# CONCUR: A Framework for Continual Constrained and Unconstrained Routing

arXiv: https://arxiv.org/abs/2512.09386 · HTML: https://mlsanity.com/paper/2512.09386/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 24 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [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)
- [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)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [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)
- [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)
- [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)
- [Learning How Hard to Think: Input-Adaptive Allocation of LM Computation](https://mlsanity.com/paper/2410.04707/) (2024)
- [MixLLM: Dynamic Routing in Mixed Large Language Models](https://mlsanity.com/paper/2502.18482/) (2025)
- [EmbedLLM: Learning Compact Representations of Large Language Models](https://mlsanity.com/paper/2410.02223/) (2024)
- [MetaLLM: A High-performant and Cost-efficient Dynamic Framework for Wrapping LLMs](https://mlsanity.com/paper/2407.10834/) (2024)
- [Routoo: Learning to Route to Large Language Models Effectively](https://mlsanity.com/paper/2401.13979/) (2024)
- [Tryage: Real-time, intelligent Routing of User Prompts to Large Language Models](https://mlsanity.com/paper/2308.11601/) (2023)
- [Route to Reason: Adaptive Routing for LLM and Reasoning Strategy Selection](https://mlsanity.com/paper/2505.19435/) (2025)
- [OptLLM: Optimal Assignment of Queries to Large Language Models](https://mlsanity.com/paper/2405.15130/) (2024)
- [EllieSQL: Cost-Efficient Text-to-SQL with Complexity-Aware Routing](https://mlsanity.com/paper/2503.22402/) (2025)

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

- [RouteGoT: Node-Adaptive Routing for Cost-Efficient Graph of Thoughts Reasoning](https://mlsanity.com/paper/2603.05818/) (2026)

## Abstract (arXiv)

AI tasks differ in complexity and are best addressed with different computation strategies (e.g., combinations of models and decoding methods). Hence, an effective routing system that maps tasks to the appropriate strategies is crucial. Most prior methods build the routing framework by training a single model across all strategies, which demands full retraining whenever new strategies appear and leads to high overhead. Attempts at such continual routing, however, often face difficulties with generalization. Prior models also typically use a single input representation, limiting their ability to capture the full complexity of the routing problem and leading to sub-optimal routing decisions. To address these gaps, we propose CONCUR, a continual routing framework that supports both constrained and unconstrained routing (i.e., routing with or without a budget). Our modular design trains a separate predictor model for each strategy, enabling seamless incorporation of new strategies with low additional training cost. Our predictors also leverage multiple representations of both tasks and computation strategies to better capture overall problem complexity. Experiments on both in-distribution and out-of-distribution, knowledge- and reasoning-intensive tasks show that our method outperforms the best single strategy and strong existing routing techniques with higher end-to-end accuracy and lower inference cost in both continual and non-continual settings, while also reducing training cost in the continual setting.