FLINT: Influence-Guided Active Learning Framework for LoRA via Curvature-Aware Data Selection and Fine-Tuning

In instruction fine-tuning of large language models (LLMs), identifying beneficial samples from large-scale datasets is pivotal to maximizing model performance. Traditional methods rely on static semantic heuristics, ignoring training dynamics and failing to accurately assess sample contributions. The influence function offers a theoretically grounded approach but incur prohibitive computational cost due to Hessian inversion. Existing influence function-based methods (IF methods) resort to simplifying or omitting the second-order curvature term in the Hessian, leading to distorted contribution estimates on the non-convex parameter manifold. Going beyond such approximations, we propose FLINT: an Active Learning Framework for LoRA via Influence-Guided Data Selection and Fine-Tuning. By constraining influence computation to the LoRA parameter space, FLINT enables precise second-order curvature computation---the first method to achieve this on consumer-grade GPUs, accurately characterizing optimization trajectories and overcoming the limitations of prior approaches. Furthermore, FLINT utilizes Singular Value Decomposition (SVD) as a cold-start mechanism to address initialization instability, alongside predictive entropy pre-filtering and Kronecker-Factored Approximate Curvature (K-FAC)-based decoupling to maximize selection efficiency. Employing an iterative multi-round active learning mechanism, FLINT dynamically filters the most valuable data as the LoRA manifold evolves. Evaluated across complex reasoning benchmarks (GSM8K, BBH, StrategyQA), FLINT achieves a new state-of-the-art among IF methods, significantly accelerating training while consistently outperforming the full-dataset LoRA baseline with less than 20% of the training data, and establishing a principled approach to the non-convex optimization of underlying LLM parameters.