A graph is build from nodes #x_i# (Dots representing objects) edges #A_ij# (Lines representing connections between those) A some nodes and some edges you can define functions (graph updates) on the nodes #Eq((x_i)**(t+1),s*(x_i)**(t)+n*(A_i)**(j)*(x_j)**(t))# (one attribute per node) here we used two parameters (two matrices for more attributes) #n# describing the interaction of the nodes with their neighbours #s# describing the self interaction of each node these two parameters are learnable in the network Also the Adjacency Matrix #A_ij# encodes which nodes are connected and which are not since the whole update step is local, the size of the graph does not matter: so with just two parameters you can describe arbitrary large graphs before graph update after update Convolutional networks with learnable meaning of locality Train on more general data Implicit bias making for example each #phi# be treated the same The currently best Top Tagger is a Graph Network (ParticleNet,arXiv:1902.08570) A Graph made from nodes and edges A Graph made from nodes and edges Node information can propagate through edges Node information can propagate through edges Node information can propagate through edges