Parameter Efficient Fine-Tuning (PEFT) is a key technique for adapting a large pretrained model to downstream tasks by fine-tuning only a small number of parameters. Recent methods based on Fourier transforms have further reduced the fine-tuned parameters scale by only fine-tuning a few spectral coefficients. Its basic assumption is that the weight change δW is a spatial-domain matrix with a sparse spectrum. However, in this paper, we observe that the spectrum of weight change is not sparse, but instead distributed like power-uniform. This fact implies that fine-tuning only a few spectral coefficients is insufficient to accurately model the weight change with uniform spectrum. To address this issue, we propose to seek an invertible transformation that can transform a latent spatial-domain matrix with sparse spectrum to the weight change, and then perform PEFT on such sparse spectrum domain with few spectral coefficients, called S2FT. To seek such transformation, we first pre-estimate a coarse weight change as a prior. Then, inspired by that sparse spectrum often correspond to locally smooth spatial structures, we regard this transformation as a row and column rearrangement operation on the pre-estimated weight change that smooth spatial structures while keep the structure information of neurons. Finally, we propose to solve the rearrangement search problem in a simple nearest neighbor search manner, thereby obtaining the invertible transformation. Extensive results show our S2FT achieves superior performance by only using 0.08% training parameters.
Parameter-Efficient Fine-Tuning (PEFT) has become the de facto standard for adapting Vision Transformers (ViTs) to downstream tasks. While parameter count has been the dominant efficiency metric in PEFT, it does not imply \textit{compute efficiency}: parameter-sparse methods can still incur full-model training cost per step, and typically need long schedules to reach peak accuracy. We introduce Circuit Fine-Tuning (CFT), a compute-efficient framework that uses circuit discovery---conventionally used to explain trained models---to select modules for fine-tuning before training. Whereas attribution is conventionally formulated against a trained task head, we formulate it against a near-zero-initialized probe head, which isolates the response of the backbone to the target distribution rather than the preferences of a particular classifier. CFT then fine-tunes only the recovered subgraph. CFT needs no learning-rate warmup and reaches peak accuracy in ∼20 epochs on average---versus 44--96 for strong PEFT baselines---yielding 2.3--6.6× fewer training FLOPs and up to 16× less wall-clock time, while adding zero parameters and no inference operations. Experiments across a standard visual transfer benchmark (VTAB-1k), hierarchical backbones (Swin), domain-shifted medical imaging (CBIS-DDSM), and a vision-language model (Gemma-3 on CUB-200) demonstrate the effectiveness of CFT. Code is available at https://github.com/UriKialy/CFT
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
Popular low-rank parameter-efficient fine-tuning (PEFT) methods represent adaptation as separate updates to selected backbone weights, without maintaining an explicit task-specific state that is updated and reused across depth. These updates also require the backbone at inference and therefore cannot operate as standalone predictors. We propose ShadowPEFT, which consolidates trainable adaptation into a modular shadow component centered on a compact shadow model and lightweight Transformer layer-specific coupling modules. A persistent shadow state refines the frozen backbone representations and is updated from them in an interactive manner. Because the shadow model is trained as a complete predictor, it can be detached for shadow-only inference without executing the base model and can be initialized from a pretrained model. Experiments on text and image generation and understanding benchmarks show that ShadowPEFT matches or outperforms LoRA and DoRA under comparable trainable-parameter budgets. Additional analyses on shadow pretraining, cross-dataset transfer, parameter scaling, inference latency, and system-level evaluation suggest that centralized layer-space adaptation is a competitive and flexible alternative to conventional low-rank PEFT.