Monotonic Constrained NEURAL NETWORK

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R L 2015-7-7

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评论： Orion Wolfe 2016-3-25

I am new at the Neural Network field. Please be explicit. I have two input neurons, one output target and two hidden neurons. I want the derivative with respect to the inputs and the bias are positive. Is there a trick to constraint the Neural Network so that the derivative of the neural network's outputs with respect to the input variable is positive and the bias is positive. I believe I want that the products of the weights and the biases along all paths to be positive as long as the activation function is monotonically increasing .

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Orion Wolfe 2016-3-25

Restrict all of the gains to be positive. This can be done by using a positive mapping on the gains. For example if the network is defined using tanh(w'*x+b) activation functions replace w with g(w) where g is R to R+ mapping g(w) = log(1+e^w) is one such mapping and the activation function become tanh(g(w)*x+b)

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Answer 1

Greg Heath 2015-7-8

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If the derivative of the target with respect to the input is positive, just design a good net with as few hidden nodes as possible. It may take a lot of trials.