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

Feature learning is widely regarded as the key mechanism distinguishing neural networks from fixed-kernel methods, yet its impact on the induced function space remains poorly understood. In this work, we precisely characterize how the…

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

We extend the concept of loss landscape mode connectivity to the input space of deep neural networks. Mode connectivity was originally studied within parameter space, where it describes the existence of low-loss paths between different…

Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…

With the development of deep learning, the performance of hyperspectral image (HSI) classification has been greatly improved in recent years. The shortage of training samples has become a bottleneck for further improvement of performance.…

Deep Learning (DL) , a variant of the neural network algorithms originally proposed in the 1980s, has made surprising progress in Artificial Intelligence (AI), ranging from language translation, protein folding, autonomous cars, and more…

Hyperspectral imaging (HSI) is an advanced sensing modality that simultaneously captures spatial and spectral information, enabling non-invasive, label-free analysis of material, chemical, and biological properties. This Primer presents a…

The dynamics of gradient-based training in neural networks often exhibit nontrivial structures; hence, understanding them remains a central challenge in theoretical machine learning. In particular, a concept of feature unlearning, in which…

Hyperspectral images (HSIs) can distinguish materials with high number of spectral bands, which is widely adopted in remote sensing applications and benefits in high accuracy land cover classifications. However, HSIs processing are tangled…

Hyperspectral images (HSI) classification is a high technical remote sensing software. The purpose is to reproduce a thematic map . The HSI contains more than a hundred hyperspectral measures, as bands (or simply images), of the concerned…

Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. How this emerges from the collective action of nonlinearity, noise, learning rate, and other factors, has eluded first-principles theories built…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Advancements in deep generative models such as generative adversarial networks and variational autoencoders have resulted in the ability to generate realistic images that are visually indistinguishable from real images, which raises…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

We consider the problem of data classification where the training set consists of just a few data points. We explore this phenomenon mathematically and reveal key relationships between the geometry of an AI model's feature space, the…

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate…

Recently it was reported that deeply subwavelength features of free space superoscillatory electromagnetic fields can be observed experimentally and used in optical metrology with nanoscale resolution [Science 364, 771 (2019)]. Here we…

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…

We present a new and effective approach for Hyperspectral Image (HSI) classification and clutter detection, overcoming a few long-standing challenges presented by HSI data characteristics. Residing in a high-dimensional spectral attribute…