In iterated-learning chains, compositionality rises then falls (non-monotonic) unless compression is grounded in communication

A natural assumption about degenerative transmission chains — human or machine — is that structure erodes monotonically: each generation is a little worse than the last. Guo, Wu & Yiu (2026) find otherwise for compositional structure specifically. Across their self-training chains, compositionality first increases before it decreases: "compression without communicative grounding drives … non-monotonic compositionality." The mechanism they point to is that compression pressure alone (the tendency of a transmission bottleneck to favor whatever is most learnable) initially rewards compositional regularities because they compress well, but absent a communicative task that keeps compression tethered to meaning, that same pressure eventually over-regularizes past the point of useful structure.

This complicates the tidy story in claim-iterated-learning-theory-reframes-model-collapse-as-cultural-evolution that transmission chains simply "converge to the prior": the convergence path is not monotonic, and the rise-then-fall shape is itself evidence for why the bottleneck matters, not just that it does. It is a mechanism claim, not yet linked to a specific measurable stage boundary (how much compression is "enough" before it turns destructive) — that threshold is not given in the capture and would need the paper's full §2.2 methodology to pin down.