6 docs tagged with "calculus"

Mastering the Chain Rule, the fundamental calculus tool for differentiating composite functions, and its direct application in the Backpropagation algorithm for training neural networks.

An introduction to derivatives, their definition, rules, and their crucial role in calculating the slope of the loss function, essential for optimization algorithms like Gradient Descent.

Defining the Gradient vector, its mathematical composition from partial derivatives, its geometric meaning as the direction of maximum increase, and its role as the central mechanism for learning in Machine Learning.

Defining partial derivatives, how they are calculated in multi-variable functions (like the Loss Function), and their role in creating the Gradient vector for optimization.

Understanding the Hessian matrix, second-order derivatives, and how the curvature of the loss surface impacts optimization and model stability.

Understanding the Jacobian matrix, its role in vector-valued functions, and its vital importance in backpropagation and modern deep learning frameworks.