Three Tokens Force Exponential Feature Rank in Nonnegative Kernel Attention
How much feature rank does comparison require in kernel attention? On Min-IP over $m$-bit tokens, rank one solves every sequence of length at most two exactly. At length three, the minimum feature rank of one normalized nonnegative kernel-attention head is $2^{Θ(m)}$ for error strictly below $1/2$ on every input, even with arbitrary finite-dimensional tokenwise values and query-dependent affine readouts. Dense softmax solves this three-token task with $m$-dimensional scores and temperature constant in $m$. For every fixed number of heads $H$, the minimum total feature rank is $2^{Θ_H(m)}$ for the same error guarantee at exact length $H+2$ in one attention layer with affine mixing. These b...
| Authors | Vicente Opazo |
|---|---|
| Primary category | cs.LG |
| Published | 11 August 2026 |
| Last updated at source | 29 September 2026 |
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