Parameter-Efficient Fine-Tuning with Learnable Rank

Parameter-efficient fine-tuning (PEFT) methods face a tradeoff between adapter size and expressivity: ultra-low-parameter adapters are confined to fixed low-rank subspaces, capping performance even with extended training. We propose BoostLoRA, a gradient-boosting framework that overcomes this limit by iteratively training and merging minimal adapters on the examples the current model gets wrong. A ROTATE SVD basis strategy assigns each round to an orthogonal subspace, so cumulative effective rank grows linearly with the number of rounds while each adapter remains ultra-low-rank. After merging, adapters are discarded, leaving zero inference overhead. On Qwen2.5-3B, BoostLoRA reaches 89.1% on GSM8K and 68.8% on MATH-500, surpassing both the best single-shot ultra-low parameter adapter (TinyLoRA) and full fine-tuning; on code generation it reaches 57.2% on MBPP and 80.4% on HumanEval while full fine-tuning drops below the zero-shot baseline. We also demonstrate cross-architecture transfer on protein binding classification with ESM2-650M and cross-entropy training. BoostLoRA is, to our knowledge, the first PEFT method whose effective rank grows with training, separating per-round parameter cost from total representational capacity.

Exponential growth in the scale of modern foundation models has led to the widespread adoption of Low-Rank Adaptation (LoRA) as a parameter-efficient fine-tuning technique. However, standard LoRA implementations disregard the varying intrinsic dimensionality of model layers and enforce a uniform rank, leading to parameter redundancy. We propose Post-Optimization Adaptive Rank Allocation (PARA), a data-free compression method for LoRA that integrates seamlessly into existing fine-tuning pipelines. PARA leverages Singular Value Decomposition to prune LoRA ranks using a global threshold over singular values across all layers. This results in non-uniform rank allocation based on layer-wise spectral importance. As a post-hoc method, PARA circumvents the training modifications and resulting instabilities that dynamic architectures typically incur. We empirically demonstrate that PARA reduces parameter count by 75-90% while preserving the predictive performance of the original, uncompressed LoRA across multiple vision and language benchmarks. Code will be published upon acceptance.

Low-Rank Adaptation (LoRA) has become a widely adopted parameter-efficient fine-tuning method for large language models, with its effectiveness largely influenced by the allocation of ranks and scaling factors, as well as initialization. Existing LoRA variants typically address only one of these factors, often at the cost of increased training complexity or reduced practical efficiency. In this work, we present Task-aware Low-Rank Adaptation (TLoRA), a unified framework that jointly optimizes initialization and resource allocation at the outset of training. TLoRA introduces a data-driven initialization strategy that aligns the LoRA $A$ matrix with task-relevant subspaces by performing singular value decomposition on the product of pre-trained weights and input activation covariance. After this, the $A$ matrix is frozen, and only the $B$ matrix is trained. Furthermore, TLoRA employs a sensitivity-based importance metric to adaptively allocate ranks and scaling factors across layers under a fixed parameter budget. We conduct extensive experiments that demonstrate TLoRA consistently performs excellently across various tasks, including natural language understanding, commonsense reasoning, math reasoning, code generation, and chat generation, while significantly reducing the number of trainable parameters.