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 generalization of planar flows. Sylvester normalizing flows remove the well-known single…
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48 results for “Sylvester Normalizing Flows”
This work uses Sylvester normalizing flows for more accurate metabolite quantification in MRS.
problem Challenges in accurate metabolite quantification in MRS due to spectral overlap, low SNR, and artifacts.
method Bayesian inference framework with physics-informed Sylvester normalizing flows.
result Accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.
New linear flows using exponential of linear transformations improve generative models.
problem Improving generative models in machine learning.
method Developed convolution exponentials and generalized Sylvester Flows using the exponential of linear transformations.
result Convolution exponentials and Convolutional Sylvester Flows outperform other models in log-likelihood.
Woodbury transformations improve deep generative models with efficient invertibility and determinant calculation.
problem Efficiently invertible and determinant-calculable functions for deep generative models.
method Introducing Woodbury transformations that leverage matrix identities for efficient invertibility and determinant calculation.
result Woodbury transformations enable high-dimensional interactions, efficient sampling, and likelihood evaluation, outperforming other flow architectures.
SyGlasso models tensor data dependencies using Sylvester equations.
problem Capturing multiway dependencies in tensor-valued data.
method Based on Sylvester equation, uses nodewise regression for estimation.
result Demonstrates simultaneous estimation of brain connectivity and temporal dependencies.
This method infers models from data with physical insights, minimizing model order.
problem Learning models from data while preserving physical insights.
method Structure preservation and rank minimization via Sylvester equations.
result Models of low order are obtained with fewer degrees of freedom.
SG-PALM learns interpretable tensor models for high-dimensional data.
problem Learning interpretable tensor models for high-dimensional data.
method SG-PALM combines Sylvester generative model and fast proximal alternating linearized minimization.
result SG-PALM converges linearly to global optimum and scales to high dimensions.
Study algebraic invariants from lightning self-attention models.
problem Understanding polynomial coefficients of self-attention mechanisms.
method Identify algebraic invariants using polynomial coefficients and coordinate geometry.
result Found linear and nonlinear families of algebraic invariants.
Simon's knot genus problem solved with 3-manifold groups.
problem If epimorphism exists between knot groups, knot genus of one is greater than or equal to the other.
method Proved conjecture linking 3-manifold groups and Thurston norms, showed locally indicable groups are Lewin groups.
result Existence of epimorphism between knot groups implies knot genus inequality.
The study calibrates neural networks' parameters through optimal contraction in prediction problems.
problem Ensuring the existence and uniqueness of optimal parameters in neural networks.
method Transforming RNNs into contractions and solving matrix equations involving Sylvester equations.
result Optimal parameters exist, are unique, and can be found through an algorithm with desired precision.
New method trains normalizing flows using entropy-regularized transport.
problem Training continuous normalizing flows efficiently.
method Formulates flows as gradients of scalar potentials, training only these potentials.
result Trains normalizing flows without explicit flow computation during training.
PL-MCMC samples from normalizing flows' conditional distributions.
problem Sampling from complex conditional distributions learned by normalizing flows.
method Metropolis-Hastings implementation of PL-MCMC.
result PL-MCMC asymptotically samples from exact conditional distributions.
Fractal Flow enhances normalizing flows with interpretable latent space and hierarchical modeling.
problem High-dimensional density estimation and generative modeling challenges.
method Integrates topic modeling (LDA) and fractal strategy into normalizing flows.
result Achieves latent clustering, controllable generation, and superior estimation accuracy.
SurVAE Flows combine VAEs and flows using surjective transformations.
problem Combining the strengths of VAEs and flows to model complex densities.
method Modular framework of composable deterministic and stochastic transformations.
result Exact likelihood computation and lower bound on likelihood.
QMME balances cost and speed in convex optimization.
problem Slow convergence of first-order methods and high cost of second-order methods.
method Minimizing quadratic majorants with fixed curvature at each iteration.
result QMME framework achieves sequential convergence under standard assumptions.
