# Dynamic Mixed-Precision Routing for Efficient Multi-step LLM Interaction

arXiv: https://arxiv.org/abs/2602.02711 · HTML: https://mlsanity.com/paper/2602.02711/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 36 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 30 of 31)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Executable Code Actions Elicit Better LLM Agents](https://mlsanity.com/paper/2402.01030/) (2024)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [ScienceWorld: Is your Agent Smarter than a 5th Grader?](https://mlsanity.com/paper/2203.07540/) (2022)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Trial and Error: Exploration-Based Trajectory Optimization for LLM Agents](https://mlsanity.com/paper/2403.02502/) (2024)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [MasRouter: Learning to Route LLMs for Multi-Agent Systems](https://mlsanity.com/paper/2502.11133/) (2025)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [Quantization Hurts Reasoning? An Empirical Study on Quantized Reasoning Models](https://mlsanity.com/paper/2504.04823/) (2025)
- [Router-R1: Teaching LLMs Multi-Round Routing and Aggregation via Reinforcement Learning](https://mlsanity.com/paper/2506.09033/) (2025)
- [DeepAgent: A General Reasoning Agent with Scalable Toolsets](https://mlsanity.com/paper/2510.21618/) (2025)
- [WebResearcher: Unleashing unbounded reasoning capability in Long-Horizon Agents](https://mlsanity.com/paper/2509.13309/) (2025)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [A Comprehensive Evaluation of Quantization Strategies for Large Language Models](https://mlsanity.com/paper/2402.16775/) (2024)
- [Can Compressed LLMs Truly Act? An Empirical Evaluation of Agentic Capabilities in LLM Compression](https://mlsanity.com/paper/2505.19433/) (2025)
- [CATP-LLM: Empowering Large Language Models for Cost-Aware Tool Planning](https://mlsanity.com/paper/2411.16313/) (2024)

## Built on by (most cited first, 2 of 2)

- [TAP: Efficient Long-Horizon Agent Pruning via Trajectory-Anchored Recovery](https://mlsanity.com/paper/2610.09074/) (2026)
- [Handoff Curves: Initial Selection, Later Handoff, and Supervision Targets in Multi-turn LLM Routing](https://mlsanity.com/paper/2610.15993/) (2026)

## Abstract (arXiv)

Large language models (LLMs) achieve strong performance in long-horizon decision-making tasks through multi-step interaction and reasoning at test time. While practitioners commonly believe a higher task success rate necessitates the use of a larger and stronger LLM model, multi-step interaction with a large LLM incurs prohibitive inference cost. To address this problem, we explore the use of low-precision quantized LLMs in the long-horizon decision-making process. Based on the observation of diverse sensitivities among interaction steps, we propose Dynamic Mixed-Precision Routing (DMR), a framework that adaptively selects between high-precision and low-precision LLMs at each decision step. The router is trained via a two-stage pipeline, consisting of KL-divergence-based supervised learning that identifies precision-sensitive steps, followed by Group-Relative Policy Optimization (GRPO) to further improve task success rates. Experiments on ALFWorld and WebShop demonstrate that our approach achieves a strong accuracy-cost trade-off over single-precision baselines.