THE DYNAMICS OF HEBBIAN SYNAPSES CAN BE STABILIZED BY A NONLINEAR DECAY TERM

In the field of neural networks, the dynamics of the connections (synapses) between neurones are often assumed to follow Hebb's rule. The corresponding differential equations are, however, unstable; stability is usually achieved by introducing a subsequent step of normalization or saturation. Here we propose a nonlinear decay term in the equation describing the dynamics of synaptical strengths. With this term the dynamics of synapses becomes intrinsically stable and subsequent normalization is not needed.