# DOT-MoE: Differentiable Optimal Transport for MoEfication

arXiv: https://arxiv.org/abs/2606.01666 · HTML: https://mlsanity.com/paper/2606.01666/

## Key facts

- Cited by 1 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 21 of its 45 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [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)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (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)
- [SLEB: Streamlining LLMs through Redundancy Verification and Elimination of Transformer Blocks](https://mlsanity.com/paper/2402.09025/) (2024)
- [MoDeGPT: Modular Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2408.09632/) (2024)
- [The LLM Surgeon](https://mlsanity.com/paper/2312.17244/) (2023)
- [LLaMA-MoE v2: Exploring Sparsity of LLaMA from Perspective of Mixture-of-Experts with Post-Training](https://mlsanity.com/paper/2411.15708/) (2024)
- [Analytical FFN-to-MoE Restructuring via Activation Pattern Analysis](https://mlsanity.com/paper/2502.04416/) (2025)

## Built on by (most cited first, 1 of 1)

- [Spectral-MoE: Heterogeneous Per-Layer Expert Utilization in Dense-to-MoE Conversion](https://mlsanity.com/paper/2610.19232/) (2026)

## Abstract (arXiv)

The scaling of Large Language Models (LLMs) has driven significant performance gains but created substantial challenges in inference efficiency. While Mixture of Experts (MoEs) architectures address this by decoupling model size from inference cost, training MoEs from scratch is often unstable and compute intensive. Conversion of pre-trained dense models into sparse MoEs has emerged as an alternative solution; however, existing methods typically rely on heuristic neuron clustering or random splitting to partition the Feed-Forward Network (FFN) into experts. In this work, we propose DOT-MoE, a novel framework that formulates the decomposition of dense layers as a Differentiable Optimal Transport (DOT) problem. Instead of static heuristics, we model neuron assignment as a balanced transport problem, utilizing differentiable Sinkhorn-Knopp iterations to enforce strict expert capacity constraints. Furthermore, we utilize Straight-Through Estimators (STE) to jointly learn the discrete neuron-to-expert assignment and the token-to-expert routing policy end-to-end. Extensive experiments across multiple architectures and benchmarks demonstrate that DOT-MoE significantly outperforms structured pruning, heuristic clustering, and random-split baselines, retaining 90% of the original dense model's performance while reducing active parameters by 50%.