Counterfactual Mode

Where it sits

The current framework (7 - DIRAC Multi-Mode Framework) covers rung 1 (Mode 1 — evidence clamp / conditioning) and rung 2 (Modes 2 & 3 — hard and soft intervention). A counterfactual is rung 3 of Pearl’s ladder, and it is not reachable by running the existing modes in sequence on a single model.

The query

“Given that I actually observed , what would have been had been set to ?” Concretely: a patient took the drug and recovered — would they have recovered had they not taken it? The conditioning event and the intervention refer to the same world, so they cannot be applied to two independent runs.

Why it is its own mode (abduction → action → prediction)

1. Abduction. Use the observed evidence to update belief over the background/exogenous noise (the latent state that produced the factual world): . This must use the original mechanisms.
2. Action. Apply — mutilate / swap ‘s mechanism — while holding the abducted noise fixed.
3. Prediction. Read in the modified model with pinned.

The catch: step 1 needs the un-intervened mechanisms and step 2 needs the intervened ones, but they must share the same . A single model cannot hold both.

Realisation sketch — twin network

Compile two copies of the graph that share the exogenous-noise nodes :

• Factual side: original mechanisms, evidence clamped (Mode 1) — this is what fixes .
• Counterfactual side: intervened mechanisms (Mode 2 / Mode 3), reading the query variable.
• The shared nodes couple the two sides.

So the counterfactual mode composes Mode 1 and Mode 2/3, but on a doubled, noise-augmented model — it is not Mode 1 followed by Mode 2 on one graph.

What it would need before promotion to a real mode

• An explicit noise/twin representation for BN-derived energy models (exogenous made explicit, since CPT-only BNs marginalise it away).
• A proposition analogous to Prop. 3 for the twin construction (correctness + behaviour).
• Numerical validation on a toy SCM where the ground-truth counterfactual is computable.
• Hardware cost: the twin roughly doubles variable count and adds shared- couplings — factor-order impact per 3 - Higher-Order Factor and Hardware-Profile to be assessed.

Status

Parked. Beyond the current work plan (Phases 1–12 stop at rungs 1–2). Revisit only if a concrete use case makes the counterfactual query worth the twin-model overhead.