# ProxRouter: Proximity-Weighted LLM Query Routing for Improved Robustness to Outliers

arXiv: https://arxiv.org/abs/2510.09852 · HTML: https://mlsanity.com/paper/2510.09852/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 66 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 30 of 39)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [MPNet: Masked and Permuted Pre-training for Language Understanding](https://mlsanity.com/paper/2004.09297/) (2020)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Universal Sentence Encoder](https://mlsanity.com/paper/1803.11175/) (2018)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (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)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [RouterEval: A Comprehensive Benchmark for Routing LLMs to Explore Model-level Scaling Up in LLMs](https://mlsanity.com/paper/2503.10657/) (2025)

## Built on by (most cited first, 6 of 6)

- [LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing](https://mlsanity.com/paper/2601.07206/) (2026)
- [Not All Turns Are Equally Hard: Adaptive Thinking Budgets For Efficient Multi-Turn Reasoning in Agents](https://mlsanity.com/paper/2604.05164/) (2026)
- [Federate the Router: Learning Language Model Routers with Sparse and Decentralized Evaluations](https://mlsanity.com/paper/2601.22318/) (2026)
- [LOCUS: Low-Dimensional Model Embeddings for Efficient Model Exploration, Comparison, and Selection](https://mlsanity.com/paper/2601.21082/) (2026)
- [Mind the Delay: Latency-aware Query Routing for Heterogeneous LLM pools](https://mlsanity.com/paper/2607.18253/) (2026)
- [Embedding Geometry Shapes LLM Routing: Tracing Failure Modes and Improving Generalization](https://mlsanity.com/paper/2610.19198/) (2026)

## Abstract (arXiv)

Large language model (LLM) query routers are critical to modern AI platforms as they seek to improve efficiency by assigning inference queries to accurate, yet low-cost models. Parametric routers typically use trained neural networks for LLM selection but suffer from retraining and maintenance overheads. Nonparametric routers are training-free, instead estimating LLM accuracy and cost via similarity between encodings of the input query and training set queries. However, like their parametric counterparts, nonparametric routers struggle to generalize to outlier queries, an issue exacerbated by limited diversity in training sets which are costly to expand and difficult to keep current with ever-evolving use cases. We propose ProxRouter, which applies an exponentially tilted aggregation mechanism to balance bias and variance in nonparametric routers, improving their robustness to outliers. Experiments show ProxRouter enhances outlier routing while preserving inlier performance with minimal overhead.