title: How to modify backpropagation for a standard multilayer network including a scalar gain at each layer?
body: <p>Considering a standard multilayer network including a scalar gain at each layer. The net input at layer m would be computed as : 
  n^m = β^m [W^m α^m − 1 + b^m]</p>
  
  <p>where β^m is the scalar gain at layer m . This gain would be trained like the weights and biases of the network.</p>
  
  <p>How can I modify the backpropagation algorithm for this new network ?</p>
  
  <p>What would be a new equation added to update β^m ?</p>
  
  <p>This is an exercise from this <a href="http://hagan.okstate.edu/NNDesign.pdf" rel="nofollow noreferrer">book</a> .</p>
  
  <p>E11.13</p>
  
  <p>Neural Network Design (2nd Edition) - Martin T. Hagan, Howard B. Demuth, Mark H. Beale, Orlando De Jesus</p>