arXiv research

VES-Gamma adapts EI using information-theoretic principles.

We consider a mean curvature flow in a cone, that is, a hypersurface in a cone which moves toward the opening with normal velocity equaling to the mean curvature, and the contact angle between the hypersurface and the cone boundary being $\varepsilon$-periodic in its position. First, by constructing a family of self-si…

F.: Good morning Hermann, I would like to talk with you about infinitesimals. G.: Tell me Pierre. F.: I'm fed up of all these slanders about my attitude to be non rigorous, so I've started to study nonstandard analysis (NSA) and synthetic differential geometry (SDG). G.: Yes, I've read something ... F.: Ok, no problem …

This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface $M$ which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by $Ω(M)$. Firstly, we've obtained the topological classificat…

We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesia…

In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the loca…

Unified framework connects EI and information-theoretic acquisition functions.

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from readers, I've decided to make a presentable half-finished version available here.…

These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic for advanced bachelor students or early master students with little to no previ…

A new method improves estimation of COVID-19 vaccine effectiveness.

This study compares Bitcoin and Litecoin using cryptocurrency metrics and trading strategies.

Study uses neural processes to predict and classify crack patterns in moving disks.

New metrics with constant Q-curvature created by gluing.

The paper analyzes the score field of diffusion models using Burgers dynamics.

We created financial benchmarks for distribution shifts in crude oil prices and volatility.

We consider the following singularly perturbed Neumann problem \begin{eqnarray*} \ve^2 Δu -u +u^p = 0 \, \quad u>0 \quad {\mbox {in}} \quad Ω, \quad {\partial u \over \partial ν}=0 \quad {\mbox {on}} \quad \partial Ω, \end{eqnarray*} where $p>2$ and $Ω$ is a smooth and bounded domain in $\R^2$. We construct a new class…

We derive a new, exact and transparent expansion for option smiles, which lends itself both to analytical approximation and, perhaps more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is par…

A new diffusion sampling method combines Krylov subspace and diffusion models for faster and more efficient inverse problems.

Nontrivial boundary Dehn twist found on K3#K3 manifold.

Every year, thousands of people receive consumer product related injuries. Research indicates that online customer reviews can be processed to autonomously identify product safety issues. Early identification of safety issues can lead to earlier recalls, and thus fewer injuries and deaths. A dataset of product reviews …

Invariants for 3D manifolds with boundaries using crossed modules.

SAIL improves graph node representation learning by distilling knowledge between graphs.

In distributed ML applications, shared parameters are usually replicated among computing nodes to minimize network overhead. Therefore, proper consistency model must be carefully chosen to ensure algorithm's correctness and provide high throughput. Existing consistency models used in general-purpose databases and moder…

iEFM trains CNF models from unnormalized densities efficiently.

Generative models (GMs) such as Generative Adversary Network (GAN) and Variational Auto-Encoder (VAE) have thrived these years and achieved high quality results in generating new samples. Especially in Computer Vision, GMs have been used in image inpainting, denoising and completion, which can be treated as the inferen…

ICYM2I corrects missingness bias in multimodal learning.

Surveying strategies for making machine learning models robust against adversarial attacks.

We consider a notion of conservation for the heat semigroup associated to a generalized Dirac Laplacian acting on sections of a vector bundle over a noncompact manifold with a (possibly noncompact) boundary under mixed boundary conditions. Assuming that the geometry of the underlying manifold is controlled in a suitabl…

A graph (digraph) $G=(V,E)$ with a set $T\subseteq V$ of terminals is called inner Eulerian if each nonterminal node $v$ has even degree (resp. the numbers of edges entering and leaving $v$ are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint $T$-paths in an inner Eulerian graph $G…

This paper generalizes Michell Truss to higher dimensions using geometric measure theory.

Systematizes blockchain decentralization taxonomy and metrics.

Study of Quillen metric on Riemann surfaces with cusps and compactification.

Tasks such as search and recommendation have become increas- ingly important for E-commerce to deal with the information over- load problem. To meet the diverse needs of di erent users, person- alization plays an important role. In many large portals such as Taobao and Amazon, there are a bunch of di erent types of sea…

Study extends geodesic ray transform results to orientable surfaces.

We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …

Introduces pseudo-codecomposition of transformation groups.

This paper investigates efficient Transformers and finds they scale with problem size.

The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the know…

Transformation Equivariant Representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of {\em translation} equivariance underlying the success of Convolutional Neural Networks (CNNs). For this purpose, we present both deterministic AutoEncoding…

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data-adaptive sparsifying transforms have demonstrated excellent performance i…

Transforms classical connections using pushforwards and gauge transformations.

Transformers interpret as probabilistic mixtures, offering new insights.

Study normal operators of double fibration transforms with conjugate points.

Transformer-MGK replaces redundant heads with Gaussian key mixtures, improving efficiency and performance.

B-cos transformers explain Vision Transformers' decisions.

Novel power transform unifies various mathematical functions.

Algorithm finds optimal affine transformation to minimize overall distortion.

XR-Transformer accelerates XMC by recursively fine-tuning on multi-resolution objectives.