The core principle is backpropagation via the chain rule calculus, which formalizes the sensitivity analysis of a loss function with respect to network parameters through multiplicative propagation of partial derivatives across layered compositions. In the domain of machine learning and artificial intelligence specifically neural networks, this mechanism relies on definitions involving activation functions (e.g., sigmoid), weighted sums ($z$), neuron activations ($a$), and cost differentials to construct gradient vectors required for optimization. The concept relates to its parent discipline by providing the mathematical foundation for computing gradients in multivariate nonlinear systems, enabling iterative descent algorithms to minimize error without explicit derivative computation at every point.
The core principle is backpropagation via the chain rule calculus, which formalizes the sensitivity analysis of a loss function with respect to network parameters through multiplicative propagation o…