相关论文: Transseries: Ratios, Grids, and Witnesses

Additional remarks and questions for transseries. In particular: properties of composition for transseries; the recursive nature of the construction of R[[[ x ]]]; modes of convergence for transseries. There are, at this stage, questions…

From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than that--they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries…

Transformer architecture has widespread applications, particularly in Natural Language Processing and computer vision. Recently Transformers have been employed in various aspects of time-series analysis. This tutorial provides an overview…

We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper.

The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and…

In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective witness sets which encode the multidegree…

In this introductory chapter, we lay the groundwork for the rest of the book by providing a more detailed picture of the expected purpose, shape, and architecture of future grid systems. We structure the chapter in terms of six questions…

Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to…

In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…

We introduce the notion of watching systems in graphs, which is a generalization of that of identifying codes. We give some basic properties of watching systems, an upper bound on the minimum size of a watching system, and results on the…

Transformers have recently been utilized to perform object detection and tracking in the context of autonomous driving. One unique characteristic of these models is that attention weights are computed in each forward pass, giving insights…

Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…

This paper is part of a study whose goal is to show the effciency of using Bayes networks to carry out model based vision calculations. [Binford et al. 1987] Recognition proceeds by drawing up a network model from the object's geometric and…

A new family of positive, trace-preserving maps is introduced. It is defined using the mutually unbiased measurements, which generalize the notion of mutual unbiasedness of orthonormal bases. This family allows one to define entanglement…

In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…

Time series forecasting is an important task in many fields ranging from supply chain management to weather forecasting. Recently, Transformer neural network architectures have shown promising results in forecasting on common time series…

We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a simple path in a rectangular grid graph from a start…

Counterfactual explanations, and their associated algorithmic recourse, are typically leveraged to understand, explain, and potentially alter a prediction coming from a black-box classifier. In this paper, we propose to extend the use of…

Recurrent Neural Networks were, until recently, one of the best ways to capture the timely dependencies in sequences. However, with the introduction of the Transformer, it has been proven that an architecture with only attention-mechanisms…

All tables can be represented as grids. Based on this observation, we propose GridFormer, a novel approach for interpreting unconstrained table structures by predicting the vertex and edge of a grid. First, we propose a flexible table…