Why back propagation goes backward

Backpropagation computes neural network gradients by propagating errors backward through the network, but the key insight is that this backward approach is more efficient than a forward pass because of how the chain rule works. Using the multivariable chain rule, computing ∂f/∂v at each node requires summing contributions from all downstream nodes, making a backward pass optimal since it avoids redundant recalculation of these dependencies. The algorithm's backward direction emerges naturally from first principles when considering the computational efficiency needed to calculate gradients for all weights in a composite function.