Related papers: Semialgebraic Neural Networks: From roots to repre…

Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…

Despite several signs of progress have been made recently, limited research has been conducted for an inductive setting where embeddings are required for newly unseen nodes -- a setting encountered commonly in practical applications of deep…

Graph neural network (GNN)'s success in graph classification is closely related to the Weisfeiler-Lehman (1-WL) algorithm. By iteratively aggregating neighboring node features to a center node, both 1-WL and GNN obtain a node representation…

Semialgebraic splines are functions that are piecewise polynomial with respect to a cell decomposition into sets defined by polynomial inequalities. We study bivariate semialgebraic splines, formulating spaces of semialgebraic splines in…

In this paper, we study semi-supervised graph classification, which aims at accurately predicting the categories of graphs in scenarios with limited labeled graphs and abundant unlabeled graphs. Despite the promising capability of graph…

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial…

Active learning (AL) on attributed graphs has received increasing attention with the prevalence of graph-structured data. Although AL has been widely studied for alleviating label sparsity issues with the conventional non-related data, how…

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…

Neural Algorithmic Reasoning (NAR) is a research area focused on designing neural architectures that can reliably capture classical computation, usually by learning to execute algorithms. A typical approach is to rely on Graph Neural…

The need for consistent treatment of uncertainty has recently triggered increased interest in probabilistic deep learning methods. However, most current approaches have severe limitations when it comes to inference, since many of these…

Deep generative models (DGMs) have achieved remarkable advances. Semi-supervised variational auto-encoders (SVAE) as a classical DGM offer a principled framework to effectively generalize from small labelled data to large unlabelled ones,…

Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…

We introduce Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of the recently proposed Kolmogorov-Arnold Networks (KAN) to graph-structured data. By adopting the unique…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have…

We propose a graph semi-supervised learning framework for classification tasks on data manifolds. Motivated by the manifold hypothesis, we model data as points sampled from a low-dimensional manifold $\mathcal{M} \subset \mathbb{R}^F$. The…

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…

Semantic segmentation is pixel-wise classification which retains critical spatial information. The "feature map reuse" has been commonly adopted in CNN based approaches to take advantage of feature maps in the early layers for the later…

Neural architecture search has shown its great potential in various areas recently. However, existing methods rely heavily on a black-box controller to search architectures, which suffers from the serious problem of lacking…