> For the complete documentation index, see [llms.txt](https://world-models-from-scratch.gitbook.io/wmfs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://world-models-from-scratch.gitbook.io/wmfs/chapters/chapter_01/01-what-is-a-world-model.md).

# 1.1 What Is a World Model?

A world is the bounded environment in which a system operates. For example: in a self-driving car, the world includes the road, nearby vehicles, pedestrians, traffic signals, and the car itself. For a computer-use agent, the world might be a browser, its interface, and the applications it can control. A robot, game-playing agent, or software agent each operates in a different world.

The boundary of the world depends on the system and its task.

| System             | World                      | Observation                 | Action                    | Predicted future              |
| ------------------ | -------------------------- | --------------------------- | ------------------------- | ----------------------------- |
| Self-driving car   | Road environment           | Cameras and vehicle sensors | Steer or brake            | Future traffic scene          |
| Robot              | Robot and workspace        | Cameras and joint state     | Move, push, or grasp      | Future robot and object state |
| Game-playing agent | Game environment           | Board state or pixels       | Game move                 | Future game state             |
| Video model        | Recorded scene             | Recent frames               | Optional control          | Future frames                 |
| Computer-use agent | Interface and applications | Screen or interface state   | Click, type, or tool call | Updated interface state       |

A world model learns how that environment changes. It uses what has already been observed, and, when relevant, an action to predict what could happen next. For example: What happens if the car brakes? If the robot moves its arm? If the computer-use agent clicks a button?

A prediction of the next observation is one predicted **transition**. A sequence of predicted future observations is a predicted trajectory. In this book, that predicted trajectory is called a **rollout**.

The way an environment changes from one time step to the next is called its **dynamics**. This includes the effect of actions on that change. A world model learns an approximation of those dynamics. Given a history of observations and, when applicable, a sequence of actions, it predicts a distribution over future trajectories, or rollouts:

$$
p\_\theta(o\_{t+1:t+H} \mid o\_{\leq t}, a\_{t:t+H-1})
$$

Here, `H` is the prediction horizon. The predicted trajectory contains the observations from step `t + 1` through step `t + H`.

![](https://565757139-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F64ikEJQaVP2LxutrTAH9%2Fuploads%2Fgit-blob-f50abdd9a44d40f26e4ead151fc74bad0e291bba%2Ffig_1_1_transition.png?alt=media)

*Figure 1.1: Encode an observation, advance the learned state under an action, then decode a prediction.*

## From One Transition to a Rollout

There are two common ways to produce a rollout. Some models generate the full trajectory in one operation. Other models predict one transition at a time and carry the predicted state into the next step.

The following pseudocode shows the second approach:

```python
def rollout(model, observation, actions):
    state = model.encode(observation)
    future = []

    for action in actions:
        state = model.step(state, action)
        future.append(model.decode(state))

    return future
```

## Generalization and Multiple Futures

Training data contains a finite set of observed transitions. A world model learns patterns from those transitions. It uses those patterns to estimate what may happen in states that were not recorded exactly in the training data.

A future is not always unique. The same observation and action may lead to different outcomes. A deterministic model predicts one trajectory. A probabilistic model represents a distribution over trajectories. Each sampled rollout is one trajectory from that distribution.

The playground shows one predicted transition at a time. Apply each prediction as the next observation to build a rollout. You can also compare one predicted future with several possible futures.

[Open the transition and rollout playground in a new tab](https://nahidalam.github.io/world_model_from_scratch/interactive/chapter_01/transition_playground.html).


---

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