The study finds abundant normal generators for mapping class groups.
problem Understanding normal generation in mapping class groups.
method Analyzing restrictions on invariant subsurfaces and Teichmüller spaces.
result Reducible mapping classes can normally generate mapping class groups based on their asymptotic translation lengths.
Optimized normalization layers improve domain generalization.
problem Improving model generalization across different domains.
method Learning separate normalization parameters per domain using multiple normalization methods (batch and instance).
result State-of-the-art accuracy on domain generalization benchmarks.
Paper defines generalized braids and proves their subgroup status.
problem Understanding the structure of generalized braids and knots.
method Defined generalized braid theories and computed their generating sets.
result Quasitoric normal generalized braids form a subgroup of normal generalized braid group.
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
The paper updates Bayesian CMA-ES with normal Wishart and proves lower expected covariance.
problem Improving the Bayesian CMA-ES algorithm with normal Wishart prior.
method Revisits Bayesian CMA-ES, proves lower expected covariance in normal Wishart, and presents a generalized model.
result Proves that the expected covariance is lower in the normal Wishart prior model due to convexity of the inverse.
Normality equations describe Newtonian dynamical systems admitting normal shift of hypersurfaces. They were first derived in Euclidean geometry, then in Riemannian geometry. Recently they were rederived in more general case, when geometry of manifold is given by generalized Legendre transformation. As appears, in this …
One of the challenges in the study of generative adversarial networks is the instability of its training. In this paper, we propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator. Our new normalization technique is computationally light and easy to in…
We say A is a quasi-normal subgroup of the group G if the commensurator of A in G is all of G. We develop geometric versions of commensurators in finitely generated groups. In particular, g is an element of the commensurator of A in G iff the Hausdorff distance between A and gA is finite. We show that a quasi-normal su…
Extends corner structure study to general case, constructs normal Trans-Sasakian structures.
problem Extending corner structure study to general case without conditions.
method Extends corner structure to general case, constructs Trans-Sasakian structures from non-normal corner structures.
result Constructs normal Trans-Sasakian structures from non-normal corner structures.
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The existence of bundle coordinates normal at a given point and/or along injective horizonta…
Topological normal generation proved for mapping class groups of certain surfaces.
problem Proving topological normal generation for mapping class groups of surfaces.
method Analyzing the end space of surfaces and using topological normal closure properties.
result Topological normal generation is equivalent to uniquely self-similar for surfaces with countable end space.
Normalization layers control deep neural network capacity, improving stability and generalization.
problem Excessive capacity in deep neural networks leads to overfitting and poor generalization.
method Developed a theoretical framework to explain normalization's role in capacity control.
result Normalization layers reduce the Lipschitz constant exponentially, smoothing the loss landscape and enhancing generalization.
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.
We provide a simple criterion for an element of the mapping class group of a closed surface to have normal closure equal to the whole mapping class group. We apply this to show that every nontrivial periodic mapping class that is not a hyperelliptic involution is a normal generator for the mapping class group when the …
Study shows torsion normal generators in non-orientable surface mapping class groups.
problem Understanding normal generators of mapping class groups for non-orientable surfaces.
method Analyzes periodic elements and their normal closures in non-orientable surfaces.
result Provides conditions for normal generation and examples of elements.
The study explores normal generators for mapping class groups and their properties.
problem Understanding normal generators for mapping class groups of surfaces.
method Examined the relation between normal generation and asymptotic translation lengths on Teichmüller space and curve graph.
result Discussed several open questions related to normal generators.
Improves deep networks' performance by applying Bayesian learning to batch normalization.
problem Improving generalization performance of deep networks.
method Bayesian learning applied to deterministic normalization techniques.
result Significant improvement in generalization performance compared to traditional methods.
A new model uses normalizing flows for discrete sequences, improving generation speed.
problem Modeling discrete sequences like text using normalizing flows poses challenges.
method Proposes a VAE-based model with autoregressive and non-autoregressive flow architectures.
result Flow-based models can match or improve on autoregressive baselines for discrete sequence tasks.
New algorithm tackles nonconvex machine learning problems with adaptive normalization and independent sampling.
problem Nonconvex machine learning problems with generalized-smoothness.
method Adaptive gradient normalization, independent sampling, and gradient clipping.
result Achieves an O(ε^(-4)) sample complexity for fast convergence.
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…
Four improvements to Batch Normalization improve deep learning performance.
problem Improving Batch Normalization for better deep learning performance.
method Proposed improvements include reasoning about current examples, Ghost Batch Normalization, weight decay regularization, and a new normalization algorithm for small batch sizes.
result Performance gains across all batch sizes with no additional computation during training.
The study develops a quadrature method for the generalized hyperbolic distribution using finite normal-mixture approximation.
problem Efficiently approximating and computing expectations under the generalized hyperbolic distribution.
method Derived a numerical quadrature from Gauss-Hermite quadrature, approximated the distribution as a finite normal variance-mean mixture.
result Accurately computed expectations and sampled generalized hyperbolic random variates using the proposed method.
This paper analyzes how normalization layers improve neural network training.
problem Improving generalization performance and training speed of neural networks.
method Global convergence analysis of two-layer neural networks with ReLU activations and Weight Normalization.
result Introduction of normalization layers changes the optimization landscape, enabling faster convergence.
