Topological Data Analysis for Neural Network Analysis: A Comprehensive Survey
This survey provides a comprehensive exploration of applications of Topological Data
Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology …
Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology …
Locally linear attributes of ReLU neural networks
B Sattelberg, R Cavalieri, M Kirby… - Frontiers in Artificial …, 2023 - frontiersin.org
A ReLU neural network functions as a continuous piecewise linear map from an input space
to an output space. The weights in the neural network determine a partitioning of the input …
to an output space. The weights in the neural network determine a partitioning of the input …
Integrating geometries of ReLU feedforward neural networks
This paper investigates the integration of multiple geometries present within a ReLU-based
neural network. A ReLU neural network determines a piecewise affine linear continuous …
neural network. A ReLU neural network determines a piecewise affine linear continuous …
Defining Neural Network Architecture through Polytope Structures of Dataset
Current theoretical and empirical research in neural networks suggests that complex
datasets require large network architectures for thorough classification, yet the precise …
datasets require large network architectures for thorough classification, yet the precise …
SkelEx and BoundEx-Geometrical Framework for Interpretable ReLU Neural Networks
Every ReLU Neural Network (NN) tessellates its input space into activation regions.
Studying this tessellation provides insights into some of the architecture's properties. Recent …
Studying this tessellation provides insights into some of the architecture's properties. Recent …
A rank decomposition for the topological classification of neural representations
K Beshkov, GT Einevoll - arXiv preprint arXiv:2404.19710, 2024 - arxiv.org
Neural networks can be thought of as applying a transformation to an input dataset. The way
in which they change the topology of such a dataset often holds practical significance for …
in which they change the topology of such a dataset often holds practical significance for …
A Relative Homology Theory of Representation in Neural Networks
K Beshkov - arXiv preprint arXiv:2502.01360, 2025 - arxiv.org
Previous research has proven that the set of maps implemented by neural networks with a
ReLU activation function is identical to the set of piecewise linear continuous maps …
ReLU activation function is identical to the set of piecewise linear continuous maps …
Piecewise polynomial regression of tame functions via integer programming
Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide
range of applications: functions encountered in the training of deep neural networks with all …
range of applications: functions encountered in the training of deep neural networks with all …
Data geometry and topology dependent bounds on network widths in deep ReLU networks
S Lee, A Mammadov, JC Ye - openreview.net
The geometrical perspective of deep ReLU networks is important to understand the learning
behavior and generalization capability of the neural networks. As such, here we investigate …
behavior and generalization capability of the neural networks. As such, here we investigate …