arXiv research

In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear unit (PReLU) and a new randomized leaky rectified linear units (RReLU). We evalu…

Study evaluates Tree-Ring Watermarking in rectified flow-based models, revealing detection and separability limitations.

CRITS improves time series classification with interpretable local explanations.

Paper proposes efficient image inversion and editing using rectified stochastic differential equations.

This paper improves domain adaptation methods using graph embedding.

Study rectifying curves in 3D multiplicative Euclidean space.

Investigates Darboux rectifying curves on smooth surfaces.

A new acquisition function RMES improves Bayesian optimization performance.

A space curve in a Euclidean 3-space $\mathbb E^3$ is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [Amer. Math. Monthly {\bf 110} (2003), no. 2, 147-152]. In this present article, we introduce and study the n…

Study characterizes $k$-rectifiable sets in homogeneous groups.

Recalls and refines the concept of algebraically rectifiable curves.

Harmonic maps to Euclidean buildings have rectifiable singular strata.

We prove (without using Federer's structure theorem) that a finite-mass flat chain over any coefficient group is rectifiable if and only if almost all of its 0-dimensional slices are rectifiable. This implies that every flat chain of finite mass and finite size is rectifiable. It also leads to a simple necessary and su…

New methods for solving hydrodynamic-type equations using quasi-rectifiable Lie algebras.

Rectifies singular set of harmonic maps into complex.

The paper generalizes rectifying and normal curves in Lorentzian n-space.

Neural networks can approximate rectifiable measures with small error.

We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable, showing the equivalence of this notion of rectifiability with that of Franchi, Serra Cassano and Serapioni for such surfaces.

The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and n_2 of the curve. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifyin…

In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …

In Heisenberg groups, rectifiability is studied for subsets using $C^{1,α}$-regular surfaces.

The paper characterizes rectifying curves on smooth surfaces using isometries and Darboux frames.

The paper proves smoothness of stationary varifolds.

In this paper, we introduce a new class of curves αcalled a f-rectifying curves, which its f-position vector defined by α_{f}(s)=\int f(s)T(s)ds always lie in the rectifying plane of α, where f is an integrable function and T is the speed curve of α. In particular case, when the function f=0 or constant, the class of f…

Rectified flows achieve optimal sample complexity for generating data.

The paper explores rectified flows and their relation to optimal transport.

We extend rectified flow to infinite-dimensional Hilbert space.

AReLU uses attention-based rectification to improve neural network performance.

The rectified flow method is analyzed for its statistical properties.

Improves AI-prior reliability for Bayesian inference.

The paper studies harmonic map flows and proves rectifiability of singular sets.

Study rectifying submanifolds with anti-torqued axis in Riemannian manifolds.

In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We characterize rectifying curves in the $n$-dimensional Euclidean space in different ways…

Paper proposes a new activation function to reduce overfitting and large weight update issues.

Study local minimizers of Ginzburg-Landau functionals in high dimensions, showing energy measures converge to rectifiable measures.

This paper studies rectifiability in Carnot groups and proves geometric area formulas.

Study on harmonic maps in special geometric spaces.

In this paper, we define a rectifying spacelike curve in the Minkowski space-time $E_1^4$ as a curve whose position vector always lies in orthogonal complement $N^{\bot}$ of its principal normal vector field $N$. In particular, we study the rectifying spacelike curves in $E_1^4$ and characterize such curves in terms of…

The paper generalizes a theorem about rectifiability of sets.

Let $(M,g,f)$ be a 3-dimensional complete steady gradient Ricci soliton. Assume that $M$ is rectifiable, that is, the potential function can be written as $f=f(r)$, where $r$ is a distance function. Then, we prove that $M$ is isometric to (1) a quotient of $\mathbb{R}^3$, or (2) the Bryant soliton. In particular, we sh…

FlowChef steers RFMs to efficiently guide image generation tasks.

Rectangular peg problem solved for many curves.

We show that any $d$-Ahlfors regular subset of $\mathbb{R}^{n}$ supporting a weak $(1,d)$-Poincaré inequality with respect to surface measure is uniformly rectifiable.

We prove that monotonicity of density and energy inequality imply the rectifiability of the singular sets for Yang-Mills flow.

We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is the Lipschitz image of a positive measure subset of N. First, we discuss the implications of N-rectifiability, where N is a Carnot group (n…

Rectifies flat singular points for area-minimizing currents.

We defined normal and rectifying curves in Pseudo-Galilean Space G_3^1. Also we obtained some characterizations of this curves in G_3^1.

Rectifies flat singular points of area-minimizing currents with singularity degree > 1.