Related papers: Topology Distance: A Topology-Based Approach For E…

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.…

Generative Adversarial Networks have become one of the most studied frameworks for unsupervised learning due to their intuitive formulation. They have also been shown to be capable of generating convincing examples in limited domains, such…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the…

While recent deep monocular depth estimation approaches based on supervised regression have achieved remarkable performance, costly ground truth annotations are required during training. To cope with this issue, in this paper we present a…

Generative adversarial networks (GANs) are successful deep generative models. GANs are based on a two-player minimax game. However, the objective function derived in the original motivation is changed to obtain stronger gradients when…

Auto-encoding generative adversarial networks (GANs) combine the standard GAN algorithm, which discriminates between real and model-generated data, with a reconstruction loss given by an auto-encoder. Such models aim to prevent mode…

Structural topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance, is vital in engineering design applications in aerospace, mechanical, and civil engineering. Generative adversarial…

Fr\'echet Inception Distance (FID) is the primary metric for ranking models in data-driven generative modeling. While remarkably successful, the metric is known to sometimes disagree with human judgement. We investigate a root cause of…

Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…

Generative artificial intelligence (AI) models in smart grids have advanced significantly in recent years due to their ability to generate large amounts of synthetic data, which would otherwise be difficult to obtain in the real world due…

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…

Applying generative adversarial networks (GANs) to text-related tasks is challenging due to the discrete nature of language. One line of research resolves this issue by employing reinforcement learning (RL) and optimizing the next-word…

Generative Adversarial Networks (GANs) have high computational costs to train their complex architectures. Throughout the training process, GANs' output is analyzed qualitatively based on the loss and synthetic images' diversity and…

Generative methods have recently seen significant improvements by generating in a lower-dimensional latent representation of the data. However, many of the generative methods applied in the latent space remain complex and difficult to…

Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement…

Generative adversarial networks have seen rapid development in recent years and have led to remarkable improvements in generative modelling of images. However, their application in the audio domain has received limited attention, and…

Existing brain network distances are often based on matrix norms. The element-wise differences in the existing matrix norms may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A major…

Generative Adversarial Networks (GANs) are by far the most successful generative models. Learning the transformation which maps a low dimensional input noise to the data distribution forms the foundation for GANs. Although they have been…

In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…