# BitsMoE: Efficient Spectral Energy-Guided Bit Allocation for MoE LLM Quantization

arXiv: https://arxiv.org/abs/2606.00079 · HTML: https://mlsanity.com/paper/2606.00079/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 36 of its 45 references that are in the map.
- First posted on arXiv 22 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 36)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [Not All Experts are Equal: Efficient Expert Pruning and Skipping for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2402.14800/) (2024)
- [MoE-I2: Compressing Mixture of Experts Models through Inter-Expert Pruning and Intra-Expert Low-Rank Decomposition](https://mlsanity.com/paper/2411.01016/) (2024)
- [Efficient Expert Pruning for Sparse Mixture-of-Experts Language Models: Enhancing Performance and Reducing Inference Costs](https://mlsanity.com/paper/2407.00945/) (2024)
- [MARLIN: Mixed-Precision Auto-Regressive Parallel Inference on Large Language Models](https://mlsanity.com/paper/2408.11743/) (2024)
- [MoEQuant: Enhancing Quantization for Mixture-of-Experts Large Language Models via Expert-Balanced Sampling and Affinity Guidance](https://mlsanity.com/paper/2505.03804/) (2025)

## Abstract (arXiv)

Mixture-of-Experts (MoE) large language models incur substantial memory costs due to their large expert parameter counts. Mixed-precision quantization reduces these costs by allocating different bit-widths to experts or linear blocks according to their importance. However, assigning a single precision within each expert or linear block overlooks its internal structural heterogeneity. This limitation motivates two key questions: (1) how to define a fine-grained unit for quantization within a linear transformation; and (2) how to characterize the quantization cost of each unit under actual activation patterns and different bit-widths. To address these two questions, we propose BitsMoE, a cost-aware mixed-precision quantization framework built on two complementary techniques: (1) Shared-basis Spectral Decomposition (SSD) separates expert weights into a shared basis and expert-specific spectral components, defining structural quantization units while exploiting cross-expert redundancy. (2) Factorized Quantization Cost Modeling (FQCM) estimates component-wise costs from output reconstruction loss by combining intrinsic spectral importance, activation-dependent importance, and bit-width-dependent distortion. Using these component-wise costs, we formulate bit allocation as an integer linear program (ILP) that minimizes total modeled quantization cost under a fixed memory budget. On Qwen3-30B-A3B at 2-bit, BitsMoE achieves 64.29% average accuracy over seven downstream tasks, outperforming the evaluated MoE-specific methods, including those using ILP-based bit allocation, and exceeding GEMQ by 2.80 percentage points. Under the same setting, it achieves a 16.47× end-to-end offline quantization speedup over GEMQ. It also achieves up to 6.46× the decode throughput of GPTQ.