Why back propagation goes backward (gregorygundersen.com)

A recent exploration into the backpropagation algorithm has clarified why it operates in reverse, enhancing our understanding of a core technique in neural network training. Traditionally, backpropagation has been framed as propagating errors backward through a network, but this analysis suggests that a forward propagation approach is suboptimal due to computational inefficiencies. The challenge arises because each node's output may depend on multiple downstream nodes, making it impossible to compute gradients earlier in the graph without access to those dependencies. As a result, attempting to use a forward pass would require recalculating the same gradients repeatedly, leading to a potential quadratic increase in computation time. This insight into why backpropagation uses a backward pass is significant for the AI/ML community, as it highlights the algorithm's efficiency in handling the relationships between nodes in a directed acyclic graph. By leveraging the multivariable chain rule and focusing on local computations at each node, backpropagation effectively reduces the complexity of computing gradients to linear time. This foundational understanding not only reinforces the rationale behind backpropagation but also offers a clearer perspective on the underlying mechanics of neural network training.