Related papers: Exploring the high dimensional geometry of HSI fea…

The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…

We consider dynamical and geometrical aspects of deep learning. For many standard choices of layer maps we display semi-invariant metrics which quantify differences between data or decision functions. This allows us, when considering random…

When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse" phenomenon. More specifically, for the output features of the penultimate…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

This paper introduces a new technique to measure the feature dependency of neural network models. The motivation is to better understand a model by querying whether it is using information from human-understandable features, e.g.,…

Recently, interesting empirical phenomena known as Neural Collapse have been observed during the final phase of training deep neural networks for classification tasks. We examine this issue when the feature dimension d is equal to the…

Integrating hyperspectral imagery (HSI) with deep neural networks (DNNs) can strengthen the accuracy of intelligent vision systems by combining spectral and spatial information, which is useful for tasks like semantic segmentation in…

The Hyperspectral image (HSI) classification is a standard remote sensing task, in which each image pixel is given a label indicating the physical land-cover on the earth's surface. The achievements of image semantic segmentation and deep…

Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric…

Hyperspectral image (HSI) classification is a hot topic in the remote sensing community. This paper proposes a new framework of spectral-spatial feature extraction for HSI classification, in which for the first time the concept of deep…

Existing deep learning-based hyperspectral image (HSI) classification works still suffer from the limitation of the fixed-sized receptive field, leading to difficulties in distinctive spectral-spatial features for ground objects with…

This survey aims to investigate fundamental deep learning (DL) based 3D reconstruction techniques that produce photo-realistic 3D models and scenes, highlighting Neural Radiance Fields (NeRFs), Latent Diffusion Models (LDM), and 3D Gaussian…

Neural multivariate regression underpins a wide range of domains, including control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit…

Hyperspectral images are of crucial importance in order to better understand features of different materials. To reach this goal, they leverage on a high number of spectral bands. However, this interesting characteristic is often paid by a…

The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…