# Choosing the Number of Attention Heads from Intrinsic Dimension: A Small-Scale Study

arXiv: https://arxiv.org/abs/2610.19966 · HTML: https://mlsanity.com/paper/2610.19966/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 16 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Learning Ordered Representations with Nested Dropout](https://mlsanity.com/paper/1402.0915/) (2014)

## Abstract (arXiv)

The number of attention heads in a transformer is usually set by convention or grid search. We test a simple heuristic for setting it in advance: estimate the intrinsic dimension of token representations without labels, and use roughly that many heads. We estimate intrinsic dimension with a nested-dropout VAE trained on DistilBERT embeddings of WikiText-2, choosing the KL weight at the knee of the VAE's rate-distortion curve rather than by hand. This gives k^*=9.2 (95% CI [8.6, 9.8]). In a small 4-layer transformer trained from scratch, 10 heads and 32 heads are statistically equivalent on SST-2 and on MRPC (paired TOST over 10 seeds, ±1 point margin), with 69% fewer attention parameters for the 10-head model. Training 10 heads from the start also slightly outperforms training 32 heads and pruning to 10 (0.6 points, p=0.008). The evidence is narrow: two classification tasks, one small architecture, no pretrained models, and no formal link between intrinsic dimension and head count. We present the result as a practical heuristic worth testing at larger scale, not as a general principle.