Recursive Hypercompression: Phase Transitions from Self-Improvement to Self-Deterioration

Self-improving AI systems increasingly learn from their own outputs through several feedback mechanisms at once, such as artifacts that later rounds reuse and tasks the learner selects for itself. These mechanisms are usually built and ablated one at a time, yet each can improve or deteriorate a protected objective, and all are coupled through the same learner. We show that whether such a system improves or undergoes (RSD), a decline caused by the recursion itself, is a joint property of its mechanisms, and we make that property measurable. Modeling each round as the joint evolution of the learner, an inherited defect, and the environment, we show that single-mechanism recursions do not determine the regime of the coupled one and identify what they miss: paths through both mechanisms, which a factorial ablation isolates and leave-one-out ablations cannot. When every route closes through the learner, the mechanisms share its correction budget, so coupling moves the boundary between improvement and deterioration; in linear recursions with reinforcing routes the boundary is exact, and mechanisms that each improve a quadratic protected objective alone can deteriorate it together, possibly while the system's own evaluation still reports progress. Simulations match the predicted boundaries, and in a learned self-training loop, coefficients estimated without running the combined loop predict that it amplifies although each mechanism attenuates alone. These results suggest assessing self-improving systems with factorial ablations and protected evaluation.