arXiv research

New method trains normalizing flows using entropy-regularized transport.

Study on algebraic curves' invariants and vanishing criteria.

Dual optimization connects ERM-fDR to normalization function.

Batch normalization makes deep residual networks train faster.

For orthonormal normal sections of two-dimensional immersions in R^4 we define torsion coefficients and a functional for the total torsion. We discuss normal sections which are critical for this functional. In particular, a global estimate for the torsion coefficients of a critical normal section in terms of the curvat…

Distance, normals, and double normals for real plane curves with singularities

Real analytic functions can be extended on manifolds with normal crossings.

The paper studies matrix normalization and graph balancing using a new functional and gradient descent.

Proposes adversarial normalization for multi-domain image segmentation.

We prove that among all Kollár components obtained by plt blow ups of a klt singularity $o \in (X, D)$, there is at most one that is (log-)K-semistable. We achieve this by showing that if such a Kollár component exists, it uniquely minimizes the normalized volume function introduced in [Li15a] among all divisorial valu…

Proves minimum number of normals to curves in 3D space.

Recent seminal work at the intersection of deep neural networks practice and random matrix theory has linked the convergence speed and robustness of these networks with the combination of random weight initialization and nonlinear activation function in use. Building on those principles, we introduce a process to trans…

Enhances DNN robustness and accuracy with $L_{2,\infty}$ normalization.

A new method normalizes activations to match batch normalization without batch dependence.

Flexible approach for normal approximations in geometric and topological statistics.

Evidential Softmax preserves multimodality in sparse probability distributions for generative models.

The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.

The paper studies estimating the normalizing constant using queries to a black-box function in RKHS.

In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces in the affine space, endowed with a distinguished "relative normal vector field" …

The study simplifies complex functions on surfaces using a special transformation.

ImpFlows generalize normalizing flows by implicitly defining transformations.

This is a survey on the recent theory on minimizing the normalized volume function attached to any klt singularities.

Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.

Researchers study the normalizing constant of a continuous categorical distribution.

New method for mesh denoising using TGV of normal vector field.

Automatically designs normalization and activation layers together.

This paper analyzes how normalization layers improve neural network training.

Proposes a unified normalization method for multi-domain medical images.

The minimizer of a volume function is unique for klt singularities.

GraN-GAN normalizes gradients for better GAN performance.

We investigate the notion of H-subdifferential and H-normal map of a function on the Heisenberg group, based on its sub-Riemannian structure. In particular, a characterization of the convexity of a function is given via the nonemptiness of the H-subdifferential at every point.

Layer normalization with activations prevents Gram matrix rank collapse at initialization.

Recently, self-normalizing neural networks (SNNs) have been proposed with the intention to avoid batch or weight normalization. The key step in SNNs is to properly scale the exponential linear unit (referred to as SELU) to inherently incorporate normalization based on central limit theory. SELU is a monotonically incre…

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated…

Study eigenvalues of conformal Laplacian under Sire-Xu normalization.

Self Normalizing Flows improve normalizing flows by reducing computational complexity.

We study surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space. On any such surface we introduce special isothermal parameters (canonical parameters) and describe these surfaces in terms of three invariant functions. We prove that any surface with parallel normalized mean curva…

We consider the isometric deformation problem for oriented non simply connected immersed minimal surfaces $f:M \to S^{4}$. We prove that the space of all isometric minimal immersions of $M$ into $S^{4}$ with the same normal curvature function is, within congruences, either finite or a circle. Furthermore, we show that …

Novel power transform unifies various mathematical functions.

Study on curves around a Whitney umbrella focusing on geodesic and normal curvatures.

Method uses normalizing flows to efficiently sample from complex target densities.

New algorithms estimate normalizing constants for log-concave distributions efficiently.

In a binary classification problem the feature vector (predictor) is the input to a scoring function that produces a decision value (score), which is compared to a particular chosen threshold to provide a final class prediction (output). Although the normal assumption of the scoring function is important in many applic…

Normal forms prove dynamical results for magnetic fields on surfaces.

We study the negative gradient flow of the spinorial energy functional (introduced by Ammann, Weiß, and Witt) on 3-dimensional Berger spheres. For a certain class of spinors we show that the Berger spheres collapse to a 2-dimensional sphere. Moreover, for special cases, we prove that the volume-normalized standard 3-sp…

A method for eliciting expert beliefs using preferential questions and normalizing flows.

The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.

In the Engel group with its Carnot group structure we study subsets of locally finite subRiemannian perimeter and possessing constant subRiemannian normal. We prove the rectifiability of such sets: more precisely we show that, in some specific coordinates, they are upper-graphs of entire Lipschitz functions (with respe…