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I have implemented backpropagation algorithm for neural network. The neural network is trained using online stochastic gradient descent. (with regularization). I have used a separate training and validation data sets. would like to know the how to determine the optimum number of epochs. Thanks

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Empirically. People typically define a patience, i.e. the number of epochs to wait before early stop if no progress on the validation set. The patience is often set somewhere between 10 and 100 (10 or 20 is more common), but it really depends on your dataset and network.

Example with patience = 10:

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