The explanation of gradient descent as a method for minimizing the loss function is provided here. It introduces the concept of the gradient as a vector pointing in the direction of the steepest ascent of the loss function, and how moving in the opposite direction (negative gradient) helps decrease the loss and improve model accuracy. The general case for any neuron and dataset is also introduced. This segment tackles the problem of zero gradients in classification using step functions and introduces the sigmoid activation function as a smooth approximation. It explains the sigmoid function's behavior, its derivative, and how using it solves the zero-gradient issue, enabling gradient descent for classification problems. This segment meticulously derives the partial derivatives of the loss function with respect to an arbitrary weight and the bias. It uses the chain rule and clarifies the mathematical steps involved, leading to a formula for calculating the gradient that is applicable to both regression and classification problems. The concept of error in each data point is also introduced. A single neuron computes by weighting inputs, adding bias, and applying an activation function (step for binary classification, linear for regression). Loss is measured using mean squared error (MSE), minimized via gradient descent. The gradient, a vector of partial derivatives (one per parameter), indicates the direction of steepest ascent; moving opposite this direction improves the model. For classification, a sigmoid activation function replaces the step function to enable gradient calculation.
