Related papers: Ricci-Notation Tensor Framework for Model-based Ap…

We propose an Encoder-Classifier framework to model the Mandarin tones using recurrent neural networks (RNN). In this framework, extracted frames of features for tone classification are fed in to the RNN and casted into a fixed dimensional…

The Retinex theory models the image as a product of illumination and reflection components, which has received extensive attention and is widely used in image enhancement, segmentation and color restoration. However, it has been rarely used…

A major challenge in matching images and text is that they have intrinsically different data distributions and feature representations. Most existing approaches are based either on embedding or classification, the first one mapping image…

Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…

Data in the form of images or higher-order tensors is ubiquitous in modern deep learning applications. Owing to their inherent high dimensionality, the need for subquadratic layers processing such data is even more pressing than for…

This paper presents a novel framework for tensor eigenvalue analysis in the context of multi-modal data fusion, leveraging topological invariants such as Betti numbers. Traditional approaches to tensor eigenvalue analysis often extend…

Image Super-Resolution (ISR) has seen significant progress with the introduction of remarkable generative models. However, challenges such as the trade-off issues between fidelity and realism, as well as computational complexity, have also…

A \emph{tensor-relational} computation is a relational computation where individual tuples carry vectors, matrices, or higher-dimensional arrays. An advantage of tensor-relational computation is that the overall computation can be executed…

Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including…

Cross-modal retrieval is gaining increasing efficacy and interest from the research community, thanks to large-scale training, novel architectural and learning designs, and its application in LLMs and multimodal LLMs. In this paper, we move…

While initially devised for image categorization, convolutional neural networks (CNNs) are being increasingly used for the pixelwise semantic labeling of images. However, the proper nature of the most common CNN architectures makes them…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

Using Dirac Notation as a powerful tool, we investigate the three classical Information Retrieval (IR) models and some their extensions. We show that almost all such models can be described by vectors in Occupation Number Representations…

A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…

Image classification is one of the most fundamental tasks in Computer Vision. In practical applications, the datasets are usually not as abundant as those in the laboratory and simulation, which is always called as Data Hungry. How to…

Electromagnetic tracking (EMT) is a core platform technology in the navigation and visualisation of image-guided procedures. The technology provides high tracking accuracy in non-line-of-sight environments, allowing instrument navigation in…

Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…

This paper introduces Multidimensional Task Learning (MTL), a unified mathematical framework based on Generalized Einstein MLPs (GE-MLPs) that operate directly on tensors via the Einstein product. We argue that current computer vision task…

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…