VC Dimension and Expressivity of Real-Valued Transformers
Whereas previous results on abilities and limitations of transformers have restricted the definition of transformers in various ways, here we study softmax-attention, multi-layer transformers operating on real values, with very few additional assumptions. Applying results from real geometry, we obtain upper bounds on the VC dimension and split VC dimension of such transformers ($O(n^4)$ and $O(n^6)$, respectively, where $n$ is the input length). Conversely, we also construct specific transformers witnessing lower bounds on these quantities ($Ω(n)$ in each case). These results have some notable consequences. For example, within the class of symmetric (permutation-invariant) functions, we s...
| Authors | Gavin Dooley, Andy Yang, Yijia Jessica Zhu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 25 September 2026 |
| Last updated at source | 25 September 2026 |
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