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for a multi-layer neural network is stochastic gradient descent(SGD) guaranteed to reach a global optimum?

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It depends on the complexity of the data. If the data representation is enough for one hidden layer then yes, it is possible, or at least it'll be able to find the best solution possible.

If the dataset is highly dimensional then it's unlikely that the neural network reaches a good generalization of the problem. So a local optimum is probably the only conclusion that the network will be able to find.

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