Related papers: Fiber Bundle Networks: A Geometric Machine Learnin…

We propose a geometric extension of restricted Boltzmann machines (RBMs) by allowing weights to take values in abstract groups such as \( \mathrm{GL}_n(\mathbb{R}) \), \( \mathrm{SU}(2) \), or even infinite-dimensional operator groups. This…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum…

Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…

Semantic segmentation of ultra-high-resolution (UHR) remote sensing imagery is critical for applications like environmental monitoring and urban planning but faces computational and optimization challenges. Conventional methods either lose…

The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…

This paper presents a basic property of region dividing of ReLU (rectified linear unit) deep learning when new layers are successively added, by which two new perspectives of interpreting deep learning are given. The first is related to…

A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the…

In this paper, we present a novel deep learning approach, deeply-fused nets. The central idea of our approach is deep fusion, i.e., combine the intermediate representations of base networks, where the fused output serves as the input of the…

In this paper, we present a strategy for training convolutional neural networks to effectively resolve interference arising from competing hypotheses relating to inter-categorical information throughout the network. The premise is based on…

Determining the dimensions of nanostructures is critical to ensuring the maximum performance of many geometry-sensitive nanoscale functional devices. However, accurate metrology at the nanoscale is difficult using optics-based methods due…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

In this paper, we propose deformable deep convolutional neural networks for generic object detection. This new deep learning object detection framework has innovations in multiple aspects. In the proposed new deep architecture, a new…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited…

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and…

Deep Convolutional Neural Networks (CNNs) are capable of learning unprecedentedly effective features from images. Some researchers have struggled to enhance the parameters' efficiency using grouped convolution. However, the relation between…

Hardware imperfections in RF transmitters introduce features that can be used to identify a specific transmitter amongst others. Supervised deep learning has shown good performance in this task but using datasets not applicable to real…

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…