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.

Geometry-Aware Bayesian Quantification via Compositional Data Analysis

Accurately estimating the unknown target label distribution is the critical first step for adapting to label shift. This task, widely known as quantification or class prevalence estimation, has recently seen significant advances through continuous KDE-based methods which model the density of multiclass classifier posteriors. Posterior vectors might be regarded as compositional data, since they lie on the probability simplex. However, existing KDE-based quantifiers typically rely on Euclidean Gaussian kernels, which ignore simplex geometry and incorrectly assign probability mass outside its boundaries. We introduce a geometry-aware KDE model for multiclass quantification based on log-ratio representations and Aitchison geometry, together with a shrinkage regularization that improves robustness near the simplex boundary. Combined with a maximum-likelihood interpretation of KDE-based quantification, we derive both point-estimation and Bayesian inference procedures for class prevalences. Experiments on 42 datasets across tabular, text, and image domains show that the proposed method is competitive with state-of-the-art quantifiers, often improving over standard KDE-based baselines, while also yielding strong results among Bayesian quantification methods.

Kernel-Based Functional Balancing for Causal Inference with Compositional Treatments

We study causal effect estimation with compositional treatments, where the exposure lies on a simplex and the estimand is defined over compositions rather than scalar or binary values. By considering a projection of the average potential outcome onto the treatment space, a kernel-based covariate functional balancing approach is adopted for weight construction. The weights are obtained by directly minimizing a worst-case balancing error over a reproducing kernel Hilbert space (RKHS) defined on the joint space of treatments and covariates, instead of being estimated under a treatment assignment model. Building on these weights, an augmented weighted estimator (AWE) is proposed, where the outcome function is estimated via kernel ridge regression and combined with a marginal augmentation over the covariate distribution. Despite the complex structure of the resulting objective, a finite-dimensional convex optimization problem is formulated via a representer theorem and a low-rank approximation. The proposed estimator achieves $\sqrt{n}$-consistency without requiring consistent estimation or smoothness of the weights. An asymptotic normality result is established around a sample-specific target. Empirical performance is demonstrated through simulation studies and a real data application.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex

Compositional data -- vectors encoding relative proportions -- arise across scientific domains, including ecology, geochemistry, and genomics. The features in these data often come with known hierarchical structure (e.g., taxonomies, phylogenies, ontologies), yet existing methods either ignore this structure, discard the intrinsic Aitchison geometry, are designed for binary trees, or yield incomplete coordinate systems. We describe PolyILR, a canonical orthonormal decomposition of the Aitchison tangent space aligned with any tree topology. Our construction defines a weighted local geometry at each internal node capturing full branching structure, then lifts these to a global orthonormal basis where every coordinate corresponds to a specific tree location. On microbiome and single-cell benchmarks, PolyILR yields stable, interpretable features and enables inference at multiscale tree resolution. We also establish a novel theoretical connection to softmax classifiers, suggesting possible applications to probabilistic modeling.