MatryoshkaLoRA: Learning Accurate Hierarchical Low-Rank Representations for LLM Fine-Tuning

With the rise in scale for deep learning models to billions of parameters, the computational cost of fine-tuning remains a significant barrier to deployment. While Low-Rank Adaptation (LoRA) has become the standard for parameter-efficient fine-tuning, the need to set a predefined, static rank $r$ requires exhaustive grid searches to balance efficiency and performance. Existing rank-adaptive solutions such as DyLoRA mitigate this by sampling ranks during the training from a predefined distribution. However, they often yield sub-optimal results at higher ranks due to lack of consistent gradient signals across the full hierarchy of ranks, thus making these methods data-inefficient. We propose MatryoshkaLoRA, a general, Matryoshka-inspired training framework for LoRA-like techniques that learns accurate hierarchical low-rank representations by inserting a fixed, carefully crafted diagonal matrix $P$ between the existing LoRA adapters to scale their sub-ranks accordingly. By introducing this simple modification, our general framework recovers LoRA and DyLoRA only by changing $P$ and ensures all sub-ranks embed the available gradient information efficiently. Our MatryoshkaLoRA supports dynamic rank selection with minimal degradation in accuracy and show it is general enough by applying it to other LoRA-inspired techniques, such as DoRA and PiSSA. We theoretically justify a potential train–test mismatch by bounding the average optimality gap across the supported ranks, guaranteeing that the learned hierarchy remains close, on average, to independently optimized rank-specific adapters during inference. We further propose Area Under the Rank Accuracy Curve (AURAC), a metric that consistently evaluates the performance of hierarchical low-rank adapters. Our results demonstrate that MatryoshkaLoRA learns more accurate hierarchical low-rank representations than prior rank-adaptive approaches and achieves superior accuracy-performance trade-offs across ranks.