# Routing Should Pay for Itself: Sparse Supervision for Economical LLM Routing

arXiv: https://arxiv.org/abs/2609.37402 · HTML: https://mlsanity.com/paper/2609.37402/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 31 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 27 of 27)

- [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)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [AutoMix: Automatically Mixing Language Models](https://mlsanity.com/paper/2310.12963/) (2023)
- [Fly-Swat or Cannon? Cost-Effective Language Model Choice via Meta-Modeling](https://mlsanity.com/paper/2308.06077/) (2023)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [Active Testing: Sample-Efficient Model Evaluation](https://mlsanity.com/paper/2103.05331/) (2021)
- [Efficient Benchmarking of Language Models](https://mlsanity.com/paper/2308.11696/) (2023)
- [TensorOpera Router: A Multi-Model Router for Efficient LLM Inference](https://mlsanity.com/paper/2408.12320/) (2024)
- [EmbedLLM: Learning Compact Representations of Large Language Models](https://mlsanity.com/paper/2410.02223/) (2024)
- [IRT-Router: Effective and Interpretable Multi-LLM Routing via Item Response Theory](https://mlsanity.com/paper/2506.01048/) (2025)
- [LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing](https://mlsanity.com/paper/2601.07206/) (2026)
- [Active Evaluation Acquisition for Efficient LLM Benchmarking](https://mlsanity.com/paper/2410.05952/) (2024)
- [OmniRouter: Budget and Performance Controllable Multi-LLM Routing](https://mlsanity.com/paper/2502.20576/) (2025)
- [Beyond GPT-5: Making LLMs Cheaper and Better via Performance-Efficiency Optimized Routing](https://mlsanity.com/paper/2508.12631/) (2025)
- [Causal LLM Routing: End-to-End Regret Minimization from Observational Data](https://mlsanity.com/paper/2505.16037/) (2025)
- [Learning to Route LLMs from Bandit Feedback: One Policy, Many Trade-offs](https://mlsanity.com/paper/2510.07429/) (2025)
- [MMR-Bench: A Comprehensive Benchmark for Multimodal LLM Routing](https://mlsanity.com/paper/2601.17814/) (2026)
- [When Routing Collapses: On the Degenerate Convergence of LLM Routers](https://mlsanity.com/paper/2602.03478/) (2026)
- [Task-Aware LLM Routing with Multi-Level Task-Profile-Guided Data Synthesis for Cold-Start Scenarios](https://mlsanity.com/paper/2604.09377/) (2026)
- [INFERENCEDYNAMICS: Efficient Routing Across LLMs through Structured Capability and Knowledge Profiling](https://mlsanity.com/paper/2505.16303/) (2025)
- [From Sampled Outcomes to Capability Distributions: Rethinking Supervision for LLM Routing](https://mlsanity.com/paper/2606.06924/) (2026)
- [WISERouter: LLM Routing with Workload Budget Constraint](https://mlsanity.com/paper/2607.23765/) (2026)

## Abstract (arXiv)

Large language model (LLM) routing reduces serving cost by assigning each query to an appropriate model while preserving response quality. Learning such a router, however, often requires executing multiple candidate models on historical queries to collect query--model quality feedback, creating a nontrivial supervision cost before deployment. Existing work largely focuses on serving-time efficiency, overlooking whether the resulting savings are sufficient to recover this upfront expenditure. We further observe that routing quality often saturates well before all query--model feedback is collected, suggesting that dense supervision can be economically over-provisioned. We propose SaveRouter, a sparse-supervision routing framework that selectively acquires informative model feedback and shares capability information across related queries, while retaining query-level refinement for fine-grained routing. We evaluate routing by jointly accounting for supervision expenditure and subsequent serving-time savings. Across four routing benchmarks, the main setting uses only about 33--41% of available training feedback while maintaining competitive or better routing quality, and reduces the break-even deployment volume by approximately 1.9--9.5 times compared with the fastest conventional router. Further analysis shows that acquiring more supervision is not always economically preferable: the supervision level that minimizes serving cost can differ from the one that achieves the earliest payback. Our code is publicly available at https://github.com/LAMDA-Model-Reuse/SaveRouter.