相关论文: Jacobian Determinant of Normalizing Flows

Normalizing flows are diffeomorphic, typically dimension-preserving, models trained using the likelihood of the model. We use the SurVAE framework to construct dimension reducing surjective flows via a new layer, known as the funnel. We…

Given the growth in the variety and precision of astronomical datasets of interest for cosmology, the best cosmological constraints are invariably obtained by combining data from different experiments. At the likelihood level, one…

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…

While the neural ODE formulation of normalizing flows such as in FFJORD enables us to calculate the determinants of free form Jacobians in O(D) time, the flexibility of the transformation underlying neural ODEs has been shown to be…

The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean…

Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space,…

The scalability of continuous normalizing flows (CNFs) for unbiased Boltzmann sampling remains limited in high-dimensional systems due to the cost of Jacobian-determinant evaluation, which requires $D$ backpropagation passes through the…

Iterative Gaussianization is a fixed-point iteration procedure that can transform any continuous random vector into a Gaussian one. Based on iterative Gaussianization, we propose a new type of normalizing flow model that enables both…

Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible…

Normalizing flows are a class of deep generative models that are especially interesting for modeling probability distributions in physics, where the exact likelihood of flows allows reweighting to known target energy functions and computing…

We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…

We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common…

Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain…

Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in…

The local Lipschitz constant of a neural network is a useful metric with applications in robustness, generalization, and fairness evaluation. We provide novel analytic results relating the local Lipschitz constant of nonsmooth vector-valued…

Normalizing flows have grown more popular over the last few years; however, they continue to be computationally expensive, making them difficult to be accepted into the broader machine learning community. In this paper, we introduce a…

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a…

We propose a new starting point for comparing dose distributions in therapeutic radiation physics using a Jacobian-based measure. The measure is normalization independent, free of tunable parameters, bounded and converges to a unique value…

Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is…

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…