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Training with backpropagation (BP) in standard deep learning consists of twomain steps: a forward pass that maps a data point to its prediction, and abackward pass that propagates the error of this prediction back through thenetwork. This process is highly effective when the goal is to minimize aspecific objective function. However, it does not allow training on networkswith cyclic or backward connections. This is an obstacle to reaching brain-likecapabilities, as the highly complex heterarchical structure of the neuralconnections in the neocortex are potentially fundamental for its effectiveness.In this paper, we show how predictive coding (PC), a theory of informationprocessing in the cortex, can be used to perform inference and learning onarbitrary graph topologies. We experimentally show how this formulation, calledPC graphs, can be used to flexibly perform different tasks with the samenetwork by simply stimulating specific neurons, and investigate how thetopology of the graph influences the final performance. We conclude bycomparing against simple baselines trained~with~BP.

Learning on Arbitrary Graph Topologies via Predictive Coding