Rotation-Preserving Supervised Fine-Tuning

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

Supervised fine-tuning (SFT) is an efficient approach for downstream task adaptation and often serves as the initialization stage for reinforcement learning (RL), but it can show weaker generalization than RL. A key limitation is its off-policy objective: SFT fits fixed demonstrations token by token, including targets poorly aligned with the model's pretrained distribution, which can lead to overfitting. A recent line of work addresses this issue by assigning larger training weights to tokens better aligned with the current model's predictive distribution, with the intuition that fitting these tokens are less distortive to the model's pretrained knowledge and representations. However, computing the token weights from the model that is currently fine-tuned entangles token weights with the optimization trajectory, inducing a self-reinforcing dynamics as the distribution rapidly departs from the pretrained model. To address this, we propose PriFT (Prior-support guided Fine-Tuning), which derives token weights from a frozen pretrained reference to obtain a stable reweighting signal unaffected by fine-tuning. This signal estimates prior support: the extent to which each target token is supported by the pretrained distribution. Across multiple existing token-reweighting rules, replacing the reweighting signal from the online model to pretrained model consistently improves performance. We introduce two instantiations: PriFT-prob uses pretrained token probability, while PriFT-mass selects tokens by cumulative probability mass under the pretrained distribution. Extensive experiments on mathematical reasoning, code generation, and medical question answering show that PriFT achieves state-of-the-art results among SFT baselines and provides a better initialization for subsequent RL training.

Full fine-tuning remains a strong way to adapt pretrained LLMs, but it updates all weights and can be expensive. LoRA reduces the number of trainable parameters, but it does not directly answer which pretrained components should be trained and which can be frozen during adaptation. We introduce TopoTuner, a topology-guided fine-tuning framework for selective freezing of attention projection matrices. \method treats each projection matrix as a row cloud and uses Wasserstein distances between persistence diagrams to measure how its topology changes during fine-tuning. TopoTuner learns a reusable freezing profile from a source dataset and transfers it to efficiently fine-tune models on out-of-domain datasets, evaluating whether task-specific topological drift generalizes across question answering and sentiment analysis tasks. Across LLaMA-3.1-8B, Mistral-7B-v0.3, and Qwen3-8B-Base, TopoTuner is competitive with full fine-tuning while training only 1-2% of the model parameters, and outperforms LoRA in 7 out of 9 model-dataset settings, which can change up to 39.57% of the projection parameters. Along with minimized updates, TopoTuner reduces training time by 20.4% relative to full fine-tuning and 5.5% relative to LoRA on average. TopoTuner opens a new direction for reusable freezing profiles, where fine-tuning behavior learned on one dataset can be shared across multiple tasks.