Related papers: A Survey on the Local Divisor Technique
A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence…
Local binary descriptors are attracting increasingly attention due to their great advantages in computational speed, which are able to achieve real-time performance in numerous image/vision applications. Various methods have been proposed…
We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Recent advances in explainable machine learning have highlighted the potential of sparse autoencoders in uncovering mono-semantic features in densely encoded embeddings. While most research has focused on Large Language Model (LLM)…
When dealing with continuous numeric features, we usually adopt feature discretization. In this work, to find the best way to conduct feature discretization, we present some theoretical analysis, in which we focus on analyzing correctness…
We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…
The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields…
The Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. Nevertheless, the intrinsic geometric constraint forces it to focus on the regions with close spatial distance,…
In this paper, we introduce a new family of codes relevent for rank and sum-rank metrics. These codes are based on an effective Chinese remainders theorem for linearized polynomials over finite fields. We propose a decoding algorithm for…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
We show that, possibly after a compactification of spacetime, constant functions are local maximizers of the Tomas-Stein adjoint Fourier restriction inequality for the cone and paraboloid in every dimension, and for the sphere in dimension…
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage…
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…
Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the…
This paper settles the computational complexity of model checking of several extensions of the monadic second order (MSO) logic on two classes of graphs: graphs of bounded treewidth and graphs of bounded neighborhood diversity. A classical…
We propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present numerical examples. We employ the recurrence from the Gr\"obner…
To ensure that text generated by large language models (LLMs) is in an expected format, constrained decoding proposes to enforce strict formal language constraints during generation. However, as we show in this work, not only do such…
This work is a further study on the Generalized Constraint Neural Network (GCNN) model [1], [2]. Two challenges are encountered in the study, that is, to embed any type of prior information and to select its imposing schemes. The work…
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a…