The World-Model Qualification Test › Criterion 2: Action Conditioning

The second question separates world models from forecasters. A forecaster maps past observations to future observations. A world model maps past observations and a proposed action to future observations. The action must enter as a cause.

This sounds trivial, and architecturally it often is: concatenate the action vector onto the model input. But several subtle failures hide behind a nominally action-conditioned interface.

• The ignored-action model. The network receives the action but learns to rely on it so little that its predictions are nearly identical for all actions. This happens routinely when training data comes from a smooth feedback controller, because in such data the action is almost predictable from the state, and the easiest way to minimize loss is to predict the continuation of the state trajectory. The model passes every open-loop test on the logging distribution and is useless for planning.
• The spurious-correlation model. The model latches onto correlations between actions and outcomes that hold in the dataset but are not causal. Human drivers press the brake when the car ahead is close, so a naive model can learn "brake pressed $\to$ obstacle was near" and infer the wrong direction of influence. We will return to this confusability when we discuss causal world models in Part IV: Space, Physics, and Causality.
• The wrong-granularity model. The model conditions on high-level commands ("turn left") when the downstream planner issues low-level controls (wheel torques), or vice versa. The action interface must match the decision interface of the agent that will consume the model.

Each of these failures deserves a brief anatomy, because they fail for different reasons and are caught by different tests. The ignored-action model is a failure of data: the behavior policy made actions statistically redundant with states, so gradient descent had no incentive to use the action channel. It is caught by intervening on the action input and observing whether predictions change. The spurious-correlation model is a failure of causal identification: the model found real correlations and assigned them the wrong direction or mechanism. It is caught by testing predictions against interventions that break the correlation structure of the logging policy. The wrong-granularity model is a failure of interface design: the model is fine at its own level of abstraction but cannot answer the questions the consumer asks. It is caught not by statistics at all but by an integration review comparing the planner's action space against the model's conditioning space. Note that none of these three is reliably caught by held-out prediction loss on logged data, which is exactly why action conditioning gets its own criterion.

The deep reason this criterion is separate from accuracy is the difference between observational and interventional distributions. Accuracy on logged data measures $p(o_{t+1} \mid o_{\le t}, a_t)$ under the data-collecting policy. Planning requires the response function $p(o_{t+1} \mid o_{\le t}, \mathrm{do}(a_t))$: what would happen if we chose $a_t$, possibly contrary to habit. They coincide when the conditioned history blocks every common cause of action and outcome and the relevant actions have data support. Logged policies rarely guarantee both conditions. Data collection is therefore inseparable from qualification.

If the $\mathrm{do}(\cdot)$ notation is new, here is the intuition in plain language. Conditioning answers "given that you observe action $a_t$ was taken, what typically follows?" Intervention answers "if you force action $a_t$ to happen regardless of circumstances, what follows?" These differ whenever the observed action carried information about the situation, which it almost always does: a braking driver is usually braking because something is ahead. The observational query entangles the effect of the brake with the reason the brake was pressed. Only an intervention, or data collected under randomized actions, severs that entanglement. This is the same distinction that powers randomized controlled trials in medicine, transplanted into the training of predictive models, and it explains why exploration is a precondition for causal world modeling rather than a reinforcement-learning nicety.