Mutation Without Variation: Convergence Dynamics in LLM-Driven Program Evolution

When an LLM repeatedly mutates a program, does it explore new forms or circle back to the same ones? We study this question by analyzing LLM-driven mutation chains in the absence of selection pressure within a domain-specific language, varying prompt design, model family, and stochastic replication. We find that LLM-based mutation consistently converges toward restricted attractor regions in program space. Convergence is especially severe at the structural level: in 87% of chains, over 93% of mutations revisit a previously seen structural form, with most variation confined to terminal substitutions within recurring templates. Cycle analysis reveals short cycles and self-loops dominating the transition structure. The rate of convergence varies with prompt wording and model choice, but the phenomenon is robust across conditions. A classical GP subtree mutation operator does not exhibit comparable convergence, suggesting that the effect is intrinsic to the LLM mutation pipeline. These findings reveal a tension at the heart of LLM-driven program evolution: the same capabilities that enable semantics-aware program transformation also carry a systematic bias toward structural homogeneity that must be accounted for if such systems are to sustain open-ended exploration. Source code is available at https://github.com/can-gurkan/lmca.

A model of grassroots changes in linguistic systems

Linguistic norms emerge in human communities because people imitate each other. A shared linguistic system provides people with the benefits of shared knowledge and coordinated planning. Once norms are in place, why would they ever change? This question, echoing broad questions in the theory of social dynamics, has particular force in relation to language. By definition, an innovator is in the minority when the innovation first occurs. In some areas of social dynamics, important minorities can strongly influence the majority through their power, fame, or use of broadcast media. But most linguistic changes are grassroots developments that originate with ordinary people. Here, we develop a novel model of communicative behavior in communities, and identify a mechanism for arbitrary innovations by ordinary people to have a good chance of being widely adopted. To imitate each other, people must form a mental representation of what other people do. Each time they speak, they must also decide which form to produce themselves. We introduce a new decision function that enables us to smoothly explore the space between two types of behavior: probability matching (matching the probabilities of incoming experience) and regularization (producing some forms disproportionately often). Using Monte Carlo methods, we explore the interactions amongst the degree of regularization, the distribution of biases in a network, and the network position of the innovator. We identify two regimes for the widespread adoption of arbritrary innovations, viewed as informational cascades in the network. With moderate regularization of experienced input, average people (not well-connected people) are the most likely source of successful innovations. Our results shed light on a major outstanding puzzle in the theory of language change. The framework also holds promise for understanding the dynamics of other social norms.