Related papers: Mathematical Foundations of Geometric Deep Learnin…

One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization…

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…

Probabilistic generative deep learning for molecular design involves the discovery and design of new molecules and analysis of their structure, properties and activities by probabilistic generative models using the deep learning approach.…

Geometric understanding - including depth and height perception - is fundamental to intelligence and crucial for navigating our environment. Despite the impressive capabilities of large Vision Language Models (VLMs), it remains unclear how…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

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…

We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge…

This article provides an expository account of training dynamics in the Deep Linear Network (DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results by several authors are unified into a thermodynamic…

The basic concepts of gravitational microlensing are introduced. We start with the lens equation, and then derive the image positions and magnifications. The statistical quantities of optical depth and event rate are then described. We…

We present SkelNetOn 2019 Challenge and Deep Learning for Geometric Shape Understanding workshop to utilize existing and develop novel deep learning architectures for shape understanding. We observed that unlike traditional segmentation and…

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…

In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations,…

We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.

We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…

In many domains where data are represented as graphs, learning a similarity metric among graphs is considered a key problem, which can further facilitate various learning tasks, such as classification, clustering, and similarity search.…

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…

This article introduces the groundbreaking concept of the financial differential machine learning algorithm through a rigorous mathematical framework. Diverging from existing literature on financial machine learning, the work highlights the…

Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…