arXiv research

Finite approximations help reconstruct countable metric and ultrametric spaces.

The paper reconstructs Lorentzian spacetimes from causal sets.

Lower bounds on query complexity for reconstructing private learner's training data.

New findings on how conformal rescalings affect spacetime metrics.

A solution of Hilberts fourth problem lead to integral equation of the type generalized cosine transform. The present paper considers the solution that integral equation by integral geometry methods and propose an inversion formula for reconstruction of Crofton measures from projective smooth Finsler metrics in R3.

The paper discusses algorithms for reconstructing curves with given Euclidean or affine curvatures.

Survey of deep learning methods for fMRI natural image reconstruction.

We discuss whether it is possible to reconstruct a metric by its unparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are umparameterized geodesics of a certain affine conne…

DCAE learns compact latent representations for one-class novelty detection.

In this paper, we study the reconstruction problem of the holomorphic tangent bundle $\mathbb{T}_{\mathbb{P}^2}$ of the complex projective plane $\mathbb{P}^2$. We introduce the notion of tropical Lagrangian multi-section and cook up one by tropicalizing the Chern connection associated the Fubini-Study metric. Then we …

This paper aims to address two issues existing in the current speech enhancement methods: 1) the difficulty of phase estimations; 2) a single objective function cannot consider multiple metrics simultaneously. To solve the first problem, we propose a novel convolutional neural network (CNN) model for complex spectrogra…

Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this end, we study analytic paths of metrics that induce isospectral Laplace-Beltram…

Researchers reconstruct simple Riemannian manifolds from boundary wave arrival times.

Improves point-cloud reconstruction by optimizing projections with self-attention.

Using a metric related to the returns correlation, a method is proposed to reconstruct an economic space from the market data. A reduced subspace, associated to the systematic structure of the market, is identified and its dimension related to the number of terms in factor models. Example were worked out involving sets…

Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that…

The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define inverse persistence as a new kind of persistence process.

End-to-end deep metric learning tackles multi-label image classification.

Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is stated which implies uniqueness and stability for this problem. If the conformal c…

New benchmark for EEG-eye movement reconstruction from functional data.

This paper proposes a new evaluation metric and boosting method for weight separability in neural network design. In contrast to general visual recognition methods designed to encourage both intra-class compactness and inter-class separability of latent features, we focus on estimating linear independence of column vec…

Study complex-valued VAEs for radar OOD detection.

Study the tradeoff between signal distortion and human perception over finite channels.

A ML-based method reconstructs 3D organ doses from 2D radiographs for pediatric abdominal radiotherapy.

Unified SVD compression fails in practical tasks, highlighting the importance of per layer activation reconstruction.

We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold reconstruction where a smooth $n$-dimensional submanifold $S\subset {\mathbb R}^m$, $m>n$ needs to be constructed to approximate a point clo…

Topolow embeds dissimilarity data into Euclidean space robustly against non-metricity and sparsity.

It is well-known that a compact Riemannian spin manifold can be reconstructed from its canonical spectral triple which consists of the algebra of smooth functions, the Hilbert space of square integrable spinors and the Dirac operator. It seems to be a folklore fact that the metric can be reconstructed up to conformal e…

Reconstructs Riemannian geometry from diffusion properties.

iTimER learns from reconstruction errors to represent irregularly sampled time series.

Probabilistic Autoencoder learns latent space weights' distribution.

ENSURE framework trains deep image recon algorithms without clean data.

We prove that a potential $q$ can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator $-Δ_g + q$ in a fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that an admissible metric $g$ in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for $Δ_…

Study improves confidence measures in medical imaging pipelines by addressing bias.

RADAR uses diffusion models to detect anomalies without reconstruction, improving accuracy and efficiency.

This paper reconstructs complex graph signals using kernel methods on manifolds.

Given a bounded domain $M$ in $\mathbb{R}^n$ with a conformally Euclidean metric $g=ρ\,dx^2$, in this paper we consider the inverse problem of recovering a semigeodesic neighborhood of a domain $Γ\subset \partial M$ and the conformal factor $ρ$ in the neighborhood from the travel time data (defined below) and the Carte…

This article explores the concepts of ocean wave multivariate multistep forecasting, reconstruction and feature selection. We introduce recurrent neural network frameworks, integrated with Bayesian hyperparameter optimization and Elastic Net methods. We consider both short- and long-term forecasts and reconstruction, f…

From the perspective of network analysis, the ubiquitous networks are comprised of regular and irregular components, which makes uncovering the complexity of network structures to be a fundamental challenge. Exploring the regular information and identifying the roles of microscopic elements in network data can help us …

We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the ca…

Recent literature on unsupervised learning focused on designing structural priors with the aim of learning meaningful features, but without considering the description length of the representations. In this thesis, first we introduce the $\varphi$ metric that evaluates unsupervised models based on their reconstruction …

This paper uses β-VAE for unsupervised anomaly detection in NSL-KDD.

Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography deals with the inverse problem of recreating an image from a number of projections.…

The paper introduces a method for dimension reduction using sub-Riemannian geometry.

Develops a new robustness criterion for VAEs and provides theoretical guarantees.

The paper analyzes discrete approximations to minimize curve length in Euclidean space.

We propose a permutation-invariant loss function designed for the neural networks reconstructing a set of elements without considering the order within its vector representation. Unlike popular approaches for encoding and decoding a set, our work does not rely on a carefully engineered network topology nor by any addit…

This paper analyzes how training data can be leaked from gradients in neural networks and proposes a metric for measuring model security.