arXiv Machine Learning October 23, 2026 By Sebastian Loeschcke, Ivan Koryakovskiy, Tycho F. A. van der Ouderaa, Riccardo Del Chiaro, Mart van Baalen, Paul N. Whatmough, Markus Nagel

SQuAT: Spherical Lattice Vector Quantization-Aware Training

Read the original on arXiv Machine Learning →

SQuAT introduces a shape‑gain vector quantization‑aware training (VQ‑QAT) method that separates weight direction and magnitude, using an $E_8$‑derived spherical codebook for directions and low‑bit scalar quantizers for gains. By applying distinct straight‑through estimators (STE) to each component, SQuAT induces tangent‑space updates that act as an implicit spherical (Riemannian) optimization, improving training dynamics over standard STE approaches. A distributed exact nearest‑neighbor assignment scheme further reduces training time by 12.8×, enabling scaling to 10 B tokens and achieving state‑of‑the‑art accuracy on several large language models.

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