On the other hand this method requires little more added complexity to the network than it already has. Each element requires a bias, an error signal, and the desired final output, these things being uniform for all elements in a network. Some external device must manipulate the bias properly, but this is a simple behavior depending only on an error signal and the desired final output—not on the state of individual elements in the network. What one has, then, is a network consisting of elements which are nearly autonomous as regards their decisions to change weights. Such a scheme appears to be the only way to avoid constructing a central weight-change decision apparatus of great complexity. This rather sophisticated decision is made possible by utilizing the computational capabilities the network already possesses in producing outputs from inputs. It should be noted here that this varying bias method requires that the variable bias be furnished to just those elements which have variable weights and to no others. Any fixed portion of the network, such as preliminary layers or final majority function for example, must operate independently of the variable bias. Otherwise, the final output may go from right to wrong as the bias moves towards zero and no variable-weight element be to blame. In such a case the network would be hung up. Logical Redundancy in the Network A third aspect of the network model is that for all the care taken in the previous steps, they will not suffice in settling quickly to a set of weights that will generate the required logical function unless there is a great multiplicity of ways in which this can be done. This is to say that a learning network needs to have an excess margin of weights and elements beyond the minimum required to generate the functions which are to be learned. This is analogous to the situation that prevails for a single element as regards the allowed range of values on its weights. It can be shown for example, that any function for n=6 that can be generated by a single element can be obtained with each weight restricted to the range of integer values -9,-8, ..., +9. Yet no modification of the stated weight change rule is known which restricts weight values to these and yet has any chance of ever being learned for most functions. Fatigued Elements