# Routing with Generated Data: Annotation-Free LLM Skill Estimation and Expert Selection

arXiv: https://arxiv.org/abs/2601.09692 · HTML: https://mlsanity.com/paper/2601.09692/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 14 Jan 2026.

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

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [On LLMs-Driven Synthetic Data Generation, Curation, and Evaluation: A Survey](https://mlsanity.com/paper/2406.15126/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning](https://mlsanity.com/paper/2312.12241/) (2023)
- [Do Androids Laugh at Electric Sheep? Humor "Understanding" Benchmarks from The New Yorker Caption Contest](https://mlsanity.com/paper/2209.06293/) (2022)
- [Examining Inter-Consistency of Large Language Models Collaboration: An In-depth Analysis via Debate](https://mlsanity.com/paper/2305.11595/) (2023)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [Synthetic Data Generation Using Large Language Models: Advances in Text and Code](https://mlsanity.com/paper/2503.14023/) (2025)
- [BoardgameQA: A Dataset for Natural Language Reasoning with Contradictory Information](https://mlsanity.com/paper/2306.07934/) (2023)
- [MoCa: Measuring Human-Language Model Alignment on Causal and Moral Judgment Tasks](https://mlsanity.com/paper/2310.19677/) (2023)
- [The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giants](https://mlsanity.com/paper/2505.19797/) (2025)
- [Smoothie: Label Free Language Model Routing](https://mlsanity.com/paper/2412.04692/) (2024)
- [Small Language Models Learn Enhanced Reasoning Skills from Medical Textbooks](https://mlsanity.com/paper/2404.00376/) (2024)
- [Reverse Thinking Makes LLMs Stronger Reasoners](https://mlsanity.com/paper/2411.19865/) (2024)
- [Causal LLM Routing: End-to-End Regret Minimization from Observational Data](https://mlsanity.com/paper/2505.16037/) (2025)
- [DataEnvGym: Data Generation Agents in Teacher Environments with Student Feedback](https://mlsanity.com/paper/2410.06215/) (2024)
- [Humor in AI: Massive Scale Crowd-Sourced Preferences and Benchmarks for Cartoon Captioning](https://mlsanity.com/paper/2406.10522/) (2024)
- [S-DAG: A Subject-Based Directed Acyclic Graph for Multi-Agent Heterogeneous Reasoning](https://mlsanity.com/paper/2511.06727/) (2025)
- [MEXA: Towards General Multimodal Reasoning with Dynamic Multi-Expert Aggregation](https://mlsanity.com/paper/2506.17113/) (2025)
- [Performance Characterization of Expert Router for Scalable LLM Inference](https://mlsanity.com/paper/2404.15153/) (2024)

## Built on by (most cited first, 4 of 4)

- [Uno-Orchestra: Parsimonious Agent Routing via Selective Delegation](https://mlsanity.com/paper/2605.05007/) (2026)
- [Error-Aware Reverse Auction Mechanism for Large Language Model Routing](https://mlsanity.com/paper/2608.12719/) (2026)
- [Admission Without Answers: Label-Free Certification and Experience Learning for LLM-Based Optimization Modeling](https://mlsanity.com/paper/2608.15565/) (2026)
- [Learning What to Activate: Combinatorial Capability Allocation for Long-Horizon Multimodal Agents](https://mlsanity.com/paper/2609.27869/) (2026)

## Abstract (arXiv)

Large Language Model (LLM) routers dynamically select optimal models for given inputs. Existing approaches typically assume access to ground-truth labeled data, which is often unavailable in practice, especially when user request distributions are heterogeneous and unknown. We introduce Routing with Generated Data (RGD), a challenging setting in which routers are trained exclusively on generated queries and answers produced from high-level task descriptions by generator LLMs. We evaluate query-answer routers (using both queries and labels) and query-only routers across four diverse benchmarks and 12 models, finding that query-answer routers degrade faster than query-only routers as generator quality decreases. Our analysis reveals two crucial characteristics of effective generators: they must accurately respond to their own questions, and their questions must produce sufficient performance differentiation among the model pool. We then show how filtering for these characteristics can improve the quality of generated data. We further propose CASCAL, a novel query-only router that estimates model correctness through consensus voting and identifies model-specific skill niches via hierarchical clustering. CASCAL is substantially more robust to generator quality, outperforming the best query-answer router by 4.6% absolute accuracy when trained on weak generator data.