Map & Footsteps

A game about parametric vs. nonparametric learning

Linear regression assumes the world is a line. It learns a fixed number of parameters, discards the training data, and works from those numbers alone. KNN has no such conviction about shapes. It stores every example and, when it needs to predict, polls its neighbors directly.

Parametric Models

FIXED STRUCTURE · COMPACT MEMORY

A parametric model commits to the world's shape before seeing any data. It fits a fixed number of parameters to that assumption, then discards the raw data. The map is drawn. The structure is final.

Fast to store, fast to query. But if the assumption is wrong, more data will not save it.

Linear regression, logistic regression, neural networks. A network with a hundred million weights is still parametric: the number of parameters was fixed at design time.

Nonparametric Models

FLEXIBLE STRUCTURE · MEMORY GROWS WITH DATA

A nonparametric model makes no fixed assumption about shape. The data defines the structure. More data means a more complex boundary, and more memory to store it.

Flexible and expressive. But slow to query, expensive in memory, and fragile when the data distribution shifts.

k-Nearest Neighbours, kernel density estimation, decision trees. KNN literally stores every training point and queries them all at prediction time.

Below, you can play both sides. The Map-Maker commits to a route using a fixed number of waypoints. Compact, but brittle when terrain changes. The Trailblazer remembers every cell visited and reasons from those memories. Adaptive, but costly to store, and snow erases everything. Trigger a snowstorm. See what breaks.

↓   PLAY BELOW   ↓

Current Mode

MAP-MAKER · PARAMETRIC

Draw your map before journeying. Commit to a path using a fixed number of waypoints. Efficient memory, but rigid when terrain surprises you.

Stats

Actions taken0
Footprints stored0
Cells explored0%
Snow events0

Parameters

Waypoints (k) 4
Neighbours checked 3

If a danger is among the checked neighbours, step away from it.

Actions

● CLICK MAP TO PLACE WAYPOINTS

Legend

Goal
Danger
Waypoint
Footprint
Agent
Wall