Gradient Descent and Loss Functions

About this app

Gradient Descent and Loss Functions is an interactive mathematics learning app that visualizes prediction error, a loss curve, and the search for its minimum. Explore how changing the weight w changes the loss, then take gradient-descent steps using w ← w − α·L'(w). A dedicated learning-rate section demonstrates slow convergence, stable convergence, oscillation, and divergence when the step size is too large.

Use cases

• High school students learning calculus and AI mathematics
• Teachers demonstrating loss functions and optimization in class
• Learners exploring how model weights affect prediction error
• Beginners studying learning rates and gradient descent

Features

• Visualizes five data points, the prediction line y = w·x, error bars, squared-error areas, and loss L(w)
• Adjusts the weight w to inspect how the loss changes and locate the minimum at w = 2
• Animates gradient-descent updates with a current-position ball and tangent slope
• Lets users choose a starting point and take one step at a time
• Adjusts the learning rate α to compare slow movement, convergence, oscillation, and divergence
• Includes guided missions across loss functions, individual steps, and learning rates