Related papers: A New Class of Searchable and Provably Highly Comp…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…
Context-dependent rewrite rules are used in many areas of natural language and speech processing. Work in computational phonology has demonstrated that, given certain conditions, such rewrite rules can be represented as finite-state…
In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
The combinatorics of reduced words and commutation classes plays an important role in geometric representation theory. A string polytope is a lattice polytope associated to each reduced word of the longest element $w_0$ in the symmetric…
Biclustering is a powerful approach to search for patterns in data, as it can be driven by a function that measures the quality of diverse types of patterns of interest. However, due to its computational complexity, the exploration of the…
This paper proposes a novel approach to word embeddings in Transformer models by utilizing spinors from geometric algebra. Spinors offer a rich mathematical framework capable of capturing complex relationships and transformations in…
We first review how we can store a run-length compressed suffix array (RLCSA) for a text $T$ of length $n$ over an alphabet of size $\sigma$ whose Burrows-Wheeler Transform (BWT) consists of $r$ runs in $O \left( \rule{0ex}{2ex} r \log (n /…
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…
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…
Context-dependent fusion grammars were recently introduced as devices for the generation of hypergraph languages. In this paper, we show that this new type of hypergraph grammars, where the application of fusion rules is restricted by…
A word over an ordered alphabet is said to be clustering if identical letters appear adjacently in its Burrows-Wheeler transform. Such words are strictly related to (discrete) interval exchange transformations. We use an extended version of…
The scheme of the sliding window is known in Information Theory, Computer Science, the problem of predicting and in stastistics. Let a source with unknown statistics generate some word $... x_{-1}x_{0}x_{1}x_{2}...$ in some alphabet $A$.…
We present an unusual algorithm involving classification trees where two trees are grown in opposite directions so that they are matched at their leaves. This approach finds application in a new data mining task we formulate, called…
Traditional supervised bearing fault diagnosis methods rely on massive labelled data, yet annotations may be very time-consuming or infeasible. The fault diagnosis approach that utilizes limited labelled data is becoming increasingly…
Many words have evolved in meaning as a result of cultural and social change. Understanding such changes is crucial for modelling language and cultural evolution. Low-dimensional embedding methods have shown promise in detecting words'…
Neural networks have achieved remarkable success in time series classification, but their reliance on large amounts of labeled data for training limits their applicability in cold-start scenarios. Moreover, they lack interpretability,…
Modern language models define distributions over strings, but downstream tasks often require different output formats. For instance, a model that generates byte-pair strings does not directly produce word-level predictions, and a DNA model…
String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of cross-site scripting (XSS). A popular string analysis technique includes symbolic…
Transformers are arguably the main workhorse in recent Natural Language Processing research. By definition a Transformer is invariant with respect to reordering of the input. However, language is inherently sequential and word order is…