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Are there any toy classification problems that can't be solved with logistic regression, but can be solved with a NN with exactly one hidden node?

With exactly one hidden neuron, I believe the answer is no. The hidden neuron has one input and one output, and thus all it does is scale the final output by its activation function. Thus, it does not ...
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Are there any toy classification problems that can't be solved with logistic regression, but can be solved with a NN with exactly one hidden node?

With one hidden node, there is one single input to the output neuron. Therefore, the two neurons are equivalent to a single neuron with activation function the composition of the two activation ...

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