As the number of model parameters increases, parameter-efficient fine-tuning (PEFT) has become the go-to choice for tailoring pre-trained large language models. Low-rank Adaptation (LoRA) uses a low-rank update method to simulate full parameter fine-tuning, which is widely used to reduce resource requirements. However, decreasing the rank encounters challenges with limited representational capacity. Theory suggests that LoRA fine-tuning with rank r converges toward the top r singular values of the pre-trained weight matrix. As the rank increases, more principal singular directions are preserved, which generally improves the model's performance. However, a larger rank also introduces more trainable parameters, leading to higher computational cost. To overcome this dilemma, we propose SMoA, a \textbf{S}pectrum \textbf{Mo}dulation \textbf{A}dapter that enlarges the accessible family of spectrum-aware updates under a smaller parameter budget. SMoA partitions the layer into multiple aligned spectral blocks and applies one in-block Hadamard-modulated low-rank branch to each diagonal block, yielding broader coverage of pretrained spectral directions. We provide theoretical analysis and empirical results on multiple tasks. In our experiments, SMoA improves average performance in the current lower-budget setting over LoRA and competitive LoRA-style baselines.
Low-rank adaptation (LoRA) has emerged as the de facto standard for parameter-efficient fine-tuning (PEFT) of foundation models, enabling the adaptation of billion-parameter networks with minimal computational and memory overhead. Despite its empirical success and rapid proliferation of variants, it remains elusive which architectural choices, optimization techniques, and deployment constraints should guide practical method selection. This overview revisits LoRA through the lens of signal processing (SP), bridging modern adapter designs with classical low-rank modeling tools and inverse problems, as well as highlighting how SP principles can inform principled advances of fine-tuning approaches. Rather than providing a comprehensive enumeration and empirical comparisons of LoRA variants, emphasis is placed on the technical mechanisms underpinning these approaches to justify their effectiveness. These advances are categorized into three complementary axes: architectural design, efficient optimization, and pertinent applications. The first axis builds on singular value decomposition (SVD)-based factorization, rank-augmentation constructions, and cross-layer tensorization, while the second axis deals with initialization, alternating solvers, gauge-invariant optimization, and parameterization-aware methods. Beyond fine-tuning, emerging applications of LoRA are accounted across the entire lifecycle of large models, ranging from pre- and post-training to serving/deployment. Finally, open research directions are outlined at the confluence of SP and deep learning to catalyze a bidirectional frontier: classical SP tools provide a principled vocabulary for designing principled PEFT methods, while the unique challenges facing modern deep learning, especially the overwhelming scale and prohibitive overhead, also offer new research lines benefiting the SP community in return.
Both full fine-tuning (Full FT) and parameter-efficient fine-tuning methods such as LoRA introduce weight updates without accounting for the spectral structure established during pretraining. As a result, noisy gradients from limited fine-tuning data can perturb robust pretrained features. We identify spectral preconditioning as the missing ingredient: reparameterizing each weight matrix through its full-rank singular value decomposition (SVD) and freezing one singular basis constrains updates to the pretrained column space, yielding a preconditioned optimization scheme that outperforms unconstrained Full FT at the same trainable parameter count. Building on this insight, we propose FuRA (Full-Rank Adaptation), an efficient full-rank adaptation framework based on a block tensor-train factorization W = LSR, where the large core L is fixed to the pretrained block-wise SVD basis, while only the compact core R and the block-wise singular values S are optimized. This design simultaneously provides full-rank spectral preconditioning, preserves full-rank update expressivity, and achieves parameter, memory, and step-time efficiency comparable to LoRA. FuRA consistently outperforms Full FT across multiple settings, including LLM fine-tuning (+1.37 on LLaMA-3-8B commonsense reasoning), LLM reinforcement learning for mathematical reasoning, and visual instruction tuning for VLMs. Furthermore, the 4-bit quantized variant, QFuRA, also surpasses QLoRA. Code is available at https://github.com/olokevin/FuRA-NIPS
Adapting foundation models under resource budgets relies heavily on Parameter-Efficient Fine-Tuning (PEFT), with LoRA being a standard modular solution. However, LoRA suffers from spectral interference. Low-rank updates often concentrate energy on the leading singular directions of pretrained weights, perturbing general capabilities and causing catastrophic forgetting and fragile multi-adapter merging. To resolve this, we propose HiP-LoRA, a spectrum-aware adaptation framework. Utilizing the cached singular value decomposition (SVD) of pretrained layers, HiP-LoRA decomposes updates into two channels: a principal channel within the dominant singular subspace, and a residual low-rank channel in the orthogonal complement. A singular-value-weighted stability budget on the principal channel continuously balances pretrained behavior preservation with task-specific plasticity. Experiments on Llama-3.1-8B demonstrate that under matched budgets, HiP-LoRA drastically reduces pretraining degradation and multi-adapter MergeFail, robustly outperforming baselines in interference-sensitive tasks like continual tuning and knowledge editing.