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

Yinghui Jiang, Bocheng Xu, Jianye Xie, Haotong Sun
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:53280-53307, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-jiang26aw, title = {{BRIDGE}: Triangular Fixed-Point Refinement for Long-Horizon Persona Consistency}, author = {Jiang, Yinghui and Xu, Bocheng and Xie, Jianye and Sun, Haotong}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {53280--53307}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/jiang26aw/jiang26aw.pdf}, url = {https://proceedings.mlr.press/v306/jiang26aw.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T BRIDGE: Triangular Fixed-Point Refinement for Long-Horizon Persona Consistency %A Yinghui Jiang %A Bocheng Xu %A Jianye Xie %A Haotong Sun %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-jiang26aw %I PMLR %P 53280--53307 %U https://proceedings.mlr.press/v306/jiang26aw.html %V 306 %X 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.
APA
Jiang, Y., Xu, B., Xie, J. & Sun, H.. (2026). BRIDGE: Triangular Fixed-Point Refinement for Long-Horizon Persona Consistency. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:53280-53307 Available from https://proceedings.mlr.press/v306/jiang26aw.html.

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