GAST: Gradient-aligned Sparse Tuning of Large Language Models with Data-layer Selection

Existing Supervised Fine-Tuning paradigms, particularly Full Parameter Fine-Tuning are often plagued by parameter redundancy, inconsistent data quality, and catastrophic forgetting, which current methods typically address in isolation and lack a unified optimization signal to bridge data selection, parameter updates, and knowledge preservation. To address this, we propose Neuron-Guided Fine-Tuning (NGFT), a holistic framework that leverages neuron activation patterns as a universal proxy to unify the fine-tuning lifecycle. NGFT operates via three synergistic mechanisms: (1) Adaptive Task-Specific Neuron Selection, which identifies essential neurons in a single forward pass to concentrate updates and reduce redundancy; (2) Activation-Based Data Selection, which prioritizes information-dense samples that maximize contribution to key neurons; and (3) Neuron Activation Alignment, a novel loss function that anchors activations to pre-trained states, deepening representation learning and preserving general knowledge. Experimental results across three models across both domain-specific and general benchmarks demonstrate that NGFT significantly outperforms existing mainstream fine-tuning methods in both efficiency and performance, while effectively mitigating catastrophic forgetting.

Full-parameter fine-tuning of large language models is constrained by substantial GPU memory requirements. Low-rank adaptation methods mitigate this challenge by updating only a subset of parameters. However, these approaches often limit model expressiveness and yield lower performance than full-parameter fine-tuning. Layer-wise fine-tuning methods have emerged as an alternative, enabling memory-efficient training through static layer importance sampling strategies. However, these methods overlook variations in layer importance across tasks and training stages, resulting in suboptimal performance on downstream tasks. To address these limitations, we propose GRASS, a gradient-based adaptive layer-wise importance sampling framework. GRASS utilizes mean gradient norms as a task-aware and training-stage-aware metric for estimating layer importance. Furthermore, GRASS adaptively adjusts layer sampling probabilities through an adaptive training strategy. We also introduce a layer-wise optimizer state offloading mechanism that overlaps computation and communication to further reduce memory usage while maintaining comparable training throughput. Extensive experiments across multiple models and benchmarks demonstrate that GRASS consistently outperforms state-of-the-art methods, achieving an average accuracy improvement of up to 4.38 points and reducing memory usage by up to 19.97%.

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through the effect of an example on parameter updates. To make selection scalable, many approaches leverage optimizer statistics (e.g., Adam states) as an axis-aligned surrogate for update geometry (i.e., diagonal precondition), implicitly treating parameters as coordinate-wise independent. We show that this assumption breaks down in parameter-efficient fine-tuning (PEFT) methods such as LoRA. In this setting, the induced optimization geometry exhibits strong cross-parameter coupling with non-trivial off-diagonal interactions, while the task-relevant update directions are confined to a low-dimensional subspace. Motivated by this mismatch, we propose GIST (Gradient Isometric Subspace Transformation), a simple yet principled alternative that replaces axis-aligned scaling with robust subspace alignment. GIST recovers a task-specific subspace from validation gradients via singular value decomposition (SVD), projects training gradients into this coupled subspace, and scores examples by their alignment with target directions. Extensive experiments have demonstrated that GIST matches or outperforms the state-of-the-art baseline with only 0.29% of the storage and 25% of the computational time under the same selection budget.