Volume or Coupling? A Scale-Dependent Dissociation in Constraint Recovery of Language-Model Loops

Recent work on self-referential large-language-model (LLM) loops suggests that isolated recursive loops degrade toward closed attractor states and that exchange with an independent process supports recovery. We ask what the operative ingredient of such coupling is, using a minimal, fully specified perturbation–recovery protocol: an instruction-tuned model maintains an explicit output constraint (all-capital letters), a conflicting instruction is injected, and constraint recovery is tracked over eight exchanges under fixed criteria, across four conditions (coupled dual-agent, single, volume-matched single, and a four-fold-volume condition; 30 opener-paired runs each). At 1.5B parameters, the coupled loop’s advantage over a single model (43% vs. 17%, exact McNemar p = .039) is largely reproduced by a volume-matched single model (37%; C vs. X p = .774), a result consistent with a generation-volume account at this tier. Extending the identical protocol across scale reverses this picture. At 3B, all conditions are at or near ceiling (90–100%): the perturbation rarely produces persistent capture. At 7B, single and volume-matched conditions recover in 0/30 runs, four-fold volume in 1/30, and coupling in 8/30 (C vs. X p = .0078), with delays of 2–7 exchanges, with recovery remaining stable over the remaining evaluation horizon in five of eight cases. Exact trajectory replays reproduce all eight delays and reveal the mechanism: the directly perturbed agent is deeply captured, while its partner—whose history excludes the instruction—is captured only shallowly by mimicry and rapidly re-anchors, supplying constraint-consistent evidence that pulls the system back. We propose a unified account: recovery depends on the availability of constraint-consistent generation that is not bound by the perturbing instruction—supplied largely by raw volume at small scale, and at larger scale substantially by structural shielding. The deflationary volume account is thus itself scale-bounded. An anonymized reproduction package with code, raw outcomes, and exact replays has been prepared; where supported, it can accompany review, and a versioned public release will follow de-anonymization.