Study shows limits of certain normalizing flows in higher dimensions.
problem Understanding the representation power of normalizing flows in different dimensions.
method Rigorously established bounds on expressive power of basic normalizing flows.
result Limited representation power in higher dimensions, especially with moderate depth.
The paper connects complex normalizing flows to Kähler-Ricci flows using geometric and statistical perspectives.
problem Understanding the relationship between complex normalizing flows and Kähler-Ricci flows.
method Develops connections between complex normalizing flows and Kähler-Ricci flows by relating the log determinant to Ricci curvature and using a Bayesian perspective.
result Reconciles the complex normalizing flow and Kähler-Ricci flow, showing they are related under certain conditions.
Riemannian flows model curved spaces better.
problem Normalizing flows misspecified on curved spaces.
method Riemannian continuous normalizing flows using ODE solutions.
result Improves modeling on spheres, torii, and hyperbolic spaces.
New framework explains normalizing flows' power and limitations.
problem Understanding the expressive power and limitations of normalizing flows.
method Theoretical framework for well-conditioned coupling-based normalizing flows and volume-preserving flows.
result RealNVP is distributionally universal, but volume-preserving flows are not.
A new method learns latent space normalizing flow for approximate inference in generator models.
problem Approximate inference in generator models with complex posterior distributions.
method Jointly learns latent space normalizing flow and generator model using MCMC-based maximum likelihood.
result The short-run Langevin flow approximates the posterior and aligns with the normalizing flow prior.
TCNF models SDEs using time deformation of Brownian motion.
problem Modeling SDEs with existing methods.
method Time-changed normalizing flows (TCNF) based on time deformation of Brownian motion.
result Improved modeling of SDEs, including Ornstein-Uhlenbeck process.
Paper introduces Categorical Normalizing Flows for better handling of categorical data.
problem Limited application of normalizing flows on categorical data due to lack of intrinsic order.
method Categorical Normalizing Flows use continuous transformations to model latent relations in categorical data, optimizing both continuous representation and model likelihood.
result GraphCNF, a permutation-invariant generative model, outperforms state-of-the-art on molecule generation.
This study evaluates different normalizing flow architectures for MCMC.
problem Lack of systematic comparison of normalizing flow architectures in MCMC.
method Extensive evaluation of various normalizing flow architectures on different MCMC methods and target distributions.
result Contractive residual flows are the best general-purpose models for MCMC.
Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.
problem Efficiently sampling lattice field theories with computational challenges.
method Integrates locality into autoregressive conditional normalizing flows.
result Autocorrelation times improved by orders of magnitude for theory on a 2D lattice.
Guillarmou extends X-ray transform to magnetic and thermostat flows.
problem Stability of magnetic X-ray transforms.
method Generalizes normal operator to thermostat and magnetic flows, proving ellipticity.
result Elliptic pseudodifferential operators of order -1 for generalized normal operators.
Improves normalizing flows by incorporating data dependencies.
problem Current normalizing flow learning assumes independent data, leading to errors.
method Proposes a likelihood objective with dependencies and efficient learning algorithm.
result Improves density estimation and data generation on real-world data.
New normalizing flows in hyperbolic space improve posterior modeling for hierarchical data.
problem Limited flexibility of existing normalizing flows in Euclidean space for hierarchical data.
method Elevated normalizing flows to hyperbolic spaces using coupling transforms and Wrapped Hyperboloid Coupling.
result Improved performance on density estimation and hierarchical graph data.
Normalizing flows are shown to be equivalent to Bayesian networks, revealing new insights.
problem Understanding the limitations and capabilities of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models and analyzing their structure.
result Normalizing flows can be reduced to Bayesian networks, revealing new insights into their structure and capabilities.
