Eckart–Young says the truncated SVD is the optimal low-rank approximation. This post turns that theorem into engineering — factorized layers, truncated-SVD compression, LoRA and its descendants QLoRA, DoRA, and GaLore, and nuclear-norm minimization for matrix completion.
Eckart–Young says the truncated SVD is the optimal low-rank approximation. This post turns that theorem into engineering — factorized layers, truncated-SVD compression, LoRA and its descendants QLoRA, DoRA, and GaLore, and nuclear-norm minimization for matrix completion.
LoRA works because weight matrices are empirically low-rank. SVD explains why, and the math of low-rank approximation explains how LoRA exploits it to fine-tune billion-parameter models on a laptop.
LoRA works because weight matrices are empirically low-rank. SVD explains why, and the math of low-rank approximation explains how LoRA exploits it to fine-tune billion-parameter models on a laptop.