PYTHON · NUMPY

Imagine a trajectory

Roll the model on its own predictions to imagine the future — and watch prediction error compound.

01Challenge

Feed a world model its own output to imagine a 40-step trajectory, then measure how the error grows with the horizon.

Predict firstA learned world model predicts one step with a small error ε. Over a 50-step imagined rollout, the error…

02Model

One-step prediction is easy; the power — and the danger — is in rolling it forward. Feed the model its own prediction as the next input and it imagines a whole future without ever touching the real world. That is how a world model dreams, and how planning and training-in-imagination become possible. But every small error feeds the next step, so the imagined future slowly drifts from the real one. Understanding that compounding is the key to using world models well: trust them over short horizons, re-ground them often. Here you imagine a pendulum's trajectory and measure exactly how the error grows.

03Guided practice

1. Roll forward. state → model → state → model … imagines a future from actions alone. 2. Compare. The real step() gives the truth at each horizon. 3. Compounding. Error at horizon 1 is tiny; by horizon 40 it has grown — because each prediction feeds the next. Short-horizon trust, frequent re-grounding: the practical rule for every world model.

04Feedback

PASS WHEN PASS when you compute the error-vs-horizon curve and it grows.

If your run fails, check:

A cell errored — run them in order.
Error should grow from horizon 1 to horizon 40.

05Retrieve & space

What makes a rollout an act of imagination? (the model consumes its own predictions, not real data).
Why does error compound? (each step's error becomes the next step's input).
What's the practical rule this implies? (trust short horizons; re-ground with real observations often).

06Mastery & project

You can roll a world model forward and reason about where its imagined future can be trusted.

Before trusting an imagined plan, ask over what horizon the model's error stays small.

← Predict the next state A model that bends →

PYTHON · NUMPY

Imagine a trajectory

Imagine a rollout and measure how error compounds with the horizon.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you