Cosine similarity normalizes both sides; dot product normalizes neither. We propose a 2x2 framework that independently controls query-side and document-side normalization, exposing two intermediate variants (QNorm, DNorm) that have not been previously studied. On retrieval with four encoders, evaluated in-domain on MS MARCO and out-of-domain on BEIR, BRIGHT, and multi-hop QA, the unilateral variants outperform both cosine and dot product, with relative gains of up to +72% out-of-domain and +24% on downstream RAG. Cross-evaluation reveals the mechanism: document magnitude scales inference scores while query magnitude modulates training gradients, and the Fisher Information Matrix condition number predicts which side to normalize. We then classify tasks by functional symmetry, defined as whether the aggregate scoring procedure treats Q and C as interchangeable, and test whether the mechanism extends beyond retrieval. On five additional task families (semantic textual similarity, CLIP, knowledge graph completion, few-shot classification, recommender systems), the coarse prediction (cosine for symmetric, magnitude-preserving for asymmetric) holds in every case examined; the unilateral variants beat Cosine on recommendation, and on few-shot classification DNorm beats both Cosine and the standard Euclidean default of Prototypical Networks.
Nonlinear functional regression by functional deep neural network with kernel embedding
Department of Statistics and Actuarial Science, University of Hong Kong（香港大学统计与精算科学系）；Department of Mathematics, Hong Kong Baptist University（香港 Baptist 大学数学系）；School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学学院）；Department of Electrical Engineering, ESAT-STADIUS, KU Leuven（KU Leuven 电子工程系）
Community-preserving Graph Convolutions for Structural and Functional Joint Embedding of Brain Networks
Tongji University（同济大学）；Google Research（谷歌研究院）；Intel Labs（英特尔实验室）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；The University of Chicago（芝加哥大学）；Northwestern University（西北大学）
What on Earth is AlphaEarth? Hierarchical structure and functional interpretability for global land cover
The Institute for Experiential Artificial Intelligence（体验式人工智能研究所）；Northeastern University（东北大学）；Gulf of Maine Research Institute（缅因湾研究机构）；School of Engineering and Architecture（工程与建筑学院）；Universidad Católica de Manizales（曼地拉天主教大学）；Grupo de Investigación en Recursos Hidrobiológicos（水资源生物学研究组）；Departamento de Ingeniería（工程系）；Universidad Nacional de Colombia（哥伦比亚国家大学）
pLMFPPred: a novel approach for accurate prediction of functional peptides integrating embedding from pre-trained protein language model and imbalanced learning
School of Mathematics and Computer Science, Guangdong Ocean University（广东海洋大学数学与计算机学院）；School of Basic Medical Sciences, Lanzhou University（兰州大学基础医学院）；Department of Hematology, Affiliated Hospital of Guangdong Medical University（广东医科大学附属医院血液科）
Functional embeddings enable Aggregation of multi-area SEEG recordings over subjects and sessions
Department of Biomedical Engineering, University of California Irvine（生物医学工程系，加州大学尔湾分校）；Department of Electrical Engineering, University of California Irvine（电气工程系，加州大学尔湾分校）；Department of Neurology, Rady Children’s Health（神经病学系，Rady儿童健康中心）
Joint Embedding of Structural and Functional Brain Networks with Graph Neural Networks for Mental Illness Diagnosis
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Emory University（埃默里大学）；Lehigh University（理海大学）
Interpretable Spatio-Temporal Embedding for Brain Structural-Effective Network with Ordinary Differential Equation
University of Texas Rio Grande Valley（德克萨斯大学里奥格兰德河谷分校）；University of Maryland（马里兰大学）；University of Pittsburgh（匹兹堡大学）；Texas A&M University - Corpus Christi（德克萨斯农工大学科珀斯克里斯蒂分校）；Emory University（埃默里大学）；Lehigh University（利哈伊大学）；University of Illinois at Chicago（芝加哥伊利诺伊大学）；University of Southern California（南加州大学）
