# Logistic Regression

Canonical: https://manyspace.aporia.systems/tools/logistic-regression
Updated: 2026-10-13

A straight line, a squash function, and two clouds of dots: draw the boundary by hand, then let gradient descent show you its own.

## Try this

- Earn the clean split. On Two blobs, push the line with empty-space drags until mistakes hit 0 — then reveal and compare your line to the fit.
- Feel the squash. Park the probe far from the line (P near 0 or 1), then slide it across: probability swings fastest right at the boundary.
- Break the line. Open XOR corners and try every tilt — no straight boundary separates the corners. That failure is why neural networks have hidden layers.

## How to read the boundary

Every point gets a score, w₁x₁ + w₂x₂ + b: the line is where that score equals zero. The sigmoid squashes any score into a probability — far from the line means confident, on the line means a coin flip.

Drag the weights and watch the line tilt and slide; drag the probe and read its probability. The reveal button fits the same model with gradient descent — your hand against the algorithm, same board.

## Related tools

- [Gradient Descent Playground](https://manyspace.aporia.systems/tools/gradient-descent)
- [Loss Function Explorer](https://manyspace.aporia.systems/tools/loss-functions)
- [k-Means Visualizer](https://manyspace.aporia.systems/tools/k-means)
- [Forward Pass](https://manyspace.aporia.systems/tools/neural-network)
- [Backpropagation](https://manyspace.aporia.systems/tools/backpropagation)
- [Attention Visualizer](https://manyspace.aporia.systems/tools/attention)
- [Tokenization Explorer](https://manyspace.aporia.systems/tools/tokenization)