# Token-Level LLM Collaboration via FusionRoute

arXiv: https://arxiv.org/abs/2601.05106 · HTML: https://mlsanity.com/paper/2601.05106/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 54 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 30 of 50)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [SWE-Bench Pro: Can AI Agents Solve Long-Horizon Software Engineering Tasks?](https://mlsanity.com/paper/2509.16941/) (2025)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [InFoBench: Evaluating Instruction Following Ability in Large Language Models](https://mlsanity.com/paper/2401.03601/) (2024)
- [Revisiting Out-of-distribution Robustness in NLP: Benchmark, Analysis, and LLMs Evaluations](https://mlsanity.com/paper/2306.04618/) (2023)
- [Decoding-Time Language Model Alignment with Multiple Objectives](https://mlsanity.com/paper/2406.18853/) (2024)
- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [Ensemble Learning for Heterogeneous Large Language Models with Deep Parallel Collaboration](https://mlsanity.com/paper/2404.12715/) (2024)

## Built on by (most cited first, 9 of 9)

- [EBPO: Empirical Bayes Shrinkage for Stabilizing Group-Relative Policy Optimization](https://mlsanity.com/paper/2602.05165/) (2026)
- [Triage: Routing Software Engineering Tasks to Cost-Effective LLM Tiers via Code Quality Signals](https://mlsanity.com/paper/2604.07494/) (2026)
- [Wireless Federated Multi-Task LLM Fine-Tuning via Sparse-and-Orthogonal LoRA](https://mlsanity.com/paper/2602.20492/) (2026)
- [TARo: Token-level Adaptive Routing for LLM Test-time Alignment](https://mlsanity.com/paper/2603.18411/) (2026)
- [CPR for LLMs: Critical-Point Routing against Catastrophic Forgetting in Domain Adaptation](https://mlsanity.com/paper/2608.30158/) (2026)
- [Priority-Aware Learning-Unlearning Correction for Dynamic Decentralized LoRA Fine-Tuning](https://mlsanity.com/paper/2606.22878/) (2026)
- [Divergence Decoding: Training-Free Capability Fusion](https://mlsanity.com/paper/2607.27248/) (2026)
- [Mixture of Self-Improving Branches For Agent Harness Optimization](https://mlsanity.com/paper/2609.37834/) (2026)
- [TokenRouter: Efficient Serving System for Token-Level LLM Routing](https://mlsanity.com/paper/2610.12242/) (2026)

## Abstract (arXiv)

Large language models (LLMs) exhibit strengths across diverse domains. However, achieving strong performance across these domains with a single general-purpose model typically requires scaling to sizes that are prohibitively expensive to train and deploy. On the other hand, while smaller domain-specialized models are much more efficient, they struggle to generalize beyond their training distributions. To address this dilemma, we propose FusionRoute, a robust and effective token-level multi-LLM collaboration framework in which a lightweight router simultaneously (i) selects the most suitable expert at each decoding step and (ii) contributes a complementary logit that refines or corrects the selected expert's next-token distribution via logit addition. Unlike existing token-level collaboration methods that rely solely on fixed expert outputs, we provide a theoretical analysis showing that pure expert-only routing is fundamentally limited: unless strong global coverage assumptions hold, it cannot in general realize the optimal decoding policy. By augmenting expert selection with a trainable complementary generator, FusionRoute expands the effective policy class and enables recovery of optimal value functions under mild conditions. Empirically, across both Llama-3 and Gemma-2 families and diverse benchmarks spanning mathematical reasoning, code generation, and instruction following, FusionRoute outperforms both sequence- and token-level collaboration, model merging, and direct fine-tuning, while remaining competitive with domain experts on their respective tasks.