Neural Network Backpropagation (DL 08) | Highlights and Annotations by Gistr.

The backpropagation algorithm for training a neural network involves three steps: a feedforward pass to make predictions, a backward pass to compute partial derivatives of the loss function, and a final pass to modify network parameters using these derivatives to update weights and biases. This segment clearly outlines the core process. Backpropagation uses stochastic gradient descent to train neural networks. It involves a feedforward pass (prediction), a backward pass (calculating partial derivatives using "deltas" for each node), and a parameter update step (adjusting weights and biases based on deltas). Deltas are computed recursively, starting from the output layer and propagating backward. Stochastic gradient descent uses random data subsets for faster, approximate gradient calculations. This segment focuses on the detailed calculation of "delta" values for both output and hidden layer neurons. It explains how the weighted sum of inputs affects the loss function and demonstrates the application of the chain rule in the backward pass to compute these crucial values. This segment explains the crucial role of computing the "delta" quantity for each neuron in determining how the network's weights influence the loss function. It details the relationship between the partial derivative of the loss on a single data point and the partial derivative of the loss on the entire dataset, laying the groundwork for the backward pass. This segment explains how to use the calculated deltas to obtain the partial derivatives for weights and biases. It shows how to derive these derivatives, first for a single data point and then for the entire dataset by averaging, providing a complete picture of gradient calculation.This segment explains the practical application of the backpropagation algorithm using stochastic gradient descent. It contrasts exact gradient descent with stochastic gradient descent, highlighting the efficiency of the latter for large datasets and detailing the steps involved in a stochastic gradient descent update.