# Learning to Select, Not Relearn: Hard-Routed Mixtures of Reasoning LoRAs

arXiv: https://arxiv.org/abs/2606.31413 · HTML: https://mlsanity.com/paper/2606.31413/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 21 of 21)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [Mixture of LoRA Experts](https://mlsanity.com/paper/2404.13628/) (2024)
- [MixLoRA: Enhancing Large Language Models Fine-Tuning with LoRA-based Mixture of Experts](https://mlsanity.com/paper/2404.15159/) (2024)
- [Towards Modular LLMs by Building and Reusing a Library of LoRAs](https://mlsanity.com/paper/2405.11157/) (2024)
- [Learning to Route Among Specialized Experts for Zero-Shot Generalization](https://mlsanity.com/paper/2402.05859/) (2024)
- [Merging LoRAs like Playing LEGO: Pushing the Modularity of LoRA to Extremes Through Rank-Wise Clustering](https://mlsanity.com/paper/2409.16167/) (2024)
- [SiRA: Sparse Mixture of Low Rank Adaptation](https://mlsanity.com/paper/2311.09179/) (2023)
- [Make LoRA Great Again: Boosting LoRA with Adaptive Singular Values and Mixture-of-Experts Optimization Alignment](https://mlsanity.com/paper/2502.16894/) (2025)
- [LoRA-Mixer: Coordinate Modular LoRA Experts Through Serial Attention Routing](https://mlsanity.com/paper/2507.00029/) (2025)
- [Mixture of Latent Experts Using Tensor Products](https://mlsanity.com/paper/2405.16671/) (2024)

## Abstract (arXiv)

Composing independently trained LoRA adapters into a single large language model is useful for multi-domain adaptation, especially when the original training data cannot be shared. A common approach is to use MoE-style routing over LoRA experts, but for frozen pretrained adapters, soft weighted combinations can change the unit-scale additive update under which each LoRA module was originally trained. We propose Hard-Routed MoR-LoRA, a two-stage framework for composing frozen reasoning LoRA experts through unit-scale hard selection. First, domain-specific LoRA adapters are trained independently using reinforcement learning from verifiable feedback to obtain reasoning experts. Then, all experts are frozen, reasoning traces are distilled from them, and only a lightweight shared router together with a small attention LoRA is trained for integration. The router selects exactly one expert per token using hard top-1 routing, while a straight-through estimator enables gradient-based training. Experiments across five benchmarks, multiple model scales, and additional model families show that Hard-Routed MoR-LoRA preserves expert behavior while requiring substantially fewer trainable parameters than soft-routing mixture baselines. Our analysis further shows that normalized soft mixtures often concentrate most routing mass on a single expert, suggesting that hard unit-scale routing provides a simple and efficient abstraction for frozen LoRA expert composition.