# Smoothing the Top-k Exposure Boundary for Sparse Mixture-of-Experts

arXiv: https://arxiv.org/abs/2610.11575 · HTML: https://mlsanity.com/paper/2610.11575/

## 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 40 of its 47 references that are in the map.
- First posted on arXiv 8 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 40)

- [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)
- [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)
- [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)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [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)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [SWIFT:A Scalable lightWeight Infrastructure for Fine-Tuning](https://mlsanity.com/paper/2408.05517/) (2024)
- [BASE Layers: Simplifying Training of Large, Sparse Models](https://mlsanity.com/paper/2103.16716/) (2021)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [WinoGrande: An Adversarial Winograd Schema Challenge at Scale](https://mlsanity.com/paper/1907.10641/) (2019)

## Abstract (arXiv)

Sparse Mixture-of-Experts models scale parameter capacity efficiently while maintaining a fixed compute budget per token. However, traditional training paradigms enforce a static choice of top-k experts, which converts a continuous routing distribution into a rigid step function. This constraint introduces a brittle boundary where highly competitive experts are arbitrarily separated into full-supervision and zero-feedback zones based on minor score fluctuations. To address this issue, we propose Elastic Expert Routing, which stochastically samples the active expert budget from a localized discrete distribution centered at k. Over multiple training iterations, this mechanism softens the sharp threshold into a gradual probability distribution. Because the sampling neighborhood remains symmetric, this approach matches the expected computational cost of deterministic training, while preserving the inference budget. During supervised fine-tuning, elastic routing improves downstream macro-averages on OLMoE-1B-7B and Qwen3-30B-A3B by +0.84 and +2.02 points, respectively. In addition, in from-scratch pretraining, it reduces validation LM loss by up to 0.04 and outperforms the static top-k baseline by 1.6 points on average across downstream tasks. Comparisons on Qwen3 fine-tuning and from-scratch pretraining further show higher average scores than Noisy top-k, expert FFN dropout, and DefaultMoE.