# DTop-p MoE: Sparsity-Controlled Dynamic Top-p MoE for Foundation Model Pre-training

arXiv: https://arxiv.org/abs/2512.13996 · HTML: https://mlsanity.com/paper/2512.13996/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 48 of its 63 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## 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 48)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [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)
- [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)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [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)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus](https://mlsanity.com/paper/2104.08758/) (2021)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)

## Built on by (most cited first, 3 of 3)

- [Expert Threshold Routing for Autoregressive Language Modeling with Dynamic Computation Allocation and Load Balancing](https://mlsanity.com/paper/2603.11535/) (2026)
- [BEAM: Binary Expert Activation Masking for Dynamic Routing in MoE](https://mlsanity.com/paper/2605.14438/) (2026)
- [How Many Ranks Does a Token Need? A Noise-Floor Squelch for Rank-One LoRA Experts](https://mlsanity.com/paper/2610.19033/) (2026)

## Abstract (arXiv)

Sparse Mixture-of-Experts architectures are essential for scaling model capacity efficiently, yet the standard Top-k routing imposes a rigid sparsity pattern that ignores the intrinsic variance in token difficulty and layer-specific computational needs. Top-p routing is more adaptive because it selects experts until their cumulative routing probability reaches a threshold, allowing confident tokens to use fewer experts and ambiguous tokens to recruit more. However, we demonstrate that existing naive Top-p implementations with fixed global probability thresholds provide only marginal gains over Top-k, suffer from hyperparameter sensitivity, and result in uncontrolled computational costs. In this paper, we propose **DTop-p**, a sparsity-controllable dynamic routing mechanism that learns the Top-p probability threshold with a Proportional-Integral controller and uses dynamic routing normalization to support layer-wise expert selection under a global sparsity constraint. Extensive experiments on Large Language Models and Diffusion Transformers demonstrate that **DTop-p** consistently outperforms both Top-k and fixed Top-p baselines while matching the average FLOPs of Top-k MoE. Our analysis confirms that **DTop-p** exhibits strong scaling properties across expert granularity, total expert capacity, model size, and dataset size, offering a robust and efficient MoE framework for foundation model pre-training.