Gradient Descent and Loss Functions
by Anonymous
Roll a ball downhill, opposite the slope, to find the minimum—and see how a high learning rate makes it bounce away.
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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