相关论文: Global Minimum Depth In Edwards-Anderson Model

The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…

Deep Operator Networks are an increasingly popular paradigm for solving regression in infinite dimensions and hence solve families of PDEs in one shot. In this work, we aim to establish a first-of-its-kind data-dependent lowerbound on the…

We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…

An additive autoencoder for dimension reduction, which is composed of a serially performed bias estimation, linear trend estimation, and nonlinear residual estimation, is proposed and analyzed. Computational experiments confirm that an…

In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field…

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

Although EDM aims to unify the design space of diffusion models, its reliance on fixed Gaussian noise prevents it from explaining emerging flow-based methods that diffuse arbitrary noise. Moreover, our study reveals that EDM's forcible…

We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbor interactions, a spin-1/2 model with nearest-neighbor and…

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…

The sparse Johnson-Lindenstrauss transform is one of the central techniques in dimensionality reduction. It supports embedding a set of $n$ points in $\mathbb{R}^d$ into $m=O(\varepsilon^{-2} \lg n)$ dimensions while preserving all pairwise…

Estimation of the parameters of a 2-dimensional sinusoidal model is a fundamental problem in digital signal processing and time series analysis. In this paper, we propose a robust least absolute deviation (LAD) estimators for parameter…

The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are…

An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful. This paper pursues theoretical understanding for an…

We prove that for an $L$-layer fully-connected linear neural network, if the width of every hidden layer is $\tilde\Omega (L \cdot r \cdot d_{\mathrm{out}} \cdot \kappa^3 )$, where $r$ and $\kappa$ are the rank and the condition number of…

The behavior of the Kozachenko - Leonenko estimates for the (differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L^2-consistency of the estimates…

Learning-based monocular depth estimation leverages geometric priors present in the training data to enable metric depth perception from a single image, a traditionally ill-posed problem. However, these priors are often specific to a…

This paper proposes improvements over earlier work by Nazareth and Blei (2022) for estimating the depth of Bayesian neural networks. Here, we propose a discrete truncated normal distribution over the network depth to independently learn its…

Variational Autoencoders (VAEs) have gained significant popularity among researchers as a powerful tool for understanding unknown distributions based on limited samples. This popularity stems partly from their impressive performance and…

We prove the existence of global minimizers of Allen-Cahn equation in dimensions $8$ and above. More precisely, given any strictly area-minimizing Lawson's cones, there are global minimizers whose nodal sets are asymptotic to the cones. As…