E.g. is it possible to solve the XOR problem without backpropagation. If so, what would a solution look like?
Purpose of Backpropagation is to optimize the bias of each hidden layer and the weights on the connecting neurons. So without backpropagation you can solve the problem but you won't be getting correct results. following link may be useful: https://datascience.stackexchange.com/questions/11589/creating-neural-net-for-xor-function