ARTICLE Thimm-96.1/IDIAP The Interchangeability of Learning Rate and Gain in Backpropagation Neural Networks Thimm, Georg Moerland, Perry Fiesler, Emile (adaptive) learning rate activation function adaptive steepness backpropagation bias connectionism gain initial weight multilayer neural network neural computation neural computing neural network neurocomputing optical implementation sigmoid steepness slope EXTERNAL http://publications.idiap.ch/attachments/reports/1996/gain96.pdf PUBLIC Neural Computation 8 02 451-460 0899-7667 1996 The backpropagation algorithm is widely used for training multilayer neural networks. In this publication the gain of its activation function(s) is investigated. In specific, it is proven that changing the gain of the activation function is equivalent to changing the learning rate and the weights. This simplifies the backpropagation learning rule by eliminating one of its parameters. The theorem can be extended to hold for some well-known variations on the backpropagation algorithm, such as using a momentum term, flat spot elimination, or adaptive gain. Furthermore, it is successfully applied to compensate for the non-standard gain of optical sigmoids for optical neural networks.