Replacing activation-function derivatives with constant or random stand-ins trains small neural nets, but the paper's proof that gradient direction is unaffected is flawed.
Bottou, Stochastic gradient learning in neural networks, in: Proceedings of Neuro-N ˆımes 91, EC2, Nimes, France, 1991
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Breaking the Conventional Forward-Backward Tie in Neural Networks: Activation Functions
Replacing activation-function derivatives with constant or random stand-ins trains small neural nets, but the paper's proof that gradient direction is unaffected is flawed.