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I'm relatively new to neural networks and was wondering what an implementation of this paper would look like. More specifically, how are the correct values of Kp, Ki, and Kd determined at run time so it can be back propagated?

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In the paper there is a diagram of the network showing how there are 3 outputs which share features but have their own set of associated weights. Back propagation works by only looking at one output at a time. Network Architecture

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