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Kyle Elliott Mathewson

Publications and source records attributed to Kyle Elliott Mathewson.

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Universal Conceptual Structure in Neural Translation: Probing NLLB-200's Multilingual Geometry

Do neural machine translation models learn language-universal conceptual representations, or do they merely cluster languages by surface similarity? We investigate this question by probing the representation geometry of Meta's NLLB-200, a 200-language encoder-decoder Transformer, through six experiments that bridge NLP interpretability with cognitive science theories of multilingual lexical organization. Using the Swadesh core vocabulary list embedded across 135 languages, we find that the model's embedding distances significantly correlate with phylogenetic distances from the Automated Similarity Judgment Program ($\rho = 0.13$, $p = 0.020$), demonstrating that NLLB-200 has implicitly learned the genealogical structure of human languages. We show that frequently colexified concept pairs from the CLICS database exhibit significantly higher embedding similarity than non-colexified pairs ($U = 42656$, $p = 1.33 \times 10^{-11}$, $d = 0.96$), indicating that the model has internalized universal conceptual associations. Per-language mean-centering of embeddings improves the between-concept to within-concept distance ratio by a factor of 1.19, providing geometric evidence for a language-neutral conceptual store analogous to the anterior temporal lobe hub identified in bilingual neuroimaging. Semantic offset vectors between fundamental concept pairs (e.g., man to woman, big to small) show high cross-lingual consistency (mean cosine = 0.84), suggesting that second-order relational structure is preserved across typologically diverse languages. We release InterpretCognates, an open-source interactive toolkit for exploring these phenomena, alongside a fully reproducible analysis pipeline.

cs.CL

Magic Gems: A Polyhedral Framework for Magic Squares

We introduce Magic Gems, a geometric representation of magic squares as three-dimensional polyhedra. By mapping an n times n magic square onto a centered coordinate grid with cell values as vertical displacements, we construct a point cloud whose convex hull defines the Magic Gem. Building on prior work connecting magic squares to physical properties such as moment of inertia, this construction reveals an explicit statistical structure: we show that magic squares have vanishing covariances between position and value. We develop a covariance energy functional (the sum of squared covariances with individual row, column, and diagonal indicator variables) and prove that for all orders of n greater than or equal to three, an arrangement is a magic square if and only if this complete energy vanishes. This characterization transforms the classical line-sum definition into a statistical orthogonality condition. We also study a simpler low-mode relaxation using only four aggregate position indicators; this coincides with the complete characterization for n equals three (verified exhaustively) but defines a strictly larger class for n greater than or equal to four (explicit counterexamples computed). Perturbation analysis demonstrates that magic squares are isolated local minima in the energy landscape. The representation is invariant under dihedral symmetry D4, yielding canonical geometric objects for equivalence classes.

math.CO