Looped-RSI: When the Whole is Greater Than The Sum of Its parts

Recursive self-improvement (RSI) increasingly relies on branching search over populations of self-modified agents. We identify two structural limitations of this paradigm. First, useful progress can become fragmented across lineages: a population may accumulate complementary discoveries that are not jointly realized by any individual agent. Second, task capability and self-improvement capability are inherited together even though they require different forms of feedback. We introduce Looped-RSI, which augments branching self-improvement with periodic population-level consolidation. Rather than selecting only among existing agents, Looped-RSI reasons over the evidence accumulated across the population to construct a successor, while separately consolidating the improver according to the quality of the descendants it produces. Across interactive environments, Looped-RSI produces stronger self-improvement trajectories. We further show that consolidation can recover substantial progress from populations in which every individual agent receives zero reward, and that the resulting improvers transfer effectively to previously unseen environments. These results suggest that recursive progress need not reside in a single lineage or a single agent state, but can emerge across the search process and be made heritable through consolidation.