# Dense vs Sparse Pretraining at Tiny Scale: Active-Parameter vs Total-Parameter Matching

arXiv: https://arxiv.org/abs/2605.13769 · HTML: https://mlsanity.com/paper/2605.13769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 17 of its 17 references that are in the map.
- First posted on arXiv 13 May 2026.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 17 of 17)

- [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)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Unified Scaling Laws for Routed Language Models](https://mlsanity.com/paper/2202.01169/) (2022)
- [MegaBlocks: Efficient Sparse Training with Mixture-of-Experts](https://mlsanity.com/paper/2211.15841/) (2022)
- [Efficient Large Scale Language Modeling with Mixtures of Experts](https://mlsanity.com/paper/2112.10684/) (2021)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [Parameters vs FLOPs: Scaling Laws for Optimal Sparsity for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2501.12370/) (2025)
- [Joint MoE Scaling Laws: Mixture of Experts Can Be Memory Efficient](https://mlsanity.com/paper/2502.05172/) (2025)
- [Mixture-of-Experts Can Surpass Dense LLMs Under Strictly Equal Resource](https://mlsanity.com/paper/2506.12119/) (2025)

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

- [Dense Mixture-of-Experts as a Reparameterized Wide FFN: A Granularity Sweep at Fixed Compute](https://mlsanity.com/paper/2610.02584/) (2026)

## Abstract (arXiv)

We study dense and mixture-of-experts (MoE) transformers in a tiny-scale pretraining regime under a shared LLaMA-style decoder training recipe. The sparse model replaces dense feed-forward blocks with Mixtral-style routed experts. Dense baselines are modestly width-resized to tightly match either active or total parameter budgets, while tokenizer, data, optimizer, schedule, depth, context length, normalization style, and evaluation protocol are held fixed. Our best sparse recipe uses four experts, top-2 routing, Switch-style load balancing, and router z-loss. In a three-seed full-data comparison, the dense active-match model reaches 1.6545 +/- 0.0012 best validation loss, the MoE reaches 1.5788 +/- 0.0020, and the dense total-match model reaches 1.5608 +/- 0.0025. This yields a matched-active gap of 0.0758 +/- 0.0021 in the MoE's favor and a matched-total gap of 0.0180 +/- 0.0020 in the dense model's favor. Across training, the matched-active advantage grows while the matched-total dense advantage narrows sharply. In this sub-25M-parameter regime, MoE therefore improves validation loss under active-parameter matching but does not surpass dense training at equal total stored capacity.