Self Normalizing Flows improve normalizing flows by reducing computational complexity.
problem Efficient gradient computation in normalizing flows, especially in Jacobian determinant terms.
method Introducing Self Normalizing Flows that replace expensive terms with learned approximate inverses.
result Models can be trained more quickly and perform better than functionally constrained counterparts.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.
problem The expressivity of bi-Lipschitz Normalizing Flows in approximating specific target distributions.
method Characterization of expressivity through lower bounds on Total Variation distance and discussion of potential remedies.
result Several target distributions are difficult to approximate using bi-Lipschitz Normalizing Flows, and lower bounds on their approximation are provided.
We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs w…
Implicit Normalizing Flowsstat.ML
ImpFlows generalize normalizing flows by implicitly defining transformations.
problem Creating flexible and tractable probability distributions.
method Implicitly defined invertible transformations using roots of equations.
result ImpFlows can represent functions that ResFlows cannot, with comparable parameters.
New proof shows coupling-based flows converge linearly to diagonalize data covariance.
problem Understanding convergence of coupling-based normalizing flows to arbitrary data distributions.
method Proved linear convergence rate for whitening of data distribution.
result Coupling-based flows achieve linear convergence to diagonalize data covariance.
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
Normalizing flows fail to detect OOD data due to learning local pixel correlations.
problem Detecting out-of-distribution data in machine learning systems.
method Investigated why normalizing flows fail to distinguish between in- and out-of-distribution data, and modified flow architecture to improve OOD detection.
result Modifying flow architecture can improve OOD detection by biasing the flow towards learning semantic structure of the target data.
A new framework enhances generative modeling by learning local flows over complex manifolds.
problem Limited expressivity of current normalizing flows for low-dimensional manifolds.
method Vector quantized local normalizing flows (VQ-Flows) using a VQ-AE atlas and conditional flows.
result Enhanced modeling of complex data distributions over manifolds.
New variational flows improve Monte Carlo and normalization tasks.
problem Intractable global optimum in expressive variational families.
method Constructing asymptotically exact variational flows from involutive MCMC kernels.
result Provable total variation convergence of new variational families.
Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
We propose to improve trust region policy search with normalizing flows policy. We illustrate that when the trust region is constructed by KL divergence constraints, normalizing flows policy generates samples far from the 'center' of the previous policy iterate, which potentially enables better exploration and helps av…
Copula-based normalizing flows improve flexibility and stability for heavy-tailed data.
problem Limited expressive power of vanilla normalizing flows.
method Generalize base distribution to copula for more accurate representation of target distribution.
result Copula-based normalizing flows improve flexibility, stability, and effectiveness for heavy-tailed data.
CRAFT improves on existing methods for sampling complex distributions.
problem Sampling from complex probability distributions.
method Combines SMC with variational inference using normalizing flows.
result Improves on Annealed Flow Transport Monte Carlo and MCMC-based Stochastic Normalizing Flows.
Normalizing flows improve density estimation from noisy data.
problem Estimating underlying density from noisy samples.
method Use normalizing flows for density estimation with arbitrary noise distributions, using amortized variational inference.
result Normalizing flows can outperform Gaussian mixtures for density deconvolution.
Paper proposes CoopFlow, a two-flow generator for energy-based models.
problem Training energy-based models with Langevin flow and normalizing flow.
method CoopFlow trains an energy-based model using a normalizing flow initialization and a short-run Langevin flow revision.
result CoopFlow converges to a moment matching estimator and synthesizes realistic images.
This research tackles ordering latent variables in normalizing flows.
problem Learning low-dimensional, meaningful representations in latent space.
method Nested dropout normalizing flows with ordered latent variables.
result A trade-off exists between flow likelihood and ordering quality.
In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…
Study integrability of geodesic flow on specific Lie groups.
problem Integrability of geodesic flow on metabelian nilpotent groups.
method Symplectic reduction procedure applied to sub-Riemannian geodesic flow on metabelian nilpotent groups.
result Showed integrability of normal Hamiltonian flow in Engel-type groups.
In this article, we shall investigate the relationship between the existence or non-existence of non-singular solutions to the normalized Ricci flow and smooth structures on closed 4-manifolds, where non-singular solutions to the normalized Ricci flow are solutions which exist for all time with unif…