# C3PO: Critical-Layer, Core-Expert, Collaborative Pathway Optimization for Test-Time Expert Re-Mixing

arXiv: https://arxiv.org/abs/2504.07964 · HTML: https://mlsanity.com/paper/2504.07964/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [Stable LM 2 1.6B Technical Report](https://mlsanity.com/paper/2402.17834/) (2024)
- [JetMoE: Reaching Llama2 Performance with 0.1M Dollars](https://mlsanity.com/paper/2404.07413/) (2024)

## Built on by (most cited first, 7 of 7)

- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Two Experts Are All You Need for Steering Thinking: Reinforcing Cognitive Effort in MoE Reasoning Models Without Additional Training](https://mlsanity.com/paper/2505.14681/) (2025)
- [When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2605.07260/) (2026)
- [Routing Manifold Alignment Improves Generalization of Mixture-of-Experts LLMs](https://mlsanity.com/paper/2511.07419/) (2025)
- [Unveiling Language Routing Isolation in Multilingual MoE Models for Interpretable Subnetwork Adaptation](https://mlsanity.com/paper/2604.03592/) (2026)
- [Rewiring Experts on the Fly:Continuous Rerouting for Better Online Adaptation in Mixture-of-Expert models](https://mlsanity.com/paper/2510.14853/) (2025)
- [Routing by Analogy: kNN-Augmented Expert Assignment for Mixture-of-Experts](https://mlsanity.com/paper/2601.02144/) (2026)

## Abstract (arXiv)

Mixture-of-Experts (MoE) Large Language Models (LLMs) suffer from severely sub-optimal expert pathways-our study reveals that naive expert selection learned from pretraining leaves a surprising 10-20% accuracy gap for improvement. Motivated by this observation, we develop a novel class of test-time optimization methods to re-weight or "re-mixing" the experts in different layers jointly for each test sample. Since the test sample's ground truth is unknown, we propose to optimize a surrogate objective defined by the sample's "successful neighbors" from a reference set of samples. We introduce three surrogates and algorithms based on mode-finding, kernel regression, and the average loss of similar reference samples/tasks. To reduce the cost of optimizing whole pathways, we apply our algorithms merely to the core experts' mixing weights in critical layers, which enjoy similar performance but save significant computation. This leads to "Critical-Layer, Core-Expert, Collaborative Pathway Optimization (C3PO)". We apply C3PO to two recent MoE LLMs and examine it on six widely-used benchmarks. It consistently improves the base model by 7-15% in accuracy and outperforms widely used test-time learning baselines, e.g., in-context learning and prompt/prefix tuning, by a large margin. Moreover, C3PO enables MoE LLMs with 1-3B active parameters to outperform LLMs of 7-9B parameters, hence improving MoE's advantages on efficiency. Our thorough ablation study further sheds novel insights on achieving test-time improvement on MoE.