Low-rank adaptation (LoRA) has been demonstrated effective in reducing the trainable parameter number when fine-tuning a large foundation model (LLM). However, it still encounters computational and memory challenges when scaling to larger models or addressing more complex task adaptation.In this work, we introduce **Sparse Spectrum Adaptation via Discrete Hartley Transformation (SSH)**, a novel approach that significantly reduces the number of trainable parameters while enhancing model performance. It selects the most informative spectral components across all layers, under the guidance of the initial weights after a discrete Hartley transformation (DHT). The lightweight inverse DHT then projects the spectrum back into the spatial domain for updates.Extensive experiments across both single-modality tasks—such as language understanding and generation—and multi-modality tasks—such as video-text understanding—demonstrate that SSH outperforms existing parameter-efficient fine-tuning (PEFT) methods while achieving substantial reductions in computational cost and memory requirements. For instance, during instruction tuning on the LLaMA3.1 8B model, SSH achieves higher accuracy with only 0.048M trainable parameters compared to LoRA’s 33.5M, while reducing computational intensity up to 55% compared to FourierFT.

Large language models (LLMs) often produce unsupported or unverifiable content, known as “hallucinations.” To mitigate this, retrieval-augmented LLMs incorporate citations, grounding the content in verifiable sources. Despite such developments, manually assessing how well a citation supports the associated statement remains a major challenge. Previous studies use faithfulness metrics to estimate citation support automatically but are limited to binary classification, overlooking fine-grained citation support in practical scenarios. To investigate the effectiveness of faithfulness metrics in fine-grained scenarios, we propose a comparative evaluation framework that assesses the metric effectiveness in distinguishing citations between three-category support levels: full, partial, and no support. Our framework employs correlation analysis, classification evaluation, and retrieval evaluation to measure the alignment between metric scores and human judgments comprehensively. Our results show no single metric consistently excels across all evaluations, revealing the complexity of assessing fine-grained support. Based on the findings, we provide practical recommendations for developing more effective metrics.