Related papers: How deep learning works --The geometry of deep lea…

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…

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…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

In this paper, we evaluate the accuracy of deep learning approaches on geospatial vector geometry classification tasks. The purpose of this evaluation is to investigate the ability of deep learning models to learn from geometry coordinates…

How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum…

Deep learning relies on a very specific kind of neural networks: those superposing several neural layers. In the last few years, deep learning achieved major breakthroughs in many tasks such as image analysis, speech recognition, natural…

This is a master's thesis concerning the theoretical ideas of geometric deep learning. Geometric deep learning aims to provide a structured characterization of neural network architectures, specifically focused on the ideas of invariance…

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…

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…

Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…

The great success of deep learning shows that its technology contains profound truth, and understanding its internal mechanism not only has important implications for the development of its technology and effective application in various…

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…

Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning.…

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…

Deep learning networks have been trained to recognize speech, caption photographs and translate text between languages at high levels of performance. Although applications of deep learning networks to real world problems have become…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been…

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems…