Calculus

Calculus, specifically differential calculus, is the mathematical engine that drives the process of 'learning' in many machine learning models. The core idea behind training an ML model is optimization. We define a 'cost function' or 'loss function' that measures how wrong our model's predictions are compared to the actual outcomes. The goal of training is to find the set of model parameters (weights and biases) that minimizes this cost function. This is where calculus comes in. The derivative of a function at a point tells us the rate of change or the slope of the function at that point. In ML, we use the concept of a gradient, which is a vector of partial derivatives. The gradient points in the direction of the steepest ascent of the cost function. Therefore, to minimize the cost, we need to move in the direction opposite to the gradient. This is the fundamental idea behind the Gradient Descent algorithm, the most common optimization algorithm in ML. The algorithm iteratively calculates the gradient of the cost function with respect to the model parameters and updates the parameters in the opposite direction. This process is repeated until the cost is minimized, and the model's predictions are as accurate as possible. Understanding how derivatives and gradients work is essential for grasping how models learn and for understanding more advanced optimization techniques used in deep learning, like Adam and RMSprop.