  Backpropagation (BP) has been pivotal in advancing machine learning and
remains essential in computational applications and comparative studies of
biological and artificial neural networks. Despite its widespread use, the
implementation of BP in the brain remains elusive, and its biological
plausibility is often questioned due to inherent issues such as the need for
symmetry of weights between forward and backward connections, and the
requirement of distinct forward and backward phases of computation. Here, we
introduce a novel neuroplasticity rule that offers a potential mechanism for
implementing BP in the brain. Similar in general form to the classical Hebbian
rule, this rule is based on the core principles of maintaining the balance of
excitatory and inhibitory inputs as well as on retrograde signaling, and
operates over three progressively slower timescales: neural firing, retrograde
signaling, and neural plasticity. We hypothesize that each neuron possesses an
internal state, termed credit, in addition to its firing rate. After achieving
equilibrium in firing rates, neurons receive credits based on their
contribution to the E-I balance of postsynaptic neurons through retrograde
signaling. As the network's credit distribution stabilizes, connections from
those presynaptic neurons are strengthened that significantly contribute to the
balance of postsynaptic neurons. We demonstrate mathematically that our
learning rule precisely replicates BP in layered neural networks without any
approximations. Simulations on artificial neural networks reveal that this rule
induces varying community structures in networks, depending on the learning
rate. This simple theoretical framework presents a biologically plausible
implementation of BP, with testable assumptions and predictions that may be
evaluated through biological experiments.
