Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transf…
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48 results for “Real NVP”
Stable training of deep normalizing flows for high-dimensional variational inference.
problem Training deep normalizing flows for high-dimensional posterior distributions is infeasible due to high stochastic gradient variance.
method Proposed a combination of soft-thresholding of scale and bijective soft log transformation to stabilize training.
result Stable training of Real NVPs for posterior distributions with thousands of dimensions is possible.
Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Ca…
Variational autoencoders (VAEs), that are built upon deep neural networks have emerged as popular generative models in computer vision. Most of the work towards improving variational autoencoders has focused mainly on making the approximations to the posterior flexible and accurate, leading to tremendous progress. Howe…
This paper proves the necessity and effectiveness of learning the prior in VAEs.
problem Aggregated posterior may not match unit Gaussian prior, leading to poor variational inference.
method Proves necessity and effectiveness of learning the prior, analyzes why it's needed, and proposes hypothesis.
result Learning the prior can improve reconstruction loss and achieve comparable test NLL to deep hierarchical VAEs.
Study on flow-based methods for capturing tail properties in densities.
problem Flow-based methods struggle with capturing non-Gaussian tails.
method Characterize and adapt triangular maps to capture tail properties.
result Flow models lack the ability to capture non-Gaussian tails.
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 distributions over continuous latent variables. This makes them poorly suited for m…
Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling th…
Generative models struggle with out-of-distribution data, but new methods show they can be improved.
problem Generative models struggle with assigning higher likelihood to out-of-distribution (OOD) data.
method Empirical challenge of previous reasoning, new data-set separability, and novel model architectures.
result Generative models can be improved by changing the data representation space and using PCA for anomaly detection.
Triangular flows ensure statistical consistency and fast rates in generative modeling.
problem Ensuring statistical consistency and fast rates in generative models.
method Statistical guarantees and sample complexity bounds for triangular flow models using empirical process theory.
result Established statistical consistency and finite sample convergence rates for Kullback-Leibler estimator of Knöthe-Rosenblatt measure coupling.
Gaussianization flows transform any random vector into a Gaussian, enabling efficient computation and sample generation.
problem Transforming any random vector into a Gaussian for efficient computation and sample generation.
method Iterative Gaussianization and normalizing flow model.
result Gaussianization flows are universal approximators and achieve better performance on tabular datasets.
Augmented KRnet improves flow-based generative modeling by maintaining exact invertibility.
problem Maintaining exact invertibility in flow-based generative models.
method Integrates augmented dimensions into KRnet to achieve full nonlinear updates in two iterations, keeping exact invertibility.
result Augmented KRnet achieves full nonlinear updates in two iterations, maintaining exact invertibility.
A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real structure. We call them real open book decompositions. We show that each real open b…
Classifies Real line bundles with Real connections on manifolds with involution.
problem Classifying Real line bundles with Real connections on manifolds with involution.
method Defines Real smooth Deligne cohomology to interpolate between equivariant sheaf cohomology and smooth imaginary-valued forms.
result Classifies Real line bundles with Real connections on manifolds with involution.
Every real 3-manifold can be turned into a real contact structure.
problem Understanding and constructing real contact structures on real 3-manifolds.
method Surgery along invariant knots and contact operations starting from the standard real .
result Every real 3-manifold admits a real contact structure.
Study real algebraic curves on real del Pezzo surfaces using degeneration methods.
problem Classify topological types of real algebraic curves on real del Pezzo surfaces.
method Degeneration methods and real enumerative geometry.
result Obstructions and constructions of real algebraic curves with prescribed topology.
Real del Pezzo surfaces split real lines into elliptic and hyperbolic types.
problem Understanding real lines on real del Pezzo surfaces of degree 1.
method Intrinsically defined Pin-structure on the real locus.
result The difference between hyperbolic and elliptic lines is always 16.
Classifies Real primary Hopf surfaces and their associated groups.
problem Classifying Real primary Hopf surfaces and their associated groups.
method Complete classification up to Real biholomorphisms and equivariant diffeomorphisms.
result Detailed description of groups associated with Real primary Hopf surfaces.
We list up all the candidates for the real isotopy types of real anti-bicanonical curves with one real nondegenerate double point on the 4-th real Hirzebruch surface RF_4 by enumerating the connected components of the moduli space of real 2-elementary K3 surfaces of type (S,θ)=((3,1,1), -id). We also list up all the ca…
In this note we introduce certain invariants of real Lefschetz fibrations. We call these invariants {\em real Lefschetz chains}. We prove that if the fiber genus is greater than 1, then the real Lefschetz chains are complete invariants of real Lefschetz fibrations with only real critical values. If however the fiber ge…
We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free action of a compact Lie group. We then extend a well-known result of Nomizu and Ozek…
Study real line subbundles on curves, extending classical work.
problem Understanding real line subbundles in real bundles on curves.
method Application of Atiyah's techniques and work of Lange-Narasimhan.
result Describes the Galois action on the set of lines through a real point in the moduli space of such bundles.
Classifies real rational knots and curves in a specific quadric space.
problem Classifying real rational knots and curves in a quadric space of signature .
method Classification through a study of real rational curves of low degree in the quadric.
result Provides representatives of all real rational knots of degree in the quadric.
Classifies real tight contact structures on lens spaces and solid tori.
problem Classifying real tight contact structures on specific 3-manifolds.
method Equivariant contact isotopy, real open book decompositions, and isolated real algebraic surface singularities.
result Unique real tight structures on and , at most one on , and bounds on the count.
