Learning in structured, multi-context, or non-stationary environments involves two orthogonal difficulties. The first is \emph{metric}: once the correct context is known, how hard is prediction within it? This is the domain of Statistical Learning Theory (SLT). The second is \emph{structural}: how many local contexts are required, and how can they be discovered from data? This paper develops \emph{Structural Learning Theory} (StrLT) for the structural axis. We introduce \emph{width}, the minimum number of jointly contractive and low-risk cells needed to cover a learning problem. Width is incomparable with VC dimension: either can diverge while the other remains bounded. We show that width induces a \emph{phase transition}: if the allocated number of cells \(K<w\), learning suffers an irreducible structural error floor; if \(K\ge w\), the problem reduces to ordinary within-cell statistical learning. To estimate width, we introduce the \emph{contractive-similarity} (CS) operator, a task-adaptive graph kernel combining geometric locality with predictive compatibility. Its CS Laplacian exposes contractive basins through spectral separation. We further develop the \emph{metric slingshot}, which reuses low-dimensional latent contraction maps to reduce funnel-learning cost. Together, width, CS estimation, and the slingshot decompose learning into trap discovery and funnel generalization, with deep implications for continual and lifelong learning in an open-ended environment.
Robust Neural Tucker Factorization with Bias Correction and Adaptive Initialization
School of Computer Science and Engineering, Chongqing University of Science and Technology（重庆科技大学计算机科学与工程学院）；College of Computer and Information Science, School of Software, Southwest University（西南大学计算机与信息科学学院 软件学院）
Dalian University of Technology（大连理工大学）；The American University in Cairo（开罗美国大学）
In this paper, a mechanistic data-driven approach is proposed to accelerate structural topology optimization, employing an in-house developed finite element convolutional neural network (FE-CNN). Our approach can be divided into two stages: offline training, and online optimization. During offline training, a mapping function is built between high and low resolution representations of a given design domain. The mapping is expressed by a FE-CNN, which targets a common objective function value (e.g., structural compliance) across design domains of differing resolutions. During online optimizatio…
Iowa State University（爱荷华州立大学）；Ansys Corporation（Ansys公司）
Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite element analysis iterations required to evaluate the component's performance during the optimization process. Recently, machine learning (ML)-based topology optimization methods have been explored by researchers to alleviate this issue. However, previous ML approaches have mainly been demonstrated on simple two-dimensional applications with low-resolution geome…
ShanghaiTech University（上海科技大学）；Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）
Knowledge distillation is a critical technique to transfer knowledge between models, typically from a large model (the teacher) to a more fine-grained one (the student). The objective function of knowledge distillation is typically the cross-entropy between the teacher and the student's output distributions. However, for structured prediction problems, the output space is exponential in size; therefore, the cross-entropy objective becomes intractable to compute and optimize directly. In this paper, we derive a factorized form of the knowledge distillation objective for structured prediction, w…
Korea Institute of Science and Technology（韩国科学技术研究院）；Korea University（高丽大学）
Accurate predictions of the failure progression of structural materials is critical for preventing failure-induced accidents. Despite considerable mechanics modeling-based efforts, accurate prediction remains a challenging task in real-world environments due to unexpected damage factors and defect evolutions. Here, we report a novel method for predicting material failure characteristics that uniquely combines nondestructive X-ray computed tomography (X-CT), persistent homology (PH), and deep multimodal learning (DML). The combined method exploits the microstructural defect state at the time of…
Deep learning methods for graphs have seen rapid progress in recent years with much focus awarded to generalising Convolutional Neural Networks (CNN) to graph data. CNNs are typically realised by alternating convolutional and pooling layers where the pooling layers subsample the grid and exchange spatial or temporal resolution for increased feature dimensionality. Whereas the generalised convolution operator for graphs has been studied extensively and proven useful, hierarchical coarsening of graphs is still challenging since nodes in graphs have no spatial locality and no natural order. This …
Department of Computer Science and Technology, University of Cambridge, United Kingdom（计算机科学与技术系，剑桥大学，英国）；Robotics and Biology Laboratory, Technische Universität Berlin（机器人与生物学实验室，柏林技术大学）；Science of Intelligence (SCIoI), Cluster of Excellence, Berlin, Germany（智能科学（SCIoI），卓越中心，柏林，德国）；Robotics Institute Germany（德国机器人研究所）
