Neural Networks

The base element of a neural network model, a Formal Neuron [6], computes

$$y(\bf x, w\mit) = g(\bf x\cdot w\mit)$$ (7)

the inner product of its input vector ${\bf x}=(x_0, x_1, \dots, x_n)^\top$ and its synaptic weight vector ${\bf w}=(w_0, w_1, \dots, w_n)^\top$ which then goes through activation function g to yield neuron's output y. The input x₀=1, and the corresponding synaptic weight w₀ is called the threshold of the neuron. As activation function g, either Heaviside (step) function or a sigmoid function is commonly used.

A Neural Network Model [7] is an interconnection of neurons. IFSs describe recurrent models. To be more precise, they describe binary recurrent asymmetric neural networks.