Fingerprint, Not Blueprint: How Positional Schemes Set the Default Spectral Algebra of Attention
The pre-softmax score of an attention head is a bilinear form $score(i,j) = x_i^T M x_j$ in a learned operator $M = W_q^T W_k$. Because M is generally non-symmetric, hence non-normal, it has a complex eigenspectrum and non-orthogonal eigenvectors, the regime where non-Hermitian and random-matrix tools apply. We ask what this spectrum encodes, at three levels for previous-token and induction circuits. Statically, across seven pretrained models spanning three positional schemes, the strongest previous-token heads are spectrally rotational under RoPE and non-rotational, or content-like, where position enters outside QK (learned-absolute and ALiBi); the model-level separation is perfect at ev...
| Authors | Li Hengyu |
|---|---|
| Primary category | cs.LG |
| Published | 7 July 2026 |
| Last updated at source | 7 July 2026 |
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