Related papers: Topological Autoencoders
Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…
Echoing recent calls to counter reliability and robustness concerns in machine learning via multiverse analysis, we present PRESTO, a principled framework for mapping the multiverse of machine-learning models that rely on latent…
Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…
We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly…
Layered hybrid halide compounds offer promising functional properties, particularly tunable band gaps, conductivity, light harvesting thus making them prospective for applications in photovoltaics and optoelectronics. This study exemplifies…
Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…
Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…
Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations…
We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we…
Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the…
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality…
Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and…
Deep learning based image compression has recently witnessed exciting progress and in some cases even managed to surpass transform coding based approaches that have been established and refined over many decades. However, state-of-the-art…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
Autoencoder can give rise to an appropriate latent representation of the input data, however, the representation which is solely based on the intrinsic property of the input data, is usually inferior to express some semantic information. A…
How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…
The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to…