  In the artificial neuron, I replace the dot product with the weighted Lehmer
mean, which may emulate different cases of a generalized mean. The single
neuron instance is replaced by a multiplet of neurons which have the same
averaging weights. A group of outputs feed forward, in lieu of the single
scalar. The generalization parameter is typically set to a different value for
each neuron in the multiplet.
  I further extend the concept to a multiplet taken from the Gini mean.
Derivatives with respect to the weight parameters and with respect to the two
generalization parameters are given.
  Some properties of the network are investigated, showing the capacity to
emulate the classical exclusive-or problem organically in two layers and
perform some multiplication and division. The network can instantiate truncated
power series and variants, which can be used to approximate different
functions, provided that parameters are constrained.
  Moreover, a mean case slope score is derived that can facilitate a
learning-rate novelty based on homogeneity of the selected elements. The
multiplet neuron equation provides a way to segment regularization timeframes
and approaches.
