神经受控微分方程（Neural CDEs）为序列建模提供了强大的连续时间框架，但驱动控制路径的粗糙性常限制其效率。标准样条引入高频变化，迫使自适应求解器采取过小的步长，导致函数评估次数（NFE）激增。我们提出一种新的神经CDE路径构建方法，用核和高斯过程（GP）平滑替代精确插值，从而显式控制轨迹正则性。为恢复平滑过程中丢失的细节，我们提出基于注意力的多视图CDE（MV-CDE）及其卷积扩展（MVC-CDE），它们使用可学习查询来指导路径重建。该框架允许模型将表示能力分布在多个轨迹上，每个轨迹捕获不同的时间模式。实验结果表明，与基于样条的基线相比，我们的方法MVC-CDE with GP在显著降低NFE和总推理时间的同时，实现了最先进的精度。
英文摘要：
Neural Controlled Differential Equations (Neural CDEs) provide a powerful continuous-time framework for sequence modeling, yet the roughness of the driving control path often restricts their efficiency. Standard splines introduce high-frequency variations that force adaptive solvers to take excessively small steps, driving up the Number of Function Evaluations (NFE). We propose a novel approach to Neural CDE path construction that replaces exact interpolation with Kernel and Gaussian Process (GP) smoothing, enabling explicit control over trajectory regularity. To recover details lost during smoothing, we propose an attention-based Multi-View CDE (MV-CDE) and its convolutional extension (MVC-CDE), which employ learnable queries to inform path reconstruction. This framework allows the model to distribute representational capacity across multiple trajectories, each capturing distinct temporal patterns. Empirical results demonstrate that our method, MVC-CDE with GP, achieves state-of-the-art accuracy while significantly reducing NFEs and total inference time compared to spline-based baselines.
Selfie and cartoon are two popular artistic forms that are widely presented in our daily life. Despite the great progress in image translation/stylization, few techniques focus specifically on selfie cartoonization, since cartoon images usually contain artistic abstraction (e.g., large smoothing areas) and exaggeration (e.g., large/delicate eyebrows). In this paper, we address this problem by proposing a selfie cartoonization Generative Adversarial Network (scGAN), which mainly uses an attentive adversarial network (AAN) to emphasize specific facial regions and ignore low-level details. More s…
The transduction of sequence has been mostly done by recurrent networks, which are computationally demanding and often underestimate uncertainty severely. We propose a computationally efficient attention-based network combined with the Gaussian process regression to generate real-valued sequence, which we call the Attentive-GP. The proposed model not only improves the training efficiency by dispensing recurrence and convolutions but also learns the factorized generative distribution with Bayesian representation. However, the presence of the GP precludes the commonly used mini-batch approach to…
London School of Economics（伦敦政治经济学院）；ETH Zurich（苏黎世联邦理工学院）
Causal Optimal Transport (COT) results from imposing a temporal causality constraint on classic optimal transport problems, which naturally generates a new concept of distances between distributions on path spaces. The first application of the COT theory for sequential learning was given in Xu et al. (2020), where COT-GAN was introduced as an adversarial algorithm to train implicit generative models optimized for producing sequential data. Relying on (Xu et al., 2020), the contribution of the present paper is twofold. First, we develop a conditional version of COT-GAN suitable for sequence pre…
We present a novel attention-based model for discrete event data to capture complex non-linear temporal dependence structures. We borrow the idea from the attention mechanism and incorporate it into the point processes' conditional intensity function. We further introduce a novel score function using Fourier kernel embedding, whose spectrum is represented using neural networks, which drastically differs from the traditional dot-product kernel and can capture a more complex similarity structure. We establish our approach's theoretical properties and demonstrate our approach's competitive perfor…
Amortized Filtering and Smoothing with Conditional Normalizing Flows
School of Mathematics and Statistics（数学与统计学学院）；The University of Sydney（悉尼大学）；Faculty of Science and Technology（科学与技术学院）；Beijing Normal-Hong Kong Baptist University（北京师范大学-香港 Baptist大学）；Institute of Computational Mathematics and Scientific/Engineering Computing（计算数学与科学/工程计算研究所）；Academy of Mathematics and Systems Science（数学与系统科学学院）；Chinese Academy of Sciences（中国科学院）；Department of Mathematics and Center for Computation and Technology（数学系与计算技术中心）；Louisiana State University（路易斯安那州立大学）
Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing University of Posts and Telecommunications（南京邮电大学江苏省大数据安全与智能处理重点实验室）；National Engineering Laboratory for Agri-product Quality Traceability, Beijing Technology and Business University（北京工商大学农产品质量安全追溯技术及应用国家工程实验室）；State Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；Jiangsu Key Lab of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院江苏省社会安全图像与视频理解重点实验室）
