Parameter-Efficient Fine-Tuning (PEFT) methods, especially LoRA, are widely used for adapting pre-trained models to downstream tasks due to their computational and storage efficiency. However, in the context of LoRA and its variants, the potential of activation subspaces corresponding to tail eigenvectors remains substantially under-exploited, which may lead to suboptimal fine-tuning performance. In this work, we propose Astra (Activation-Space Tail-Eigenvector Low-Rank Adaptation), a novel PEFT method that leverages the tail eigenvectors of the model output activations—estimated from a small task-specific calibration set—to construct task-adaptive low-rank adapters. By constraining updates to the subspace spanned by these tail eigenvectors, Astra achieves faster convergence and improved downstream performance with a significantly reduced parameter budget. Extensive experiments across natural language understanding (NLU) and natural language generation (NLG) tasks demonstrate that Astra consistently outperforms existing PEFT baselines across 16 benchmarks and even surpasses full fine-tuning (FFT) in certain scenarios.

Large language models (LLMs) often exhibit Context Faithfulness Hallucinations, where outputs deviate from retrieved information due to incomplete context integration. Our analysis reveals a strong correlation between token-level uncertainty and hallucinations. We hypothesize that attention mechanisms inherently encode context utilization signals, supported by probing analysis. Based on these insights, we propose Dynamic Attention-Guided Context Decoding (DAGCD), a lightweight framework that leverages attention distributions and uncertainty signals in a single-pass decoding. Experiments on open-book QA datasets demonstrate DAGCD’s effectiveness, yielding significant improvements in faithfulness and robustness while preserving computational efficiency.

Recent studies have demonstrated that many layers are functionally redundant in large language models (LLMs), enabling model compression by removing these layers to reduce inference cost. While such approaches can improve efficiency, indiscriminate layer pruning often results in significant performance degradation. In this paper, we propose GRASP (Gradient-based Retention of Adaptive Singular Parameters), a novel compression framework that mitigates this issue by preserving sensitivity-aware singular values. Unlike direct layer pruning, GRASP leverages gradient-based attribution on a small calibration dataset to adaptively identify and retain critical singular components. By replacing redundant layers with only a minimal set of parameters, GRASP achieves efficient compression while maintaining strong performance with minimal overhead. Experiments across multiple LLMs show that GRASP consistently outperforms existing compression methods, achieving 90% of the original model’s performance under a 20% compression ratio.