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title: "Min-IP — Stuff That Spins"
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# Min-IP

**Type:** topic  
## Related Articles

- [Three Tokens Force Exponential Feature Rank in Nonnegative Kernel Attention](https://stuffthatspins.com/spin/three-tokens-force-exponential-feature-rank-in-nonnegative-kernel-attention) — August 13, 2026

## Related Claims

- Any single normalized nonnegative kernel-attention head that succeeds on all three-token sequences with error strictly below $1/2$ requires $2^{\Omega(m)}$ features, even with arbitrary finite-dimensional tokenwise values and an arbitrary query-dependent affine readout.

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