Automates size normalization for fashion items.
problem Reduce merchandise returns in e-commerce.
method Uses sales data to automate size mapping.
result Automated size mappings comparable to human-generated ones.
Abstract: Proves no non-trivial normal orbits for specific Hamiltonians.
problem Analyzing normal singular geodesics in a conformally generic sub-Riemannian metric.
method Proves the absence of non-trivial normal orbits for specific Hamiltonians.
result No non-trivial normal orbits for the specified Hamiltonians.
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently pro…
We propose a theoretical framework for thinking about score normalization, which confirms that normalization is not needed under (admittedly fragile) ideal conditions. If, however, these conditions are not met, e.g. under data-set shift between training and runtime, our theory reveals dependencies between scores that c…
We introduce the notion of a ribbon-clasp surface-link, which is a generalization of a ribbon surface-link. We generalize the notion of a normal form on embedded surface-links to the case of immersed surface-links and prove that any (immersed) surface-link can be described in a normal form. It is known that an embedded…
In this paper, we study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the necessary and succient conditions to be normal a complex contact metric manifold.…
The study restricts normal subgroups of Kähler groups, proving specific cases and general restrictions.
problem Characterizing normal subgroups of Kähler groups.
method Analyzing embeddings and conjugation actions of surface groups and one-ended hyperbolic groups.
result Restrictions on normal subgroups of Kähler groups, including virtual direct products and surface group properties.
Defines and analyzes generalized normal ruled surfaces of curves in 3D space.
problem Understanding the geometry of generalized normal ruled surfaces.
method Calculates Gaussian and mean curvatures to determine surface properties and examines curve conditions.
result Determines when surfaces are flat or minimal and identifies specific curve types.
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.
Proves minimum number of normals to curves in 3D space.
problem Finding the minimum number of normals to closed curves in 3D.
method Morse theory for squared distance function and self intersections of the focal surface.
result For generic curves, points have at least 6, 8, or 10 normals depending on knotting.
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.
Graph normalizing flows use neural networks for graph prediction and generation.
problem Efficiently processing and generating graph data with reduced memory usage.
method Reversible graph neural network model combining auto-encoder and normalizing flows.
result Graph normalizing flows achieve competitive results in graph generation and prediction.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering …
This paper reviews normalization techniques for DNNs.
problem Improving training speed and generalization of DNNs.
method Taxonomy of normalization methods, decomposition of activation methods.
result Insight for designing new normalization techniques.
The paper characterizes surfaces in 4D space forms with flat normal connection.
problem Characterizing surfaces in 4D space forms with specific geometric properties.
method Analyzing linearly dependent conditions and using properties of sectional curvature.
result Characterizations of space-like and time-like surfaces with flat normal connection.
Normalizing Flows model tractable distributions for efficient sampling and evaluation.
problem Creating efficient generative models for sampling and density evaluation.
method Construct and use Normalizing Flows to learn distributions.
result Comprehensive review of current Normalizing Flow methods and future directions.
Solves the Wiegold problem by showing free products of left-orderable groups have normal rank > 1.
problem Wiegold problem about groups of normal rank > 1
method Topological argument and intricate construction of left-orders
result Free products of nontrivial left-orderable groups have normal rank > 1
Polytopes in high dimensions have at least 2n+4 normals.
problem Understanding normals to convex polytopes in high dimensions.
method Proved for generic simple polytopes in R^n, n>3.
result Each polytope contains a point with at least 2n+4 normals.
Normality equations describe Newtonian dynamical systems admitting normal shift of hypersurfaces. These equations were first derived in Euclidean geometry. Then very soon they were rederived in Riemannian and in Finslerian geometry. Recently I have found that normality equations can be derived in geometry given by clas…
Developed criteria for selecting non-normalized models using NCE and score matching.
problem No information criteria for non-normalized models estimated by NCE or score matching.
method Developed information criteria based on discrepancy measures for non-normalized models estimated by NCE or score matching.
result The proposed criteria enable selection of the appropriate non-normalized model in a data-driven manner.
For Legendrian links in the 1-jet space of S1 we show that the 1-graded ruling polynomial may be recovered from the Kauffman skein module. For such links a generalization of the notion of normal ruling is introduced. We show that the existence of such a generalized normal ruling is equivalent to sharpness of the Kau…
The paper generalizes rectifying and normal curves in Lorentzian n-space.
problem Characterizing and classifying g−rectifying and g−normal curves in Lorentzian n-space. method Introducing a g−position vector field and defining g−rectifying and g−normal curves based on this field. result Comprehensive characterization and classification of g−rectifying and g−normal curves. Following Matveev, a k-normal surface in a triangulated 3-manifold is a generalization of both normal and (octagonal) almost normal surfaces. Using spines, complexity, and Turaev-Viro invariants of 3-manifolds, we prove the following results: 1) a minimal triangulation of a closed irreducible or a bounded hyperbolic 3-…
We develop a general method for estimating a finite mixture of non-normalized models. Here, a non-normalized model is defined to be a parametric distribution with an intractable normalization constant. Existing methods for estimating non-normalized models without computing the normalization constant are not applicable …
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.