partial differential equations leads to a new broad class of GNNs that are able to address in a principled way some of the prominent issues of current Graph ML models such as depth, oversmoothing, bottlenecks, and graph rewiring. Popular GNNs can be formalized as discretized diffusion PDEs with explicit single-step Euler scheme, where an iteration corresponds to a GNN layer, and running the diffusion for multiple iterations amounts to applying a GNN layer multiple times. In Neural PDEs formalism, the diffusion time parameter acts as a continuous analogy of the layers—an interpretation allowing us to exploit more efficient and stable numerical schemes that use adaptive steps in time. It might be advantageous to decouple the graph used for diffusion from the input graph (or ""rewire"" the graph). The diffusion framework offers a principled view on graph rewiring by considering the graph as a spatial discretization of some continuous object (manifold). In particular, the popular GAT of @PetarV_93 is a nonlinear diffusion PDE with a learnable diffusivity function similar to the Perona-Malik diffusion model used in the 90s in image processing",https://arxiv.org/abs/2106.10934,"We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and spatial operators. Our approach allows a principled development of a broad new class of GNNs that are able to address the common plights of graph learning models such as depth, oversmoothing, and bottlenecks. Key to the success of our models are stability with respect to perturbations in the data and this is addressed for both implicit and explicit discretisation schemes. We develop linear and nonlinear versions of GRAND, which achieve competitive results on many standard graph benchmarks. ",GRAND: Graph Neural Diffusion,6,"['#GNNs are related to PDEs governing information diffusion on graphs. In a new paper with @b_p_chamberlain James Rowbottom @migorinova @stefan_webb @emaros96  we study a new class of Neural Graph Diffusion PDEs\n\nBlog post: <LINK>\n\nPaper: <LINK> <LINK>', 'Thinking of GNNs as partial differential equations leads to a new broad class of GNNs that are able to address in a principled way some of the prominent issues of current Graph ML models such as depth, oversmoothing, bottlenecks, and graph rewiring.', 'Popular GNNs can be formalized as discretized diffusion PDEs with explicit single-step Euler scheme, where an iteration corresponds to a GNN layer, and running the diffusion for multiple iterations amounts to applying a GNN layer multiple times.', 'In Neural PDEs formalism, the diffusion time parameter acts as a continuous analogy of the layers—an interpretation allowing us to exploit more efficient and stable numerical schemes that use adaptive steps in time.', 'It might be advantageous to decouple the graph used for diffusion from the input graph (or ""rewire"" the graph). The diffusion framework offers a principled view on graph rewiring by considering the graph as a spatial discretization of some continuous object (manifold).', 'In particular, the popular GAT of @PetarV_93 is a nonlinear diffusion PDE with a learnable diffusivity function similar to the Perona-Malik diffusion model used in the 90s in image processing']",21,06,1421