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While studying about neural networks (still on basics - not Deep Learning etc.,) two questions came on my mind.

  • What is the reason for replacing the hard limiter function in the nodes of the multilayer perceptrons (MLPs) with smoother ones?

  • Does the Back propagation algorithm always find the best possible solution for the classification problem at hand?

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  • Smooth functions has well-defined derivatives and suitable for back-propagation algorithm. There are also non-smooth ones, such as ReLU, widely used for this purpose; however, they're piecewise differentiable, while the hard-limiter function is not.

  • Back-propagation algorithm doesn't find the best solution. It is actually gradient descent, and it finds you a local optimum. Sometimes, this might be the global optimum, but frequently it is not due to the sheer size of search space.And, not all local minima are bad.

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