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.

We experimentally achieve a 19% capacity gain per Watt of electrical supply power in a 12-span link by eliminating gain flattening filters and optimizing launch powers using machine learning by deep neural networks in a massively parallel fiber context.

Given the joint distribution of a set of random variables (in the form of a Markov random field), we consider the problem of selecting a small subset of these variables to observe so as to accurately predict the remaining unobserved variables. We focus here on Gaussian processes(Rasmussen and Williams, 2006) on graphs, i.e., Gaussian Markov random fields(Gaussian MRFs). Our aim in this paper is to give a subset selection algorithm which, given a budget for the number of variables that can be observed, minimizes the expected squared prediction error averaged over all the variables. We are particularly interested in algorithms with provable guarantees on the prediction error. Our main focus is on Gaussian MRFs on trees and other treelike graphs, or to be precise, bounded tree-width graphs--such graphs have been widely studied in the context of inference, see, e.g., Sudderth (2002). We also consider a special class of Gaussian MRFs, called Gaussian free fields (or GFFs), which arise, among others, in computer vision, see, e.g., Szeliski (1990). We first explain the notation we use and formally state our problem before describing how our work relates to previous research.