As model sizes continue to grow, parameter-efficient fine-tuning has emerged as a powerful alternative to full fine-tuning. While LoRA is widely adopted among these methods, recent research has explored vector-based adaptation methods due to their extreme parameter efficiency. However, these methods typically require substantially higher ranks than LoRA to match its performance, leading to increased training costs. This work introduces GiVA, a gradient-based initialization strategy for vector-based adaptation. It achieves training times comparable to LoRA and maintains the extreme parameter efficiency of vector-based adaptation. We evaluate GiVA across diverse benchmarks, including natural language understanding, natural language generation, and image classification. Experiments show that our approach consistently outperforms or achieves performance competitive with existing vector-based adaptation methods and LoRA while reducing rank requirements by a factor of eight (8×).
Low-Rank Adaptation (LoRA) is a prominent fine-tuning method for large models, achieving competitive performance with reduced memory overhead. However, a persistent performance gap remains between LoRA and full fine-tuning. Recent studies have sought to narrow this gap by employing one-step gradient approximations of pretrained weights to align LoRA updates with the principal directions or intrinsic dimensionalities of full fine-tuning updates. Nevertheless, these approaches fail to capture the full dynamics of the gradients. In this paper, we propose LoRA-GA2, an effective fine-tuning algorithm that fully leverages multi-step gradient information. Specifically, we introduce a lightweight probe for multi-step gradients of pretrained weights that incurs no additional GPU memory cost and only marginal time overhead. We further employ a spectrum-aware, importance-based rank allocation and optimal initialization derived from multi-step gradients. Extensive experimental results demonstrate that LoRA-GA2 consistently outperforms existing LoRA variants while preserving the efficiency advantages of vanilla LoRA. For instance, LoRA-GA2 surpasses the leading baseline by an average of 0.66 points on the GLUE benchmark, and outperforms the strongest baseline by 1.03 points on GSM8K and 0.87 points on HumanEval, respectively.
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.
Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides the representational plasticity required for high-entropy knowledge injection, Low-Rank Adaptation (LoRA) can match or surpass FFT performance because many tasks only require updates in a low-rank space and benefit from LoRA's additional regularization. Through empirical evaluation across diverse tasks (SQL, Medical QA, and Counterfactual Knowledge) and varying language models (Gemma-3-1B, Qwen2.5-1.5B, and Qwen2.5-3B), we verify both trends and demonstrate that relying solely on either static architecture is structurally limited. To address this challenge, we propose a Mixture of LoRA and Full (MoLF) Fine-Tuning, a unified framework that enables continuous navigation between both training regimes. MoLF dynamically routes updates between FFT and LoRA at the optimizer level to ensure that exact gradient signals are available to both experts throughout training, yielding stable training dynamics. For memory-constrained environments, we also introduce MoLF-Efficient, which freezes base weights and only routes updates among a pair of LoRA experts of potentially varying rank. Our evaluations show that MoLF either improves on or stays within 1.5% of the better of FFT and LoRA across all settings, while MoLF-Efficient outperforms prior adaptive LoRA approaches by up to 20% on Fact and 9% on Med and SQL. Our code is open-sourced at https://github.com/11785T23/molf.git.