# Exact Quantile Balancing and Load-Error Injection for Mixture-of-Experts

arXiv: https://arxiv.org/abs/2609.28053 · HTML: https://mlsanity.com/paper/2609.28053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Efficient MoE training and inference systems, one of 12 directions in Mixture-of-experts.
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Placed in

- Mixture-of-experts / [Efficient MoE training and inference systems](https://mlsanity.com/moe/efficient-moe-training-and-inference-systems/)

## Builds on (most cited first, 12 of 12)

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- [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)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [RadiK: Scalable and Optimized GPU-Parallel Radix Top-K Selection](https://mlsanity.com/paper/2501.14336/) (2025)

## Abstract (arXiv)

Mixture-of-Experts (MoE) training requires global load balance to prevent expert under-utilization and local balance for efficient expert-parallel execution. Existing distributed Quantile Balancing (QB) uses shard-dependent or approximate global quantiles, while token-independent expert biases cannot ensure microbatch-level balance. We introduce Exact Quantile Balancing (EQB), which computes exact global-batch BF16 quantiles with negligible communication, and Load-Error Injection (LEI), which injects local load errors directly into router-score gradients. On 7.5B-parameter MoEs trained for up to 500B tokens, EQB improves global balance and downstream performance over naive QB, while LEI improves local balance and outperforms the GShard loss at comparable quality.