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

When attention concentrates on a single token, a sink, what is the model actually computing? Attention sinks are ubiquitous in softmax transformers, yet this shared visual signature can hide fundamentally different algorithms. We show that visually similar sink patterns can reflect two distinct mechanisms: (i) adaptive nop, where a head suppresses its update by routing to a null token, and (ii) broadcast, where a sink aggregates and redistributes global information. Each mechanism leaves distinct traces (nop-sinks exhibit negligible value norms; broadcast sinks induce low-rank outputs), which we formalize on synthetic tasks and use to derive practical diagnostics. Applied to pretrained vision transformers, these diagnostics reveal that both mechanisms exist at scale: sinks transition from CLS in early layers to patches in deeper layers and concentrate in specialized heads. Causal interventions further connect these signatures to near-null suppression and shared residual contributions. We then use architectural interventions to show how these computations can be reorganized: gating eliminates detected nop-like sinks but increases broadcast-like sinks, registers relocate rather than remove sink computation, and our position-free global pathway provides an explicit route for shared communication that reduces the broadcast-like sinks induced by gating. On dense probes, combining gating with the global pathway gives the strongest results among the tested variants, despite retaining some broadcast-like sinks. Overall, we find that the same attention pattern can reflect two very different computations, and that effective intervention depends not only on identifying the computation, but also on providing architectural alternatives through which the model can reorganize it.

The number of attention heads in a transformer is usually set by convention or grid search. We test a simple heuristic for setting it in advance: estimate the intrinsic dimension of token representations without labels, and use roughly that many heads. We estimate intrinsic dimension with a nested-dropout VAE trained on DistilBERT embeddings of WikiText-2, choosing the KL weight at the knee of the VAE's rate-distortion curve rather than by hand. This gives $k^*=9.2$ (95% CI [8.6, 9.8]). In a small 4-layer transformer trained from scratch, 10 heads and 32 heads are statistically equivalent on SST-2 and on MRPC (paired TOST over 10 seeds, $\pm1$ point margin), with 69% fewer attention parameters for the 10-head model. Training 10 heads from the start also slightly outperforms training 32 heads and pruning to 10 (0.6 points, $p=0.008$). The evidence is narrow: two classification tasks, one small architecture, no pretrained models, and no formal link between intrinsic dimension and head count. We present the result as a practical heuristic worth testing at larger scale, not as a general principle.

Computationally demanding and opaque deep learning models can be better understood and optimized by analyzing how they transform data. While deep transformers have been widely studied in computer vision and natural language processing, their application in tabular data remains relatively underexplored. This paper presents one of the first applications of an importance-scoring metric to interpret multi-head transformer models in learning from tabular data. Experiments conducted on 40 diverse tabular datasets demonstrate robustness to head drops based on the proposed head importance score. In 72.5% of experimental examples, the model remains most resilient to performance drops when heads with the lowest importance scores are gradually removed. In contrast, removing the most important attention head first results in the greatest reduction in classification performance. A closer look at individual head importance scores across six attention layers reveals that important heads are scattered across layers, with no consistent layer-specific trends. In contrast to the image and language domains, the importance of individual attention heads varies considerably across tabular datasets with different schemas and feature spaces. The proposed importance score can improve efficiency and redundancy within transformer architectures. We make the source code for measuring the importance of individual attention heads publicly available.