Related papers: Canonical normalizing flows for manifold learning

In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…

Disentangled representation learning aims to capture the underlying explanatory factors of observed data, enabling a principled understanding of the data-generating process. Recent advances in generative modeling have introduced new…

Fueled by the expressive power of deep neural networks, normalizing flows have achieved spectacular success in generative modeling, or learning to draw new samples from a distribution given a finite dataset of training samples. Normalizing…

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…

Representing token embeddings as probability distributions over learned manifolds allows for more flexible contextual inference, reducing representational rigidity while enhancing semantic granularity. Comparative evaluations demonstrate…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…

This paper provides a novel framework that learns canonical embeddings for non-rigid shape matching. In contrast to prior work in this direction, our framework is trained end-to-end and thus avoids instabilities and constraints associated…

Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…

This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several…

Flow Matching (FM) has recently emerged as a leading approach for high-fidelity visual generation, offering a robust continuous-time alternative to ordinary differential equation (ODE) based models. However, despite their success, FM models…

Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

It is well established that training deep neural networks gives useful representations that capture essential features of the inputs. However, these representations are poorly understood in theory and practice. In the context of supervised…

Data augmentation for deep learning benefits model training, image transformation, medical imaging analysis and many other fields. Many existing methods generate new samples from a parametric distribution, like the Gaussian, with little…

Flow-based generative models have shown an excellent ability to explicitly learn the probability density function of data via a sequence of invertible transformations. Yet, learning attentions in generative flows remains understudied, while…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for…

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…