Related papers: Decomposition with respect to outputs for Boolean …
TabPFN is a transformer that achieves state-of-the-art performance on supervised tabular tasks by amortizing Bayesian prediction into a single forward pass. However, there is currently no method for uncertainty decomposition in TabPFN.…
This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability which were introduced in previous papers. The paper presents a new geometric characterization of the…
A well-known issue of Batch Normalization is its significantly reduced effectiveness in the case of small mini-batch sizes. When a mini-batch contains few examples, the statistics upon which the normalization is defined cannot be reliably…
In the past few decades, to reduce the risk of X-ray in computed tomography (CT), low-dose CT image denoising has attracted extensive attention from researchers, which has become an important research issue in the field of medical images.…
This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of…
We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Deep neural networks have achieved a great success in solving many machine learning and computer vision problems. The main contribution of this paper is to develop a deep network based on Tucker tensor decomposition, and analyze its…
In this work we explore the previously proposed approach of direct blind deconvolution and denoising with convolutional neural networks in a situation where the blur kernels are partially constrained. We focus on blurred images from a…
Precise estimation of the probabilistic structure of natural images plays an essential role in image compression. Despite the recent remarkable success of end-to-end optimized image compression, the latent codes are usually assumed to be…
Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…
This paper defines a convertible nonconvex function(CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions and proposes algorithms for solving the…
We present a divide-and-conquer version of the Cylindrical Algebraic Decomposition (CAD) algorithm. The algorithm represents the input as a Boolean combination of subformulas, computes cylindrical algebraic decompositions of solution sets…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
Several well known large scale linear programming decomposition methodologies exist. Benders Decomposition, which covers the case where some small subset of variables link the otherwise separable subproblems. Dantzig-Wolfe decomposition and…
Convolutional Neural Networks (CNN) are the state-of-the-art in the field of visual computing. However, a major problem with CNNs is the large number of floating point operations (FLOPs) required to perform convolutions for large inputs.…
The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in which one often wishes to solve PDEs in regimes far beyond…
The high accuracy of detector simulation is crucial for modern particle physics experiments. However, this accuracy comes with a high computational cost, which will be exacerbated by the large datasets and complex detector upgrades…
The defocus deblurring raised from the finite aperture size and exposure time is an essential problem in the computational photography. It is very challenging because the blur kernel is spatially varying and difficult to estimate by…
In the applications of Boolean networks to modeling biological systems, an important computational problem is the detection of the fixed points of these networks. This is an NP-complete problem in general. There have been various attempts…