# Spectral-MoE: Heterogeneous Per-Layer Expert Utilization in Dense-to-MoE Conversion

arXiv: https://arxiv.org/abs/2610.19232 · HTML: https://mlsanity.com/paper/2610.19232/

## 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 44 references that are in the map.
- First posted on arXiv 13 Oct 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)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Outlier Weighed Layerwise Sparsity (OWL): A Missing Secret Sauce for Pruning LLMs to High Sparsity](https://mlsanity.com/paper/2310.05175/) (2023)
- [MoEfication: Transformer Feed-forward Layers are Mixtures of Experts](https://mlsanity.com/paper/2110.01786/) (2021)
- [LLaMA-MoE: Building Mixture-of-Experts from LLaMA with Continual Pre-training](https://mlsanity.com/paper/2406.16554/) (2024)
- [AI and Memory Wall](https://mlsanity.com/paper/2403.14123/) (2024)
- [Harder Tasks Need More Experts: Dynamic Routing in MoE Models](https://mlsanity.com/paper/2403.07652/) (2024)
- [AdaMoE: Token-Adaptive Routing with Null Experts for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2406.13233/) (2024)
- [LLaMA-MoE v2: Exploring Sparsity of LLaMA from Perspective of Mixture-of-Experts with Post-Training](https://mlsanity.com/paper/2411.15708/) (2024)
- [Learn To be Efficient: Build Structured Sparsity in Large Language Models](https://mlsanity.com/paper/2402.06126/) (2024)

## Abstract (arXiv)

Large language models impose substantial memory demands and arithmetic costs during inference. Dense-to-mixture-of-experts (MoE) conversion is a model optimization technique that aims to reduce these arithmetic costs. Dense-to-MoE conversion partitions pretrained feed-forward network (FFN) neurons into experts and selects a subset for each token. Leading methods fall into two categories: analytic methods produce a converted model quickly using heuristics, while learning methods produce a model much more slowly by optimizing via gradients. Both approaches, however, fix the same active expert count, or "utilization," at every layer. We introduce Spectral-MoE, which learns to allocate a utilization budget heterogeneously across layers. Its name draws a metaphor between separating a dense FFN into experts and separating a light beam into its spectrum. Spectral-MoE consists of two distinct approaches: a static approach that uses a single per-layer scalar which is shared across tokens, and a dynamic approach which emits a per-token schedule. We demonstrate that both allocators improve performance over uniform on both the analytic-based and learning-based SOTA dense-to-MoE methods. At 25% FFN utilization, dynamic allocation reduces WikiText-2 perplexity relative to uniform by 1.04, 2.96, and 2.71 points on the learned base for Llama-2-7B, Llama-3-8B, and Qwen2.5-7B, respectively. The corresponding reductions on the analytic base are 2.45, 6.26, and 2.17 points. On the learned base, dynamic allocation improves six-task mean accuracy over uniform by an average of 1.5, 4.2, and 3.6 percentage points across the three models at FFN utilizations of 12.5%, 25%, and 50%, respectively. These results establish per-layer expert utilization as a novel optimization axis in dense-to-MoE conversion.