← 研踪 PaperTrailarXiv:2611.02778 · v1
Spectral Degeneration of Self-Attention under Isotropic Score Geometry
首次提交 2026-11-02 16:54
版本更新 2026-11-02 16:54
雷达观测 2026-11-04 23:42
摘要
We study the spectral structure of the self-attention matrix in Transformer models through an idealized spectral model for the pre-softmax score matrix. Motivated by the rotational isotropy of query and key representations, our model replaces the random token-space orientation of the score matrix by its canonical singular-value representative with a logarithmic spike--bulk separation. Empirical diagnostics on pretrained vision and language transformers motivate this model: token-space singular matrices have nearly uniform eigen-angle distributions, and score spectra are dominated by a small number of effective directions. We then prove that the row-wise softmax map transforms this structure into a degenerate attention matrix: dominant modes are preserved, whereas the bulk spectral distributions concentrate at zero. Stable rank remains bounded for bidirectional attention but grows logarithmically for causal attention. Within the canonical model, these results explain how attention can preserve a small number of dominant directions while compressing the remaining bulk modes.
作者备注：NeurIPS 2026
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-02 16:54 · 最新观测版本
Spectral Degeneration of Self-Attention under Isotropic Score Geometry
We study the spectral structure of the self-attention matrix in Transformer models through an idealized spectral model for the pre-softmax score matrix. Motivated by the rotational isotropy of query and key representations, our model replaces the random token-space orientation of the score matrix by its canonical singular-value representative with a logarithmic spike--bulk separation. Empirical diagnostics on pretrained vision and language transformers motivate this model: token-space singular matrices have nearly uniform eigen-angle distributions, and score spectra are dominated by a small number of effective directions. We then prove that the row-wise softmax map transforms this structure into a degenerate attention matrix: dominant modes are preserved, whereas the bulk spectral distributions concentrate at zero. Stable rank remains bounded for bidirectional attention but grows logarithmically for causal attention. Within the canonical model, these results explain how attention can preserve a small number of dominant directions while compressing the remaining bulk modes.
查看此版本解读 →查看此版本原文 ↗