Effective Frontiers: A Unification of Neural Scaling Laws
Department of Mathematics and Statistics, Xi'an Jiaotong University（西安交通大学数学与统计学系）；Department of Artificial Intelligence, Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学人工智能学院）；University of Chinese Academy of Sciences（中国科学院大学）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
Jiaxuan Zou, Zixuan Gong, Ye Su, Huayi Tang, Yong Liu
Neural scaling laws govern the prediction power-law improvement of test loss with respect to model capacity ($N$), datasize ($D$), and compute ($C$). However, existing theoretical explanations often rely on specific architectures or complex kernel methods, lacking intuitive universality. In this paper, we propose a unified framework that abstracts general learning tasks as the progressive coverage of patterns from a long-tail (Zipfian) distribution. We introduce the Effective Frontier ($k_\star$), a threshold in the pattern rank space that separates learned knowledge from the unlearned tail. We prove that reducible loss is asymptotically determined by the probability mass of the tail a resource-dependent frontier truncation. Based on our framework, we derive the precise scaling laws for $N$, $D$, and $C$, attributing them to capacity, coverage, and optimization bottlenecks, respectively. Furthermore, we unify these mechanisms via a Max-Bottleneck principle, demonstrating that the Kaplan and Chinchilla scaling laws are not contradictory, but equilibrium solutions to the same constrained optimization problem under different active bottlenecks.
ELLIS Institute Tübingen（埃利斯研究所蒂宾根分所）；OpenEuroLLM；Eindhoven University of Technology（埃因霍温理工大学）；University of Freiburg（弗赖堡大学）；Zuse School ELIZA（楚塞ELIZA学校）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Tübingen AI Center（蒂宾根人工智能中心）
Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities
Agency for Science, Technology and Research (A*STAR)（科技研究局）；Indian Institute of Technology (IIT) Goa（印度理工学院 Goa分校）；Nanyang Technological University（南洋理工大学）
Hardware Co-Design Scaling Laws via Roofline Modelling for On-Device LLMs
AI Lab, The Yangtze River Delta Institution of Automation, Chinese Academy of Sciences（人工智能实验室，长江三角洲自动化研究所，中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；University College London（伦敦大学学院）；Institution of Automation, Chinese Academy of Sciences（自动化研究所，中国科学院）；The University of Edinburgh（爱丁堡大学）
Scaling Laws and Tradeoffs in Recurrent Networks of Expressive Neurons
University of Tübingen, Germany（图宾根大学，德国）；Max Planck Institute for Biological Cybernetics, Tübingen, Germany（生物感知研究所，图宾根，德国）；Max Planck Institute for Intelligent Systems, Tübingen, Germany（智能系统研究所，图宾根，德国）
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；The University of Hong Kong（香港大学）；University of Electronic Science and Technology of China（电子科技大学）；Tsinghua University（清华大学）；Peking University（北京大学）
