Gradient Intrinsic Dimensionality Alignment：Narrowing The Gap Between Low-Rank Adaptation and Full Fine-Tuning

Abstract

Parameter-Efficient Fine-Tuning (PEFT) techniques, such as Low-Rank Adaptation (LoRA) and its variants, have emerged as critical tools for adapting large pretrained models under limited computational resources. However, a notable performance gap persists between these LoRA methods and Full Fine-Tuning (FFT). In this paper, we investigate a key yet overlooked cause of this gap: the relationship between LoRA's low-rank adaptation subspace and true effective update directions of FFT gradients, which we define as the **gradient intrinsic dimensionality**. To systematically quantify this dimension, we first propose a novel entropy-based estimator, uncovering substantial discrepancies (up to more than 100x) between the rank of LoRA and the gradient intrinsic dimensionality. Motivated by this finding, we introduce **RaLoRA**, which adaptively aligns the ranks of LoRA adapters with layer-specific gradient intrinsic dimensions, without increasing the number of overall parameters. We further extend this approach into **RaLoRA-Pro**, integrating intra-layer rank alignment and inter-layer parameter reallocation guided by loss sensitivity, enabling finer-grained capacity relocation under comparable parameters. Extensive experiments demonstrate the effectiveness of our methods. Specifically, compared to vanilla LoRA, our methods achieve more than +5\% improvement on GLUE, +0.57 on MT-Bench, +5.23\% on GSM8K, +5.69\% on HumanEval, and +1.58\% on image classification, confirming consistent and substantial performance gains across diverse tasks and modalities.