Causal Separation: A Theory of Representation and Recursive Self-Improvement

Recursive self-improvement aims to let machines improve how they learn from experience. A system can continue to act on a familiar relation after the conditions supporting it have changed. The resulting failure exposes a dependence that sustained its activity without being represented. We characterize this problem by tracing the closed causal paths through which activity continues. An initial separation between represented and unrepresented relations leaves participating support on one side and its symbolic projection on the other. We show how this causal separation has corresponding environmental and representational forms. When the same represented state admits different consequences, we prove that their received separation cannot be generated by the old internal relations alone. A cycle of representational reproduction incorporates these symbolic effects into reusable relations and changes subsequent interaction. We derive its coupled response and conditions for learning without labels for hidden causes. In finite settings, the cycle recovers after support changes and removes error floors that further fitting within the old representation cannot overcome. For a two-layer linear family, the original gradient update rule executes the self-modifications selected from experience. With consistent estimation, selection, and execution, the system asymptotically achieves the lowest attainable expected loss after a fixed training period.