We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known the constructio…
A real 3- or 4-manifold has by definition an orientation preserving smooth involution acting on it. We consider Lefschetz fibrations of 4-dimensional manifolds-with-boundary and open book decompositions on their boundary in the existence of a real structure. We prove that there is a real open book which cannot be fille…
Study finds Hilbert square of real surfaces can be maximal even when the surface has disconnected real locus.
problem Exploring conditions for maximality of Hilbert square of real surfaces.
method Analyzing Hilbert square of maximal real surfaces and examining specific examples.
result Hilbert square can be maximal even for surfaces with disconnected real locus.
New invariant real rank identifies constant real Lie algebroids.
problem Characterizing complex Lie algebroids with constant real rank.
method Introducing real rank and minimal complex subalgebroid.
result Local splitting and characterization of complex Lie algebroids.
This paper is motivated by the real symplectic isotopy problem : does there exists a nonsingular real pseudoholomorphic curve not isotopic in the projective plane to any real algebraic curve of the same degree? Here, we focus our study on symmetric real curves on the projective plane. We give a classification of real s…
Study gauge theory of real and quaternionic parabolic bundles over real curves.
problem Examining gauge theoretic aspects of real and quaternionic parabolic bundles over real curves.
method Investigate orbits of connections under gauge groups for fixed real or quaternionic structures.
result Gauge-theoretic quotients of real or quaternionic connections are inside the real points of moduli of holomorphic bundles.
We prove that there is a unique real tight contact structure on the 3-ball with convex boundary up to isotopy through real tight contact structures. We also give a partial classification of the real tight solid tori with the real structure being antipodal map along longitudinal and the identity along meridional directi…
We show that totally real elliptic Lefschetz fibrations that admit a real section are classified by their "real loci" which is nothing but an -valued Morse function on the real part of the total space. We assign to each such real locus a certain combinatorial object that we call a \emph{necklace diagram}. On the o…
Study reduces real-world sample complexity for reinforcement learning.
problem Decrease real-world sample complexity in reinforcement learning.
method Formulates a theoretical framework for Sim-to-Real reinforcement learning using ROMDPs.
result Establishes real-world sample complexity guarantees smaller than direct learning.
Real link Floer homologymath.GT
Defines real link Floer homology for specific types of links.
problem Developing a new homology theory for certain types of links.
method Combining real Heegaard Floer homology and real sutured Heegaard Floer homology, using real grid diagrams in .
result Observes structural and property properties of strongly invertible knots.
Real Seiberg-Witten and monopole Floer homologies are equivalent for certain 3-manifolds.
problem Equivalence of two Floer homologies for real structures.
method Direct isomorphism proof between real Seiberg-Witten and monopole Floer homologies.
result Real Seiberg-Witten and monopole Floer homologies are isomorphic.
Study real Mordell-Weil group and real lines on rational elliptic surfaces and del Pezzo surfaces.
problem Characterize the real Mordell-Weil group and real lines on rational elliptic surfaces and del Pezzo surfaces.
method Explicit description of isotopy types of real lines and presentation of MW group in mapping class group.
result Explicit formula for the action of MW group in H1(XR).
Study real semi-stable degenerations and describe real loci via blow-ups.
problem Describe the homeomorphism type of real loci in degenerations.
method Use real-oriented blow-ups to describe the homeomorphism type of real loci.
result Give more explicit descriptions of real loci as stratified spaces.
We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of real points is equipped with a pair of opposite orientations and a Spin structure…
A real Bott manifold is the total space of iterated RP^1 bundles starting with a point, where each RP^1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with Z/2 coefficients are isomorphic. A real Bott manifold is a …
Real Lagrangians in toric manifolds are classified by combinatorial data.
problem Classifying real Lagrangian submanifolds in toric symplectic manifolds.
method Established a real analog of the Delzant construction.
result Real Lagrangians in toric del Pezzo surfaces have all possible diffeomorphism types.
Study real logarithms of semi-simple matrices, focusing on differential structure.
problem Understanding the differential structure of real logarithms of semi-simple matrices.
method Examines the differential structure of real logarithms of semi-simple matrices under specific matrix types.
result Characterizes the differential structure of real logarithms of semi-simple matrices.
Developed a real sutured Heegaard Floer theory.
problem Real sutured manifolds and their Floer homology.
method Real nice diagrams, combinatorial computation.
result New structural properties distinguishing from sutured Floer homology.
This thesis explores algebraic cycles and moduli spaces over real numbers.
problem Understanding the cycle class map and its image in real algebraic geometry.
method Constructing integral Fourier transforms on Chow rings of abelian varieties over any field.
result Proof of integral Hodge conjecture for real abelian threefolds and moduli space properties.
We show that the moduli space of genus zero stable maps is a real projective variety if the target space is a smooth convex real projective variety. We show that evaluation maps, forgetful maps are real morphisms. We analyze the real part of the moduli space.
Machine learning identifies boundaries of real solutions in polynomial systems.
problem Locating boundaries in parameter space for real solutions of polynomial systems.
method Supervised machine learning approach using nearest neighbor and deep learning approximations.
result Efficiently approximates the real discriminant locus for multidimensional parameter spaces.
We give an asymptotic probabilistic real Riemann-Hurwitz formula computing the expected real ramification index of a random covering over the Riemann sphere. More generally, we study the asymptotic expected number and distribution of critical points of a random real Lefschetz pencil over a smooth real algebraic variety…
Transforms uniquely determine Higgs fields on real-analytic manifolds.
problem Determining Higgs fields from transforms on manifolds.
method Matrix-weighted real-analytic double fibration transforms.
result Higgs fields can be uniquely determined from transforms.
A natural oriented (2k+2)-chain in CP^{2k+1} with boundary twice RP^{2k+1}, its complex shade, is constructed. Via intersection numbers with the shade, a new invariant, the shade number of k-dimensional subvarieties with normal vector fields along their real part, is introduced. For an even-dimensional real variety, th…