As large language models (LLMs) continue to grow, the cost of full-parameter fine-tuning has made parameter-efficient fine-tuning (PEFT) the default strategy for downstream adaptation. Constraints from inference latency in scalable serving and fine-tuning cost in edge or rapid-deployment settings make the choice of which layers to fine-tune unavoidable. Yet current practice typically applies PEFT uniformly across all layers, with limited understanding or leverage of layer selection. This paper develops a unified projected residual view of PEFT on top of a frozen base model. Under a local quadratic approximation, layerwise adaptation is governed by three quantities: (i) the projected residual norm (resnorm), which measures how much correctable bias a layer can capture; (ii) the activation energy, which determines feature conditioning; and (iii) layer coupling, which quantifies how strongly residuals interact across layers. We show that, for squared loss and linear adapters, the resnorm equals a normalized gradient norm, activation energy controls ill-conditioning and noise amplification, and weak coupling yields approximately additive layerwise contributions. Building on these insights, we introduce the Layer Card, a reusable diagnostic that summarizes residual signal strength, compute cost, and performance for each layer of a given model. With an identical model and LoRA configuration, Layer Card-guided placement refines the choice of adapted layers to flexibly prioritize different objectives, such as maximizing performance or reducing fine-tuning cost. Moreover, on Qwen3-8B, we show that selectively adapting a subset of layers can achieve performance close to full-layer LoRA while substantially reducing fine-tuning cost and the number of adapter-augmented layers during inference, offering a more cost-performance-aware alternative to full-layer insertion.
MaxSAT-Based Feedback for Guiding Vision-Language Models in Sudoku
Artificial Intelligence Research Institute (IIIA), Consejo Superior de Investigaciones Científicas (CSIC)（人工智能研究所（IIIA），西班牙科学研究高级理事会（CSIC））；Institut de Robòtica i Informàtica Industrial (IRI-CSIC-UPC)（工业机器人与信息学研究所（IRI-CSIC-UPC））
Dominant-Layer ZO: A Single Layer Dominates Zeroth-Order Fine-Tuning of LLMs
University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）；University of Houston（休斯顿大学）；State University of New York at Binghamton（纽约州立大学布法罗分校）；Arizona State University（亚利桑那州立大学）；Department of Artificial Intelligence and Informatics, Mayo Clinic（梅奥诊所人工智能与信息学系）
Optimizing and Fine-tuning Large Language Model for Urban Renewal
Tsinghua University（清华大学）；Cross-strait Tsinghua Research Institute（海峡两岸清华研究院）；Biocloo Inc（百奥科洛公司）；China Agricultural University（中国农业大学）；Zhipu AI（智谱AI）；Beijing Rongchuang Geotechnical Engineering Co., Ltd.（北京融创岩土工程有限公司）；The University of Hong Kong（香港大学）
Beyond Static Interpretability: Anticipating Post-SFT Mechanisms from Pre-SFT Parameters for Better Tuning
College of Computing and Data Science（计算与数据科学学院）；Nanyang Technological University（南洋理工大学）；School of Computer Science and Engineering（计算机科学与工程学院）；The Chinese University of Hong Kong（香港中文大学）
