相关论文: The Alternating BWT: an algorithmic perspective

Enumerating characteristic substrings (e.g., maximal repeats, minimal unique substrings, and minimal absent words) in a given string has been an important research topic because there are a wide variety of applications in various areas such…

Robotics Reinforcement Learning (RL) often relies on carefully engineered auxiliary rewards to supplement sparse primary learning objectives to compensate for the lack of large-scale, real-world, trial-and-error data. While these auxiliary…

Neural networks are powerful surrogates for numerous forward processes. The inversion of such surrogates is extremely valuable in science and engineering. The most important property of a successful neural inverse method is the performance…

The recent rise of generative artificial intelligence (AI), powered by Transformer networks, has achieved remarkable success in natural language processing, computer vision, and graphics. However, the application of Transformers in…

We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…

The k-spectrum of a string is the set of all distinct substrings of length k occurring in the string. K-spectra have many applications in bioinformatics including pseudoalignment and genome assembly. The Spectral Burrows-Wheeler Transform…

We introduce the Wasserstein Transform (WT), a general unsupervised framework for updating distance structures on given data sets with the purpose of enhancing features and denoising. Our framework represents each data point by a…

Inverted indexes are vital in providing fast key-word-based search. For every term in the document collection, a list of identifiers of documents in which the term appears is stored, along with auxiliary information such as term frequency,…

Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…

Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…

Large Language Models (LLMs) have demonstrated exceptional capabilities across diverse natural language processing benchmarks. However, the escalating scale of model parameters imposes prohibitive memory overheads during training,…

The sampling based motion planning algorithm known as Rapidly-exploring Random Trees (RRT) has gained the attention of many researchers due to their computational efficiency and effectiveness. Recently, a variant of RRT called RRT* has been…

Sentence embedding is an important research topic in natural language processing (NLP) since it can transfer knowledge to downstream tasks. Meanwhile, a contextualized word representation, called BERT, achieves the state-of-the-art…

This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…

The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several…

In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…

More recently, Bidirectional Encoder Representations from Transformers (BERT) was proposed and has achieved impressive success on many natural language processing (NLP) tasks such as question answering and language understanding, due mainly…

Recent advances in cross-lingual word embeddings have primarily relied on mapping-based methods, which project pretrained word embeddings from different languages into a shared space through a linear transformation. However, these…

In Transformer-based neural machine translation (NMT), the positional encoding mechanism helps the self-attention networks to learn the source representation with order dependency, which makes the Transformer-based NMT achieve…

In this paper we present an algorithm to compute the Lyndon array of a string $T$ of length $n$ as a byproduct of the inversion of the Burrows-Wheeler transform of $T$. Our algorithm runs in linear time using only a stack in addition to the…