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This study proposes a novel heterogeneous graph convolutional neural network (HGCNN) to handle complex brain fMRI data at regional and across-region levels. We introduce a generic formulation of spectral filters on heterogeneous graphs by…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…
The dynamics in the photosphere is governed by the multi-scale turbulent convection termed as granulation and supergranulation. It is important to derive 3-dimensional velocity vectors to understand the nature of the turbulent convection.…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…
Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…
Deep learning algorithms, especially Transformer-based models, have achieved significant performance by capturing long-range dependencies and historical information. However, the power of convolution has not been fully investigated.…
The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples ($n \to \infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled…
Neural network training is typically viewed as gradient descent on a loss surface. We propose a fundamentally different perspective: learning is a structure-preserving transformation (a functor L) between the space of network parameters…
Sheaf Neural Networks (SNNs) naturally extend Graph Neural Networks (GNNs) by endowing a cellular sheaf over the graph, equipping nodes and edges with vector spaces and defining linear mappings between them. While the attached geometric…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards…
The existence of Hopf fibrations S^{2N+1}/S^1 = CP^N and S^{4K+3}/S^3 = HP^K allows us to treat the Hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively $U(1)$ and $SU(2)$ fibers and…
Beyond the generally deployed features for microstructure property prediction this study aims to improve the machine learned prediction by developing novel feature descriptors. Therefore, Bayesian infused data mining is conducted to acquire…
Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family $H_s$ of Hilbert spaces, and the question arises if the spaces $H_s$ are canonically isomorphic. [ADW] and…
We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an…
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations…
Group convolution works well with many deep convolutional neural networks (CNNs) that can effectively compress the model by reducing the number of parameters and computational cost. Using this operation, feature maps of different group…
Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…
Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…