Kartik Sharma

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2026

Outlier dimensions are a recurring geometric property of transformer representations that have been linked to token frequency in pretrained language models. However, studies on pretrained models cannot disentangle token frequency from semantic and optimization confounds, preventing a causal understanding of whether frequency itself drives outlier formation. These distortions also degrade probing accuracy and hinder model compression, motivating a controlled study of their origin. We address this issue by isolating frequency skew as a controlled variable in a synthetic transformer trained on data with a tunable Zipfian token distribution. We find that outlier magnitude remains stable under low skew but increases sharply beyond a moderate threshold. A frozen frequency-based output bias fails to reproduce this behavior, model capacity exhibits a non-monotonic U-shaped effect, and an L2-normalized cosine softmax suppresses outlier geometry only under a large temperature not reached by standard training. These results identify frequency skew as a causal driver of outlier dimensions and show that removing their geometry requires an intervention beyond standard training.