With rising uncertainty in the real world, online Reinforcement Learning (RL) has been receiving increasing attention due to its fast learning capability and improving data efficiency. However, online RL often suffers from complex Value Function Approximation (VFA) and catastrophic interference, creating difficulty for the deep neural network to be applied to an online RL algorithm in a fully online setting. Therefore, a simpler and more adaptive approach is introduced to evaluate value function with the kernel-based model. Sparse representations are superior at handling interference, indicati…
Nanyang Technological University（南洋理工大学）；Institute of High Performance Computing（高性能计算研究所）
Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize the model from few samples, GNN usually suffers from severe over-fitting and over-smoothing as the model becomes deep, which limit the scalability. In this work, we propose a novel Attentive GNN to tackle these challenges, by incorporating a triple-attention mechanism, i.e. node self-attention, neighborhood attention, and layer memory attention. We explain why the proposed attentive modules can impro…
Huazhong University of Science and Technology（华中科技大学）；Nanyang Technological University（南洋理工大学）
Graph convolutional network (GCN) is now an effective tool to deal with non-Euclidean data, such as social networks in social behavior analysis, molecular structure analysis in the field of chemistry, and skeleton-based action recognition. Graph convolutional kernel is one of the most significant factors in GCN to extract nodes' feature, and some improvements of it have reached promising performance theoretically and experimentally. However, there is limited research about how exactly different data types and graph structures influence the performance of these kernels. Most existing methods us…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Weierstrass Institute（魏尔斯特拉斯研究所）；InstaDeep Ltd.（InstaDeep公司）
We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the Wasserstein distance and the maximum mean discrepancy. We adapt the integral operator using supremal convolution in convex analysis to form a novel function majorant used for enforcing robustness. Our method is simple in form and applies to general loss functions and machine learning models. Exploiting a connection with optimal transport, we prove theoretic…
Random Smoothing Regularization in Kernel Gradient Descent Learning
Fudan University（复旦大学）；Purdue University（普渡大学）；The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel smoothing for directional data. We generalize the classical mean shift algorithm to directional data, which allows us to identify local modes of the directional kernel density estimator (KDE). The statistical convergence rates of the directional KDE and its derivatives are derived, and the problem of mode estimation is examined. We also prove the ascending prope…
Probabilistic Smoothing with Ratio-Monotone Transforms for Global Optimization
Department of Statistics, Seoul, Korea University（首尔大学统计系）；Department of Electrical and Computer Engineering, Seoul, Seoul National University（首尔国立大学电气与计算机工程系）；Shandong University at Weihai, Weihai, China（威海山东大学）
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature similarity or temporal information present in data sets, via non-parametric kernel smoothing. We provide generalization bounds for dictionary learning using smooth sparse coding and show how the sample complexity depends on the L1 norm of kernel function used. Furthermore, we propose using marginal regression for obtaining sparse codes, which significantly improv…
Oxford-Man Institute for Quantitative Finance（牛津-曼 quantitative finance 研究所）；University of Oxford（牛津大学）
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting output. We prove that kernel smoothing biases the moments of the spectral density. We propose an information theoretically optimal approach to learn a smooth graph spectral density, which fully respects the moment information. Our method's computational cost is linear in the number of edges, and hence can be applied to large networks, with millions of nodes. W…
We propose a multidimensional smoothing spline algorithm in the context of manifold learning. We generalize the bending energy penalty of thin-plate splines to a quadratic form on the Sobolev space of a flat manifold, based on the Frobenius norm of the Hessian matrix. This leads to a natural definition of smoothing splines on manifolds, which minimizes square error while optimizing a global curvature penalty. The existence and uniqueness of the solution is shown by applying the theory of reproducing kernel Hilbert spaces. The minimizer is expressed as a combination of Green's functions for the…
