\lambda_{\mathrm{crit

Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic

arXiv:2606.08985v1 Announce Type: new Abstract: While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles. We refine the explanation of this phenomenon in three directions. First, we formalize a...