TopoTuner: Topological Finetuning of Large Language Models
Authors: Abdulkadir Erol, Yash Mahajan, Vepaul Hariprashad, Baha Rababah, Santu Karmaker, Cuneyt G. Akcora, Mubarak Shah
Abstract
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.
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.
Large language models (LLMs) remain expensive to fine-tune because full-parameter updates require substantial memory, compute, and per-task storage. We study whether saliency signals originally developed for pruning can be reused to choose where a model should adapt. We propose Super, a sparse parameter-efficient fine-tuning (PEFT) method that fixes a small trainable support using a Wanda-style activation-weighted magnitude score [Sun et al., 2023] computed from a calibration pass. We then introduce Supra, a hybrid adapter that combines this sparse update with LoRA while preserving a matched trainable-parameter budget through a simple budget-splitting rule. In single-seed Math17K arithmetic experiments on Llama-3.2-1B and Meta-Llama-3-8B, the best Super/Supra variants achieve the highest average accuracy among the tested schedule-selected adapter configurations. We also include a PaFi-style magnitude-only support as a closest training-free sparse baseline and find that low-score supports under both magnitude and Wanda-style orderings can be effective. These results suggest that simple pruning-inspired orderings can provide useful fixed sparse supports for PEFT, especially when combined with low-rank adapters.
Parameter-efficient fine-tuning adapts a large language model to one task cheaply, but across a task sequence LoRA-style methods keep stacking low-rank updates on the same frozen weight, so each new task tends to overwrite the previous ones. We present ReCoLoRA (Recursive Consolidation of Low-Rank Adapters), a spectrum-aware framework for continual fine-tuning: adapters are initialized from a randomized SVD of the pretrained weight, per-layer effective ranks are selected by an elbow criterion, and the principal subspace is adapted before residual capacity is opened. Before each new task, ReCoLoRA re-decomposes the current effective weight, rather than the original one, into a frozen residual, a slowly updated principal component, and a fresh adapter (recursive consolidation), so every task starts from the model that has already absorbed its predecessors. On a six-task continual GLUE sequence over four 7-8B backbones, ReCoLoRA attains the best final average score on three of the four backbones against rank-swept LoRA, PiSSA, AdaLoRA, and DoRA baselines while training fewer parameters; an oracle-routed task-bank variant serves as an upper bound under full task isolation. Code: https://github.com/bhqy666/ReCoLoRA.