# VDAR-Router: Adaptive LLMs Routing via Verbalized Query Difficulty Analysis Retrieval

arXiv: https://arxiv.org/abs/2607.18098 · HTML: https://mlsanity.com/paper/2607.18098/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 43 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 25 of 25)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [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)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [OpenCodeInterpreter: Integrating Code Generation with Execution and Refinement](https://mlsanity.com/paper/2402.14658/) (2024)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [TensorOpera Router: A Multi-Model Router for Efficient LLM Inference](https://mlsanity.com/paper/2408.12320/) (2024)
- [MixLLM: Dynamic Routing in Mixed Large Language Models](https://mlsanity.com/paper/2502.18482/) (2025)
- [Cost-Effective Online Multi-LLM Selection with Versatile Reward Models](https://mlsanity.com/paper/2405.16587/) (2024)
- [LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing](https://mlsanity.com/paper/2601.07206/) (2026)
- [ICL-Router: In-Context Learned Model Representations for LLM Routing](https://mlsanity.com/paper/2510.09719/) (2025)
- [Enhancing Retrieval-Augmented Generation: A Study of Best Practices](https://mlsanity.com/paper/2501.07391/) (2025)
- [SMART: Simulated Students Aligned with Item Response Theory for Question Difficulty Prediction](https://mlsanity.com/paper/2507.05129/) (2025)
- [Arch-Router: Aligning LLM Routing with Human Preferences](https://mlsanity.com/paper/2506.16655/) (2025)
- [Template-Based Financial Report Generation in Agentic and Decomposed Information Retrieval](https://mlsanity.com/paper/2504.14233/) (2025)
- [INFERENCEDYNAMICS: Efficient Routing Across LLMs through Structured Capability and Knowledge Profiling](https://mlsanity.com/paper/2505.16303/) (2025)
- [Automating Customer Needs Analysis: A Comparative Study of Large Language Models in the Travel Industry](https://mlsanity.com/paper/2404.17975/) (2024)
- [MEXA: Towards General Multimodal Reasoning with Dynamic Multi-Expert Aggregation](https://mlsanity.com/paper/2506.17113/) (2025)
- [RADAR: Reasoning-Ability and Difficulty-Aware Routing for Reasoning LLMs](https://mlsanity.com/paper/2509.25426/) (2025)
- [PersonalizedRouter: Personalized LLM Routing via Graph-based User Preference Modeling](https://mlsanity.com/paper/2511.16883/) (2025)

## Built on by (most cited first, 1 of 1)

- [TasteRoute: Personalized Routing for Video Generation](https://mlsanity.com/paper/2610.05896/) (2026)

## Abstract (arXiv)

Large language models are increasingly used in practical systems, making efficient model selection important for reducing deployment cost. LLM routing has emerged as a practical solution for allocating each input query to an appropriate model under a desired cost-performance trade-off. Existing routing methods often estimate model suitability from the surface semantics or embedding similarity of the input query. However, such methods may ignore the underlying difficulty of a query, leading to suboptimal routing decisions. To address the challenge, we propose VDAR-Router, a difficulty-aware retrieval-based routing framework. For each input query, VDAR-Router first generates an explicit difficulty analysis. It then retrieves historical examples with similar difficulty profiles. Based on the retrieved records, it estimates candidate model suitability and selects the model using a reward function that considers both performance and cost. Experiments on three datasets show that VDAR-Router consistently achieves better cost-performance trade-offs than existing baselines. These results demonstrate the effectiveness of difficulty-aware retrieval for training-free LLM routing. Case studies further show that explicit query analysis helps retrieve more relevant examples and supports more reliable routing decisions.