Related papers: Exploring the Manifold of Neural Networks Using Di…
Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative…
A prevalent assumption regarding real-world data is that it lies on or close to a low-dimensional manifold. When deploying a neural network on data manifolds, the required size, i.e., the number of neurons of the network, heavily depends on…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…
Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…
The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as…
The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…
Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork,…
A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…
This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
The subject of deep learning has recently attracted users of machine learning from various disciplines, including: medical diagnosis and bioinformatics, financial market analysis and online advertisement, speech and handwriting recognition,…