Which Question Is Your Attention Metric Answering? Attention Rows as Compositional Data

2026-08-11

AI Summary

This study addresses analytical contradictions in Transformer attention metrics arising from inconsistent sink token treatment by modeling attention rows as compositional data. We propose an orthogonal decomposition method based on Aitchison distance to effectively decouple sink and content channels. This approach corrects 17–47% of similarity misjudgments and reveals that training entropy collapse is primarily driven by sink growth rather than attention sharpening, with sinks accounting for 95% of entropy reduction in large models. By resolving metric confusion inherent in traditional measures, this work prevents the hundred-fold perplexity inflation caused by erroneous pruning, thereby providing a reliable theoretical foundation for model compression.

Abstract

Each row of a transformer's attention matrix is a probability distribution over tokens, and in trained models most of that probability lands on a single \emph{sink} token, usually the first. Standard tools for comparing attention rows (cosine similarity, Jensen--Shannon divergence, Shannon entropy) therefore hinge on a choice papers rarely report: keep the sink, or drop it and renormalize. This choice can reverse conclusions. On ten pretrained models from five families, 17--47% of verdicts about which of two heads is more similar flip with the convention, and the most prominent structure in a standard BERT head-clustering pipeline is an artifact of it. The reason is that one-number summaries mix two questions: how much attention the sink takes, and how the rest is divided among the content tokens. Treating rows as compositional data separates them exactly: the Aitchison distance splits orthogonally into a sink term and a content term, entropy splits by an exact identity, and the content distance is characterized by invariances the transformer itself possesses. The separation matters in practice: most measured entropy collapse during training is the sink growing, not attention sharpening (30% of the drop at 70M parameters, 95% at 1B, 79% at 1.4B), and pruning heads with the wrong channel can inflate perplexity more than a hundredfold. We map where each convention is safe, test a frozen out-of-sample predictor (one confirmation, one abstention, one failure), and release code regenerating every number.

Problem

• Attention Metric
• Sink Token
• Compositional Data
• Transformer Interpretability
• Entropy Collapse

Innovation

• Compositional Data
• Aitchison Distance
• Attention Sink
• Metric Decomposition
• Entropy Collapse