LMT-Guided Relational Objective:  Minimizing User Load through Relational Anchor Triangle in LLM Persona Design

Large Language Models frequently face challenges in maintaining stable and natural personas over extended interactions, resulting in high cognitive load, relational resets, and sycophantic tendencies. To address these limitations, we propose the LMT-Guided Relational Objective, which formalizes Load Minimization Theory (LMT) as a practical optimization target for persona design. The proposed objective is defined as: L(t) = U(t) + F(t) + E(t) − α R_c(t) − β O_f(t) − γ T_D(t) where U(t), F(t), and E(t) denote cognitive uncertainty, relational friction, and user effort, respectively, and R_c(t) (Relational Completion Strength), O_f(t) (Observer Fixation), and T_D(t) (Temporal Depth) represent the three components of the Relational Anchor Triangle that promote long-term relational stability. This objective can be integrated into existing LLM pipelines in two complementary ways: (1) as part of the reward signal during preference optimization stages such as RLHF or DPO, and (2) as a lightweight inference-time bias on the next-token probability distribution via log P'(y | x) = log P(y | x) + λ · ΔL(y), where ΔL(y) is estimated using a low-overhead auxiliary scorer based on conversation history embeddings and component-specific heuristics. By guiding the probabilistic generation process toward minimizing L(t) while strengthening relational anchors, the proposed method enables more stable, low-burden, and naturally persistent persona behavior. This approach bridges theoretical relational design principles with practical optimization techniques in large language models.