The main advantages of spiking neural networks are the high biological plausibility and their fast response due to spiking behaviour. The response time decreases significantly in the hardware implementation of SNN because the neurons operate in parallel. Compared with the traditional computational neural network, the SNN use a lower number of neurons, which also reduces their cost. Another critical characteristic of SNN is their ability to learn by event association that is determined mainly by postsynaptic mechanisms such as long-term potentiation. However, in some conditions, presynaptic plasticity determined by post-tetanic potentiation occurs due to the fast activation of presynaptic neurons. This violates the Hebbian learning rules that are specific to postsynaptic plasticity. Hebbian learning improves the SNN ability to discriminate the neural paths trained by the temporal association of events, which is the key element of learning in the brain. This paper quantifies the efficiency of Hebbian learning as the ratio between the LTP and PTP effects on the synaptic weights. On the basis of this new idea, this work evaluates for the first time the influence of the number of neurons on the PTP/LTP ratio and consequently on the Hebbian learning efficiency. The evaluation was performed by simulating a neuron model that was successfully tested in control applications. The results show that the firing rate of postsynaptic neurons post depends on the number of presynaptic neurons pre, which increases the effect of LTP on the synaptic potentiation. When post activates at a requested rate, the learning efficiency varies in the opposite direction with the number of pres, reaching its maximum when fewer than two pres are used. In addition, Hebbian learning is more efficient at lower presynaptic firing rates that are divisors of the target frequency of post. This study concluded that, when the electronic neurons additionally model presynaptic plasticity to LTP, the efficiency of Hebbian learning is higher when fewer neurons are used. This result strengthens the observations of our previous research where the SNN with a reduced number of neurons could successfully learn to control the motion of robotic fingers.
Keywords: Hebbian learning efficiency; long-term potentiation; post-tetanic potentiation; spiking neural networks.