Theoretical analysis establishes identification bounds for counterfactual generative capability from finite traces, highlighting conditions where unobserved repertoires can be bounded.
Key Points
To establish a formal identification framework for bounding and comparing latent generative capabilities and counterfactual repertoires using finite, partially observed trajectory samples.
Decomposed the inference problem into six structural inferential layers with distinct failure modes.
Formulated counterfactual reachable repertoires as superlevel sets of reachability functionals across observational equivalence classes.
Demonstrated that counterfactual repertoires are bounded by the core and hull of an equivalence class, collapsing to class limits if off-regime behavior can be arbitrarily spliced to on-regime paths.
Proved that under uniformly condition-Lipschitz kernels, counterfactual ambiguity is bounded by at most twice the Lipschitz constant times the distance from the observed regime.
Showed capability comparisons are identified across an entire equivalence class whenever the difference between evaluated functionals exceeds combined ambiguity.