COBRA: Contribution-Based Bayesian Rank Allocation for Parameter-Efficient Fine-Tuning

Full fine-tuning of large language models (LLMs) incurs prohibitive computational and storage costs. Parameter-efficient fine-tuning (PEFT) addresses this limitation, with Low-Rank Adaptation (LoRA) gaining widespread adoption due to its simplicity and zero inference overhead. However, LoRA and its variants typically rely on uniform rank allocation or a single importance metric such as gradient magnitude or output sensitivity to guide rank distribution. This approach fails to recognize that gradient magnitude and output contribution are decoupled properties, leading to suboptimal allocation where critical layers are under-provisioned while less important ones waste capacity. To address this challenge, we propose COBRA, a principled framework integrating dual importance factors for adaptive rank allocation. COBRA operates in three stages: (1) layer conductance attribution quantifies each layer's contribution via path-integral attribution; (2) dual-factor aggregation combines contribution with adaptation demand, producing the Task-Adaptive Layer Conductance (TA-LC) distribution; and (3) Bayesian rank allocation translates this distribution into optimal heterogeneous ranks via variational optimization. Layer conductance provides layer-level interpretability by explicitly quantifying how much each layer contributes to predictions without redundancy, directly aligning with the granularity of rank allocation decisions and enabling principled cross-layer comparison for rank distribution. Experiments across diverse architectures and tasks demonstrate that COBRA consistently outperforms existing methods, achieving up to 1.6 points improvement on GLUE and a 6.6% average MSE reduction in high-rank regression regimes under comparable parameter budgets.