Spectral Outliers Reveal Dominant Learned Structure in Transformer Attention
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.