Basis Optimization for Spectral Compression of Deep Learning Matrices

Large-scale inference pipelines are typically memory-bound, so smaller stored forms of their matrices reduce latency. Spectral compression trades a controlled error for a shorter description by discarding the least important directions of a matrix. This paper analyzes whether the basis in which the truncation occurs is an optimization target that yields savings beyond plain spectral compression. We (i) formalize basis-optimized spectral compression as a task scored by two costs, the parameters a representation stores and the values a product reads, (ii) introduce Basis-Native Disentanglement (BND), which adapts tensor disentanglement from quantum many-body physics by anchoring the basis search at the native coordinates and by building the rotation from a bounded number of planes to control its parameter cost, and (iii) run it on 1337 matrices from six families of deep learning matrices and two controls. At a relative error of one percent, BND never stores more parameters than raw storage or plain SVD and stores fewer than raw storage on 86% of the matrices. Gradients and state spaces are natively low rank and compress more than tenfold without any rotation, weights gain barely more than noise, and key value caches hold statistically significant structure beyond their spectrum that only a learned basis reveals. Saved parameters convert to load time at the rate of the channel. Our findings mark basis-optimized spectral compression as a real but narrow axis for compressing deep learning matrices.