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.