Adaptive Utilization of Low-Rank Adaptation via Conditioned Gating

Low-Rank Adaptation (LoRA) is the most widely adopted method for fine-tuning large language models. Notably, LoRA is inherently overparameterized: multiple pairs of low-rank factors can yield the same adapted weight matrix. We show--both theoretically and empirically--that these pairs exhibit significantly different condition numbers. As a result, converging to different loss minimizers directly impacts the convergence rate of LoRA. Building on this observation, we introduce Balanced Low-Rank Adaptation (BaLoRA), a variant of LoRA that projects iterates onto a balanced manifold. This manifold improves the conditioning of the loss landscape while preserving the adapted matrix. The projection step is computationally lightweight and integrates seamlessly into existing fine-tuning pipelines. Empirically, BaLoRA converges faster than standard LoRA and achieves superior performance across a range of fine-tuning tasks.

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 propose GDLoRA (Gradient-Decomposed Low-Rank Adaptation). GDLoRA reconstructs the full weight gradient from forward activations and backward signals, extracts its normal component, and directly updates the base weights with this component, while retaining standard AdamW optimization for the LoRA factors. GDLoRA incorporates complementary normal gradients without increasing standard LoRA's optimizer-state memory budget under matched adapter and optimizer configurations. Experiments on natural language understanding, mathematical reasoning, commonsense reasoning, and image classification show that GDLoRA consistently improves over LoRA and narrows the performance gap to FFT. The code is available at https://anonymous.4open.science/r/GDLoRA.

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.