Real NVP models improve image modeling with exact computations.
problem Unsupervised learning of probabilistic models.
method Real-valued non-volume preserving transformations.
result Exact log-likelihood computation, sampling, inference, interpretable latent space.
This work replaces pixel-wise reconstruction in VAEs with real NVP transformations.
problem Shortcomings of pixel-wise reconstruction in VAEs.
method Used real-valued non-volume preserving transformations (real NVP) for conditional likelihood computation.
result A simple VAE with real NVP is competitive with complex VAE structures on image modeling tasks.
Paper proposes a neural network for learning better importance sampling.
problem Improving variance reduction in Monte Carlo rendering.
method Uses a neural network to learn desired densities in the primary sample space of a rendering algorithm.
result Effective variance reduction demonstrated in practical scenarios.
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.
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.
RAD approach models both continuous and discrete data.
problem Flow models struggle with discrete structures in data.
method Domain partitioning with locally invertible functions for real and discrete latent variables.
result RAD approach models both continuous and discrete structures.
Improves autoregressive models for better density estimation.
problem Limited flexibility of autoregressive models.
method Stacked autoregressive models with random number modeling.
result Achieves state-of-the-art performance in density estimation.
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…
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 S3. result Every real 3-manifold admits a real contact structure.
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.
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…
Study on expected critical points of real Lefschetz pencils.
problem Counting critical points in real Lefschetz pencils.
method Asymptotic probabilistic real Riemann-Hurwitz formula.
result Asymptotic expected number and distribution of critical points.
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…
Real analytic submersion images are always real analytic.
problem Analyticity of submersion images
method Analyticity proof for Riemannian submersions
result Image of real analytic submersion is real analytic
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 (3,2). 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 ≤5 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 S3 and RP3, at most one on L(p,±1), 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 S1-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.
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 S3. 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.
Proves real analyticity on surfaces based on restrictions.
problem Determining analyticity on non-continuous functions on manifolds.
method Analyzes restrictions to submanifolds homeomorphic to 2-sphere.
result Analyticity on manifold follows from analytic restrictions.
Real Heegaard Floer theory shown to be natural and invariant.
problem Defining and proving naturality of real Heegaard Floer homology.
method Defined and proved naturality of real Heegaard Floer homology and other related theories.
result Real Heegaard Floer homology is shown to be natural and admits an action of the equivariant mapping class group.
Real Lie groups' invariant theory matches that of their affine counterparts.
problem Matching invariant theory of real Lie groups with affine groups.
method Simple remark showing coincidence.
result Invariant theory of real Lie groups equals that of their affine counterparts.
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 …
Study real structures on Higgs pairs over Klein surfaces, proving a correspondence.
problem Real structures on Higgs pairs over Klein surfaces.
method Establish Hitchin-Kobayashi correspondence, homeomorphism between moduli spaces.
result Real G-Higgs bundles appear as fixed points of involutions. Proper Lie groupoids have real analytic structures.
problem Finding analytic structures for proper Lie groupoids.
method Demonstrating the existence of a compatible real analytic structure.
result Proper Lie groupoids have real analytic structures.
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.