用随机矩阵理论发现Transformer注意力中的关键结构成分。
Spectral Outliers Reveal Dominant Learned Structure in Transformer Attention
- 通过MP理论分离注意力权重的随机噪声与显著信号。
- 移除信号成分后，模型在多个任务上性能接近随机水平。
- 揭示了注意力中重复出现的结构模式，适用于高效微调和剪枝。
我们应用马尔琴科-帕斯图随机矩阵理论分析预训练注意力权重，将每个投影矩阵分解为随机分布的主体部分和一组谱异常值（即信号）。通过因果验证发现：在Mistral-7B中置零MP识别出的异常值（信号）后，HellaSwag、MMLU和PIQA任务性能降至接近随机水平；而置零数量匹配的主体奇异值仅造成较小但显著的退化。在11个预训练Transformer中，我们识别出五种常见模式：谱异常值编码了主要学习结构；Q投影包含最多异常值；在分组查询注意力中，V投影无法清晰分离信号与噪声；输入级异常值在Q中形成结构化行带，在O中形成列带；特定残差流维度在K和O中跨层持续表现为带状异常值。最后，我们探讨这些发现对参数高效微调和结构化剪枝的启示。
原文摘要 · Abstract (English)
We apply Marchenko-Pastur (MP) random matrix theory to pre-trained attention weights in order to separate each projection matrix into a random-like bulk and a set of spectral outliers. We validate this decomposition causally: zeroing the MP-identified outliers (signal) in Mistral-7B drives HellaSwag, MMLU, and PIQA close to random-chance performance, whereas zeroing a count-matched subset of bulk singular values causes smaller but non-negligible degradation. Across 11 pre-trained transformers we identify five recurring patterns: spectral outliers encode a dominant component of the learned structure; Q projections carry the most outliers; V projections under grouped-query attention lack a clean signal/noise separation; entry-level outliers form structured row-bands in Q and column-bands in O; and specific residual-stream dimensions persist as band outliers across layers in K and O. We close by outlining how these observations could inform parameter-efficient fine-tuning and structured pruning.
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