A network that uses parametric weights

A conventional weight in an artificial neural network has a single trainable real value and produces a linear relationship between the weight input and the weight output. A real synaptic cleft is also trainable but provides a more complex relationship. It is obvious to wonder if adding extra complexity to the conventional weight response would lead to more capable networks. This work describes a weight with a trainable nonlinear relationship and how this may be used in an artificial neural network. As well as describing how a network with such weights should be trained, some initial proof-of-concept results are presented along with comments on practicalities of using such networks.