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

Abstract: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, $\pm1$ 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.

9 pages, 1 figure, 4 tables. Code: this https URL

Computation and Language (cs.CL); Machine Learning (cs.LG)

arXiv:2610.19966 [cs.CL]

(or arXiv:2610.19966v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2610.19966 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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