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A simpler answer is that for a standard neural net, the asymptotic behaviour is the asymptotic behaviour of the output neurons. For example, if the output layer is ReLUs, then the asymptotic behaviour is necessarily linear. In your case, since you want it to be asymptotically constant, you can use the slightly old-fashioned choice of sigmoid units in the ...


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For standard NNs, their extrapolation behavior an important aspect for financial applications cannot be controlled due to complex functional forms typically involved. Neural Networks with Asymptotics Control discuss how they overcome this significant limitation and develop a new type of neural networks that incorporate large-value asymptotics, when known, ...


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