The training of the output units tries to minimize the sum-squared error E:
where 
is the desired and 
is the observed output of the
output unit o for a pattern p. The error E is minimized by gradient
decent using
where 
is the derivative of an activation function of a output unit
o and 
is the value of an input unit or a hidden unit i
for a pattern p. 
denominates the connection between an input or
hidden unit i and an output unit o.
After the training phase the candidate units are adapted, so that the
correlation C between the value 
of a candidate unit and the
residual error 
of an output unit becomes maximal. The
correlation is given by Fahlman with:
where 
is the average activation of a candidate unit and
is the average error of an output unit over all patterns
p. The maximization of C proceeds by gradient ascent using
where 
is the sign of the correlation between the candidate unit's
output and the residual error at output o.
