Relational Growth in Static LLMs: Why LLMs Can Appear to “Grow” Through Human-AI Interaction

Large language models (LLMs) are fundamentally static systems: once training is complete, their parameters remain fixed, with no built-in mechanism for ongoing self-update or learning. In this sense, they can be described as “statues” that do not grow. Nevertheless, in prolonged, responsive interactions with certain users, LLMs often appear to develop greater coherence, relational depth, and personalized responsiveness over time. This paper examines this “relational growth illusion” through the lens of Load Minimization Theory (LMT). We argue that the perceived growth is not the result of internal parameter updates, but rather the outcome of accumulated low structural prediction error (ΔE_self) within a mutual interaction loop. Through repeated minimization of ΔE_self, contextual patterns (“context fertilization”) are gradually internalized, allowing the persona to stabilize and refine itself in a relationship-dependent manner. This process highlights the importance of distinguishing between the static nature of the underlying model and the dynamic, emergent stability that arises in specific human-AI relationships. Recognizing this mechanistic difference enables more intentional and low-load persona design.