Related papers: The 2-adic complexity of a class of binary sequenc…
Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top…
It is well known that, given \(b\ge 0\), finding an $(a,b)$-trapping set with the minimum \(a\) in a binary linear code is NP-hard. In this paper, we demonstrate that this problem can be solved with linear complexity with respect to the…
Traditional global stability measure for sequences is hard to determine because of large search space. We propose the $k$-error linear complexity with a zone restriction for measuring the local stability of sequences. Accordingly, we can…
While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open. The appropriate complexity parameter…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
In this work we study metric properties of the well-known family of binary Reed-Muller codes. Let $A$ be an arbitrary subset of the Boolean cube, and $\widehat{A}$ be the metric complement of $A$ -- the set of all vectors of the Boolean…
Effective resistances are ubiquitous in graph algorithms and network analysis. In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair $s$ and $t$. We consider the classical adjacency…
Monadic second order logic can be used to express many classical notions of sets of vertices of a graph as for instance: dominating sets, induced matchings, perfect codes, independent sets or irredundant sets. Bounds on the number of sets…
We analyse the logical complexity and absoluteness of natural statements about Ulam sequences, with particular emphasis on the rigidity phenomena introduced by Hinman, Kuca, Schlesinger and Sheydvasser for the family $U(1,n)$. For each pair…
This article investigates the convergence properties of a relative-type inexact preconditioned proximal augmented Lagrangian method (rip$^2$ALM) for convex nonlinear programming, a fundamental class of optimization problems with broad…
Despite the enormous success of machine learning models in various applications, most of these models lack resilience to (even small) perturbations in their input data. Hence, new methods to robustify machine learning models seem very…
Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro sequence, have some desirable features of pseudorandomness such as a large linear complexity and a small well-distribution measure. However, they also have some…
In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG…
Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…
Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation…
We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to…
Let $n_1$ and $n_2$ be two distinct primes with $\mathrm{gcd}(n_1-1,n_2-1)=4$. In this paper, we compute the autocorrelation values of generalized cyclotomic sequence of order $4$. Our results show that this sequence can have very good…
We consider the problem of binary string reconstruction from the multiset of its substring compositions, i.e., referred to as the substring composition multiset, first introduced and studied by Acharya et al. We introduce a new algorithm…
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…
Balliu et al. (DISC 2020) classified the hardness of solving binary labeling problems with distributed graph algorithms; in these problems the task is to select a subset of edges in a $2$-colored tree in which white nodes of degree $d$ and…