Beyond Low-Rank Parameterization: Narrowing the Gap Between LoRA and Full Fine-Tuning via Gradient Decomposition

תקציר מקורי באנגליתarXiv:2609.37027v1 Announce Type: new Abstract: Low-Rank Adaptation (LoRA) is a widely used approach to parameter-efficient fine-tuning (PEFT), yet a performance gap can remain relative to full fine-tuning (FFT). Many LoRA variants improve the initialization or optimization of low-rank factors. At each training step, however, their first-order weight-space directions are constrained by the current parameterization. We characterize the corresponding LoRA-accessible gradient space and show that it coincides with the tangent space induced by the current LoRA parameterization. This characterization yields an orthogonal decomposition of the full weight gradient at the current model parameters. We term the component orthogonal to this space the normal gradient. Based on this decomposition, we pr