Most graph neural networks ({GNNs}) utilize approximations of the general graph convolution derived in the graph Fourier domain. While {GNNs} are typically applied in the multi-input multi-output ({MIMO}) case, the approximations are performed in the single-input single-output ({SISO}) case. In this work, we first derive the {MIMO} graph convolution through the convolution theorem and approximate it directly in the {MIMO} case. We find the key {MIMO}-specific property of the graph convolution to be operating on multiple computational graphs, or equivalently, applying distinct feature transformations for each pair of nodes. As a localized approximation, we introduce localized {MIMO} graph convolutions ({LMGCs}), which generalize many linear message-passing neural networks. For almost every choice of edge weights, we prove that {LMGCs} with a single computational graph are injective on multisets, and the resulting representations are linearly independent when more than one computational graph is used. Our experimental results confirm that an {LMGC} can combine the benefits of various methods.<\/p>\n","protected":false},"excerpt":{"rendered":"
Most graph neural networks ({GNNs}) utilize approximations of the general graph convolution derived in the graph Fourier domain. While {GNNs} are typically applied in the multi-input multi-output ({MIMO}) case, the approximations are performed in the single-input single-output ({SISO}) case. In this work, we first derive the {MIMO} graph convolution through the convolution theorem and approximate it directly in the {MIMO} case. We find the key {MIMO}-specific property of the graph […]<\/p>\n","protected":false},"author":12,"featured_media":0,"template":"","meta":{"_acf_changed":false,"footnotes":""},"publication-type":[32],"class_list":["post-36765","publication","type-publication","status-publish","hentry","publication-type-inproceedings"],"acf":[],"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/36765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/types\/publication"}],"author":[{"embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":0,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/36765\/revisions"}],"wp:attachment":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/media?parent=36765"}],"wp:term":[{"taxonomy":"publication-type","embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication-type?post=36765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}