🤖 Machine Learning Classifier Lab

About this simulation

At the heart of supervised learning is a simple idea: show an algorithm many examples labelled with the right answer, and let it adjust internal numbers — its weights — until its predictions match those labels as closely as possible. This lab makes that process visible. Colored points floating above and below a base plane are a synthetic two-class dataset; the rippling surface between them is a polynomial logistic regression model's decision boundary, the line (or curve) it has learned to separate the two classes.

How it works

• Every point sits at a fixed height set only by its true label — orange points above the plane, indigo points below.
• The surface height at any (x, z) location is the model's current prediction there, computed from a weighted sum of polynomial features of x and z, squashed through a sigmoid/tanh function.
• Pressing Train runs batch gradient descent on the cross-entropy loss: each step nudges every weight slightly to reduce prediction error, which is exactly how real classifiers such as logistic regression and neural networks learn.
• As training proceeds you can watch the surface warp to hug the orange points from below and the indigo points from above — visually "fitting" the boundary — while loss falls and accuracy climbs.

Controls

• Dataset — switch between blobs (linearly separable), interleaving moons, and concentric circles (both need a curved boundary).
• Model complexity — the polynomial degree of the features. Degree 1 can only learn a flat plane (underfitting on curved data); higher degrees can bend sharply around every point (risking overfitting to noise).
• Label noise — the fraction of labels randomly flipped when the dataset is generated, simulating messy real-world data.
• Learning rate — how large each gradient-descent step is; too high can overshoot and oscillate, too low trains very slowly.
• ▶ Train / ↺ Reset — start or stop the training animation, or regenerate a fresh dataset and re-initialize the weights. Drag to rotate the scene, scroll to zoom.

Did you know?

This same gradient-descent recipe — measure the error, compute how each weight contributed to it, and nudge weights the other way — scales from this small polynomial model all the way up to large neural networks with billions of parameters. The math barely changes; only the size of the model and the amount of data do.