A linear unembedding layer's weights analytically induce a Laguerre-Voronoi cell partition of representation space, and cell-based concept boundaries outperform point-based baselines

Ma & Wolfinger (2026) prove that any real LLM's linear unembedding layer (weight W, bias b) analytically induces a Laguerre-Voronoi diagram (weighted power diagram) over representation space -- each vocabulary token j becomes a center c_j=W_j/2 with weight nu_j=b_j+||W_j||^2/4, and the space partitions into convex cells algebraically identical to the layer's own argmax rule -- redefining a "concept" as an entire cell (not a point/direction) and a "category" as a union of cells [ma-wolfinger-2026-laguerre-geometry-for-interpreting-llms] On six real pretrained LLMs (Phi-2, Gemma-2-2B/9B, Gemma-3-270M, Pythia-70M, Llama-3.1-8B), a linear probe over this cell-based concept definition reaches lower error than point/cluster-based "Categorical Geometry" and "Lattice Geometry" baselines on Phi-2 (e.g. Animal vs. Plant: 0.111 vs. 0.121 vs. 0.145), and an unsupervised hierarchy/domination-score built from cell weights reaches 58.7-88.4% accuracy on Phi-2 versus a near-random 42-56% for the Lattice baseline [ma-wolfinger-2026-laguerre-geometry-for-interpreting-llms] A diagnostic "Geometric Lens" readout of which cell an intermediate-layer hidden vector occupies recovers the factually correct answer token under adversarial in-context interference more often than Logit Lens or Patchscopes across Phi-2, Gemma-2-2B/9B and Llama-3.1-8B (e.g. Phi-2: 0.56/0.31/0.49 across three city-swap datasets, versus near-zero for greedy top-1 decoding); no causal intervention (patching/ablation/steering) is performed [ma-wolfinger-2026-laguerre-geometry-for-interpreting-llms]