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The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…
Transformers have emerged as the cornerstone of state-of-the-art natural language processing models, showcasing exceptional performance across a wide range of AI applications. However, the memory demands posed by the self-attention…
This work presents a hardware-efficient and fully parallelizable decoder for quantum LDPC codes that leverages belief propagation (BP) with a speculative post-processing strategy inspired by classical Chase decoding algorithm. By monitoring…
This paper addresses a new variant of the multi-trip single vehicle routing problem where the nodes are related to each other through AND-type precedence constraints. The problem aims at determining a sequence of trips to visit all the…
Dependency pairs (DPs) are one of the most powerful techniques for automated termination analysis of term rewrite systems. Recently, we adapted the DP framework to the probabilistic setting to prove almost-sure termination (AST) via…
We study independent sets in strong powers of circulant graphs using a transfer matrix formulation. The compatibility constraints separate into intra-layer and inter-layer components, yielding a transfer operator that is equivariant under…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…
We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with…
We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of all matchings, extended by a binary entry indicating whether the matching contains two specific edges. These polytopes are associated to the quadratic…
Non-autoregressive models achieve significant decoding speedup in neural machine translation but lack the ability to capture sequential dependency. Directed Acyclic Transformer (DA-Transformer) was recently proposed to model sequential…
In this paper, we introduce a new problem called Tree-Residue Vertex-Breaking (TRVB): given a multigraph $G$ some of whose vertices are marked "breakable," is it possible to convert $G$ into a tree via a sequence of "vertex-breaking"…
Consider an input-output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is exactly the zero…
The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer $k\geq 0$, to delete at most $k$ vertices from a given graph so that what remains is a forest. The variant in which the…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…
Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…