[2507.07580] COALA: Numerically Stable and Efficient Framework for Context-Aware Low-Rank Approximation

Computer Science > Machine Learning arXiv:2507.07580 (cs) [Submitted on 10 Jul 2025 (v1), last revised 25 Mar 2026 (this version, v3)] Title:COALA: Numerically Stable and Efficient Framework for Context-Aware Low-Rank Approximation Authors:Uliana Parkina, Maxim Rakhuba View a PDF of the paper titled COALA: Numerically Stable and Efficient Framework for Context-Aware Low-Rank Approximation, by Uliana Parkina and 1 other authors View PDF HTML (experimental) Abstract:Recent studies suggest that context-aware low-rank approximation is a useful tool for compression and fine-tuning of modern large-scale neural networks. In this type of approximation, a norm is weighted by a matrix of input activations, significantly improving metrics over the unweighted case. Nevertheless, existing methods for neural networks suffer from numerical instabilities due to their reliance on classical formulas involving explicit Gram matrix computation and their subsequent inversion. We demonstrate that this can degrade the approximation quality or cause numerically singular matrices. To address these limitations, we propose a novel inversion-free regularized framework that is based entirely on stable decompositions and overcomes the numerical pitfalls of prior art. Our method can handle possible challenging scenarios: (1) when calibration matrices exceed GPU memory capacity, (2) when input activation matrices are nearly singular, and even (3) when insufficient data prevents unique approximation. For ...