Related papers: Continuous normalizing flows on manifolds
We establish a family of subspace-based learning method for multi-view learning using the least squares as the fundamental basis. Specifically, we investigate orthonormalized partial least squares (OPLS) and study its important properties…
In this paper, we investigate image reconstruction for dynamic Computed Tomography. The motion of the target with respect to the measurement acquisition rate leads to highly resolved in time but highly undersampled in space measurements.…
Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have…
Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous…
Preserving geometric structure is important in learning. We propose a unified class of geometry-aware architectures that interleave geometric updates between layers, where both projection layers and intrinsic exponential map updates arise…
The infinite-depth paradigm pioneered by Neural ODEs has launched a renaissance in the search for novel dynamical system-inspired deep learning primitives; however, their utilization in problems of non-trivial size has often proved…
We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to…
Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size…
Despite their popularity, to date, the application of normalizing flows on categorical data stays limited. The current practice of using dequantization to map discrete data to a continuous space is inapplicable as categorical data has no…
Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type…
Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…
Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date…
In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed…
Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps…
Detecting out-of-distribution (OOD) data is crucial for robust machine learning systems. Normalizing flows are flexible deep generative models that often surprisingly fail to distinguish between in- and out-of-distribution data: a flow…
Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
Normalization techniques have only recently begun to be exploited in supervised learning tasks. Batch normalization exploits mini-batch statistics to normalize the activations. This was shown to speed up training and result in better…