# Sparsity Moves Computation: How FFN Architecture Reshapes Attention in Small Transformers

arXiv: https://arxiv.org/abs/2605.09403 · HTML: https://mlsanity.com/paper/2605.09403/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 10 May 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Using the Output Embedding to Improve Language Models](https://mlsanity.com/paper/1608.05859/) (2016)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [MoEfication: Transformer Feed-forward Layers are Mixtures of Experts](https://mlsanity.com/paper/2110.01786/) (2021)
- [Taming Sparsely Activated Transformer with Stochastic Experts](https://mlsanity.com/paper/2110.04260/) (2021)
- [Tying Word Vectors and Word Classifiers: A Loss Framework for Language Modeling](https://mlsanity.com/paper/1611.01462/) (2016)
- [Sparse MoE as the New Dropout: Scaling Dense and Self-Slimmable Transformers](https://mlsanity.com/paper/2303.01610/) (2023)
- [Understanding Addition in Transformers](https://mlsanity.com/paper/2310.13121/) (2023)
- [Bilinear MLPs enable weight-based mechanistic interpretability](https://mlsanity.com/paper/2410.08417/) (2024)
- [Counting and Algorithmic Generalization with Transformers](https://mlsanity.com/paper/2310.08661/) (2023)
- [Is Random Attention Sufficient for Sequence Modeling? Disentangling Trainable Components in the Transformer](https://mlsanity.com/paper/2506.01115/) (2025)
- [Counting in Small Transformers: The Delicate Interplay between Attention and Feed-Forward Layers](https://mlsanity.com/paper/2407.11542/) (2024)
- [Decoding Knowledge Attribution in Mixture-of-Experts: A Framework of Basic-Refinement Collaboration and Efficiency Analysis](https://mlsanity.com/paper/2505.24593/) (2025)
- [Deconstructing Pre-training: Knowledge Attribution Analysis in MoE and Dense Models](https://mlsanity.com/paper/2601.08383/) (2026)

## Abstract (arXiv)

Architectural choices inside the Transformer feedforward network (FFN) block do not merely affect the block itself; they reshape the computations learned by the rest of the model. We study this effect in one-layer Transformers trained on digit addition with carry, modular arithmetic, and histogram counting. Comparing dense FFNs, gated linear units (GLUs), mixture-of-experts (MoE), and MoE-GLUs, we find that sparse MoE routing can shift computation from FFN to attention, with the strongest ablation-visible effect on carry-based addition. We decompose this redistribution into reduced per-token FFN capacity and sparse partitioning across experts. Critically, frozen random routing nearly matches learned routing, suggesting that redistribution is driven largely by architectural sparsity rather than router-learned specialization. As a secondary finding, GLU-style multiplicative gating rotates task-relevant Fourier structure out of the per-neuron basis and into distributed subspaces, making neuron-level interpretability less informative while preserving structured computation. We validate these conclusions with random-routing, narrow-FFN, and top-2 MoE controls, plus parameter-matching, activation-function, and width-scaling analyses. Together, these results show that local FFN design choices can have nonlocal consequences for Transformer computation.