相关论文: Irregular Input Data in Convergence Acceleration a…

Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…

Fully symmetric learning rules for principal component analysis can be derived from a novel objective function suggested in our previous work. We observed that these learning rules suffer from slow convergence for covariance matrices where…

This paper presents convergence acceleration, a method for computing efficiently the limit of numerical sequences as a typical application of streams and higher-order functions.

We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…

We show that for two non-trivial lambda phi ^4 problems (the anharmonic oscillator and the Landau-Ginzburg hierarchical model), improved perturbative series can be obtained by cutting off the large field contributions. The modified series…

Medical time series are often irregular and face significant missingness, posing challenges for data analysis and clinical decision-making. Existing methods typically adopt a single modeling perspective, either treating series data as…

Zeckendorf's theorem establishes a unique representation for positive integers as sums of non-consecutive Fibonacci numbers. This result has been generalized to Positive Linear Recurrence Sequences (PLRS), where key statistical properties,…

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…

We introduce a set of image transformations that can be used as corruptions to evaluate the robustness of models as well as data augmentation mechanisms for training neural networks. The primary distinction of the proposed transformations…

The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further,…

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with…

Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast $\delta_h$ with the…

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…

Irregular multivariate time series with missing values present significant challenges for predictive modeling in domains such as healthcare. While deep learning approaches often focus on temporal interpolation or complex architectures to…

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…

We study the density of the supremum of a strictly stable L\'evy process. As was proved recently in F. Hubalek and A. Kuznetsov "A convergent series representation for the density of the supremum of a stable process" (Elect. Comm. in…