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

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.

Language Identification via Compositional Data Analysis: A Linear-Time Classifier Based on Log-Ratio Geometry

Language identification is commonly addressed using either neural architectures or statistical n-gram models. Neural approaches typically require substantial computational resources, whereas classical frequency-based methods offer efficient linear-time performance, but rely on distance metrics that are not always appropriate for compositional data. This work models character and bigram frequency distributions as compositional vectors constrained to the simplex and mapped via the centered log-ratio (CLR) transformation bijectively onto the $(D-1)$-dimensional zero-sum subspace of $\mathbb{R}^D$, where Euclidean distances correspond to Aitchison distances. A pipeline is proposed, combining CLR-transformed unigram and bigram features with Laplace smoothing to address sparsity. The method is evaluated on six languages. Experimental results show that the proposed approach achieves robust accuracy across different text lengths, with strong performance for longer sequences. These findings indicate that compositional representations provide a deterministic and computationally efficient alternative for language identification, particularly in settings where interpretability and low resource consumption are essential.