Related papers: Topology and geometry of data manifold in deep lea…

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…

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…

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…

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances…

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

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…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

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…

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…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

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…

While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…

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…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

The manifold hypothesis is a core mechanism behind the success of deep learning, so understanding the intrinsic manifold structure of image data is central to studying how neural networks learn from the data. Intrinsic dataset manifolds and…

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,…

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…

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…