MainThe credit assignment problem1 lies at the very heart of learning. Backpropagation2, as a simple yet effective credit assignment theory, has powered notable advances in artificial intelligence since its inception3,4,5 and has also gained a predominant place in understanding learning in the brain1,6,7,8. Due to this success, much recent work has focused on understanding how biological neural networks could learn in a way similar to backpropagation9,10,11,12; although many proposed models do n...