Formal Analysis of Recursive Inference: Optimality, Complexity, and Convergence in RLMs

TL;DR: Can we mathematically prove when and why recursive inference in RLMs is optimal or efficient? Let’s build formal models to analyze their convergence, computational cost, and robustness.

Research Question: How can recursive inference strategies in RLMs be formally modeled to characterize their convergence properties, computational complexity, and optimality compared to standard inference paradigms?

Hypothesis: By constructing mathematical models akin to those in Mangrum et al. (2025) and Li et al. (2024), we can derive conditions under which recursive inference converges rapidly, yields cost savings, or risks instability, guiding principled improvements to RLM design.

Experiment Plan: Develop a formal recursive state machine or probabilistic process model capturing the RLM inference loop. Theoretically analyze expected computational cost, convergence rate, and worst-case recursion depth. Simulate or empirically validate predictions on synthetic and real-world long-context tasks. Explore the impact of controlled perturbations (as in Mangrum et al., 2025) and dynamic draft tree strategies (Li et al., 2024) on model efficiency and stability.

References:

• Mangrum, M., Pemberton, J., Wetherby, B., & Montague, P. (2025). Structural Latency Perturbation in Large Language Models Through Recursive State Induction. arXiv.org.
• Li, Y., Wei, F., Zhang, C., & Zhang, H. (2024). EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees. Conference on Empirical Methods in Natural Language Processing.
• Recursive Language Models (2025). arXiv.org.