that's not what backpropagation is. Backpropagation is best thought of as a 'cheat' (algorithmic simplification) that allows you to calculate the derivative of a feed-forward neural net. You would need to calculate the derivative of a neural net in general to optimize relative to some cost function, you could use, for example, gradient descent, but that is computationally costly.

For some neural nets, you still have a gradient, but the concept of back or forward propagation is not defineable. Based on the topology and structure of biological neural nets, what would you think is the case?