# SLEM: Spectrum-Aware Latent Expert Merging

arXiv: https://arxiv.org/abs/2610.16484 · HTML: https://mlsanity.com/paper/2610.16484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 39 of its 48 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 30 of 39)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus](https://mlsanity.com/paper/2104.08758/) (2021)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Merge, Then Compress: Demystify Efficient SMoE with Hints from Its Routing Policy](https://mlsanity.com/paper/2310.01334/) (2023)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [Hyper-Representations as Generative Models: Sampling Unseen Neural Network Weights](https://mlsanity.com/paper/2209.14733/) (2022)
- [MoE-Pruner: Pruning Mixture-of-Experts Large Language Model using the Hints from Its Router](https://mlsanity.com/paper/2410.12013/) (2024)
- [Neural Functional Transformers](https://mlsanity.com/paper/2305.13546/) (2023)
- [A Survey on Inference Optimization Techniques for Mixture of Experts Models](https://mlsanity.com/paper/2412.14219/) (2024)
- [REAP the Experts: Why Pruning Prevails for One-Shot MoE compression](https://mlsanity.com/paper/2510.13999/) (2025)
- [Diffusion-Based Neural Network Weights Generation](https://mlsanity.com/paper/2402.18153/) (2024)
- [Merging Experts into One: Improving Computational Efficiency of Mixture of Experts](https://mlsanity.com/paper/2310.09832/) (2023)
- [LFM2 Technical Report](https://mlsanity.com/paper/2511.23404/) (2025)
- [Retraining-Free Merging of Sparse MoE via Hierarchical Clustering](https://mlsanity.com/paper/2410.08589/) (2024)
- [Delta Decompression for MoE-based LLMs Compression](https://mlsanity.com/paper/2502.17298/) (2025)
- [Sub-MoE: Efficient Mixture-of-Expert LLMs Compression via Subspace Expert Merging](https://mlsanity.com/paper/2506.23266/) (2025)
- [DiEP: Adaptive Mixture-of-Experts Compression through Differentiable Expert Pruning](https://mlsanity.com/paper/2509.16105/) (2025)
- [Equivariant Neural Functional Networks for Transformers](https://mlsanity.com/paper/2410.04209/) (2024)
- [Learning Useful Representations of Recurrent Neural Network Weight Matrices](https://mlsanity.com/paper/2403.11998/) (2024)
- [MoNE: Replacing Redundant Experts with Lightweight Novices for Structured Pruning of MoE](https://mlsanity.com/paper/2507.00390/) (2025)
- [Mosaic Pruning: A Hierarchical Framework for Generalizable Pruning of Mixture-of-Experts Models](https://mlsanity.com/paper/2511.19822/) (2025)

## Abstract (arXiv)

Mixture-of-Experts (MoE) models scale model capacity efficiently by activating only a small subset of experts for each input, while still requiring all parameters to be stored in memory, resulting in substantial memory overhead. Expert merging techniques have recently emerged as a promising compression paradigm that reduces this overhead by consolidating multiple experts into a smaller set. However, existing approaches have two key limitations: (i) direct convex interpolation in parameter space is not generally guaranteed to yield meaningful interpolation of expert functions; and (ii) estimating expert similarity or merging coefficients often relies on calibration data, introducing dependence on the calibration distribution. To address these limitations, we propose Spectrum-Aware Latent Expert Merging (SLEM), a calibration-free expert merging framework that occurs in a structured latent representation of expert weights using a VAE. SLEM groups experts within and across layers based on latent similarities and derives merging coefficients from expert weight spectra. It then performs geometry-aware latent interpolation and decodes the resulting representations into merged expert weights. Compared with existing expert merging methods, SLEM achieves comparable or better performance on general knowledge benchmarks and higher average performance on generation benchmarks involving mathematical reasoning and code generation.