Related papers: A Bijective String Sorting Transform
Let $T [1..n]$ be a text over an alphabet of size $\sigma \in \mathrm{polylog} (n)$, let $r^*$ be the sum of the numbers of runs in the Burrows-Wheeler Transforms of $T$ and its reverse, and let $z$ be the number of phrases in the LZ77…
We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…
Increasing the input length has been a driver of progress in language modeling with transformers. We identify conditions where shorter inputs are not harmful, and achieve perplexity and efficiency improvements through two new methods that…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
The traditional methods for data compression are typically based on the symbol-level statistics, with the information source modeled as a long sequence of i.i.d. random variables or a stochastic process, thus establishing the fundamental…
Popular sequence alignment tools such as BWA convert a reference genome to an indexing data structure based on the Burrows-Wheeler Transform (BWT), from which matches to individual query sequences can be rapidly determined. However the…
The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models,…
This paper presents a tree-to-tree transduction method for sentence compression. Our model is based on synchronous tree substitution grammar, a formalism that allows local distortion of the tree topology and can thus naturally capture…
An indexed sequence of strings is a data structure for storing a string sequence that supports random access, searching, range counting and analytics operations, both for exact matches and prefix search. String sequences lie at the core of…
We introduce a protocol called ENCORE which simultaneously compresses and encrypts data in a one-pass process that can be implemented efficiently and possesses a number of desirable features as a streaming encoder/decoder. Motivated by the…
Invariance to spatial transformations such as translations and rotations is a desirable property and a basic design principle for classification neural networks. However, the commonly used convolutional neural networks (CNNs) are actually…
We propose a new positional encoding method for a neural network architecture called the Transformer. Unlike the standard sinusoidal positional encoding, our approach is based on solid mathematical grounds and has a guarantee of not losing…
Suffix trees are one of the most versatile data structures in stringology, with many applications in bioinformatics. Their main drawback is their size, which can be tens of times larger than the input sequence. Much effort has been put into…
Most approaches to long-context processing increase the complexity of the transformer's internal architecture by integrating mechanisms such as recurrence or auxiliary memory modules. In this work, we introduce an alternative approach that…
The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…
Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In this paper we consider the basic variant where the pattern is…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can…
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…
The context transformation and generalized context transformation methods, we introduced recently, were able to reduce zero order entropy by exchanging digrams, and as a consequence, they were removing mutual information between consecutive…