BRIDGE: Triangular Fixed-Point Refinement for Long-Horizon Persona Consistency

Long-horizon dialogue agents suffer from latent state drift: what an agent says, what it internally represents, and what it stores in memory can diverge silently across turns. This creates asymmetric rupture risk—many locally coherent exchanges undone by a single high-cost contradiction. We propose BRIDGE (Behavioral Reasoning through Integrated Dynamic Gated Evolution), which performs triangular fixed-point refinement to explicitly couple Observable ($\mathcal{O}$), Latent ($\mathcal{L}$), and Memory ($\mathcal{M}$) before decoding each response. We prove that under mild conditions, the refinement operator converges to a unique fixed point, providing a theoretical guarantee that the agent's internal state remains self-consistent before each response. Empirically, BRIDGE achieves the highest scores on both PersonaGym (4.59 avg., surpassing Claude-3.7-Sonnet) and CoSER (59.5% avg., +3.1 over Claude-3.7-Sonnet), with gains concentrated on persona-specific metrics (+8.0 Character Fidelity over Qwen2.5-32B-Instruct)—while updating only 0.85% trainable parameters of the frozen backbone. We also provide a Lyapunov-style uniform drift bound for tiered memory updates, grounding bounded persona evolution in long-horizon interaction.

When an AI chatbot plays a character or acts as a companion over a long conversation, it tends to slowly slip out of character. What it says, what it is "thinking," and what it remembers can quietly fall out of step until a jarring contradiction surfaces—a forgetful detective suddenly recalling a vivid childhood memory, for example. People forgive small slips, but a single contradiction like this can shatter their trust, even after dozens of convincing exchanges. We built BRIDGE, which runs a quick internal consistency check before the AI replies: it reconciles how the character behaves, what it intends, and what it remembers so that the three agree. We also designed its memory so that fleeting details can change quickly while core personality shifts only very slowly, and we prove mathematically that the character cannot drift away uncontrollably. Across standard tests, BRIDGE stays in character better than leading systems while retraining under 1% of the AI. Most importantly, it cuts severe, trust-breaking contradictions by more than half—making AI companions more dependable for sensitive uses such as education and emotional support.