arXiv:2611.03861v1 Announce Type: new Abstract: Retaining predictive gains can require persistent errors in a model's response to interventions. For deterministic predictors with finite second moments under squared-error loss, any observational advantage over the best predictor using only an outcome's direct causes requires dependence on other inputs, regardless of the learning rule. When admissible interventions vary inputs while preserving the worldly outcome, this dependence yields a positive lower bound on root-mean-square intervention-response error. We identify conditions under which population gradient updates introduce this dependence from a parent-only baseline or damage a previously correct mechanism through shared parameters while improving other predictions. These dependencies can also make model behavior vary with how the same intervention is realized. We characterize interventional alignment through a common output mapping across internal states and physical processes realizing the same intervention target and relevant context. Correction is limited by the causal hypotheses currently admitted within inquiry. The relevant hypothesis class comprises these causal alternatives, rather than the function class the computational system could in principle represent. For predictions restricted to these alternatives, interventional mean error cannot fall below the best approximation they permit, whether evidence is observational or interventional. Reducing error below a positive limit requires admitting better hypotheses, which may entail revising the causal variables, mechanism structure, or intervention interpretation. Interventional criticism constrains replacements without determining them. We conjecture that reliably acquiring and maintaining interventional competence when causal commitments fail requires autonomous participation in proposing alternatives, testing their consequences, and revising them in response to error.
