Synaptic scaling as an essential component of Hebbian learning

Hebbian plasticity is a prominent learning mechanism for brain neural networks. However, its formal definition based on the time-matching of pre and postsynaptic activity can lead to a saturation of synaptic weights. On the one hand, the so-called forgetting function formally allows bounding the synaptic weights, but its biological basis remains unclear. On the other hand, biological neurons exhibit homeostatic plasticity, particularly synaptic scaling, which helps a neuron control (scale) the synaptic effectiveness across the synapses. This work proposes a mathematical model of Hebbian learning with synaptic scaling in a spiking neuron. Numerical simulations show that this biologically justified model exhibits behavior similar to the standard model with the forgetting function. We illustrate the results in a test-bed problem of learning frequency patterns by a high-dimensional neuron.