Expressivity Is Not Learnability in Constrained Cognitive Systems

Cognitive systems are often evaluated in terms of representational or expressive capacity, yet robust learning depends on whether transformations can be identified, stabilized, and reused under delay, noise, and partial observability. Information theory characterizes what can be represented or transmitted, but not what can be stably transformed under physical constraints. We argue that standard assumptions about learnability become problematic once delay, noise, and partial observability are treated as structural constraints rather than nuisances.We develop a unified framework in which learnability depends not only on representational structure but also on structural conditions for observability and identifiability, with stability treated as a distinct closed-loop constraint. This framework is directly relevant to psychological theories of motor learning, perception, and cognitive control, in which successful behavior depends on learning transformations that remain inferable and stable under real-world conditions. We further argue that some highly expressive transformation classes can be structurally under-constrained, making task-relevant structure difficult to infer and increasing the risk of brittle solutions.Some representations may therefore be not merely difficult to learn, but effectively unlearnable from the signals available under delay, noise, partial observability, and hidden-variable coupling. These limits do not arise solely from failures of optimization, but from feasibility constraints on inference in closed-loop systems. Viewing learned transformations as constrained functional constructs helps clarify poor generalization, instability, and context specificity in motor and cognitive learning, and provides principled guidance for interpreting behavioral and computational results.