  We present the Graph Forward-Forward (GFF) algorithm, an extension of the
Forward-Forward procedure to graphs, able to handle features distributed over a
graph's nodes. This allows training graph neural networks with forward passes
only, without backpropagation. Our method is agnostic to the message-passing
scheme, and provides a more biologically plausible learning scheme than
backpropagation, while also carrying computational advantages. With GFF, graph
neural networks are trained greedily layer by layer, using both positive and
negative samples. We run experiments on 11 standard graph property prediction
tasks, showing how GFF provides an effective alternative to backpropagation for
training graph neural networks. This shows in particular that this procedure is
remarkably efficient in spite of combining the per-layer training with the
locality of the processing in a GNN.
