Related papers: Impossibility Results for Grammar-Compressed Linea…
Large Language Models are growing in size, and we expect them to continue to do so, as larger models train quicker. However, this increase in size will severely impact inference costs. Therefore model compression is important, to retain the…
We consider the problem of decompressing the Lempel--Ziv 77 representation of a string $S$ of length $n$ using a working space as close as possible to the size $z$ of the input. The folklore solution for the problem runs in $O(n)$ time but…
The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…
Modern data compression methods are slowly reaching their limits after 80 years of research, millions of papers, and wide range of applications. Yet, the extravagant 6G communication speed requirement raises a major open question for…
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we…
We observe that any $T(n)$ time algorithm (quantum or classical) for several central linear algebraic problems, such as computing $\det(A)$, $tr(A^3)$, or $tr(A^{-1})$ for an $n \times n$ integer matrix $A$, yields a $O(T(n)) + \tilde…
A Longest Common Extension (LCE) query on a text $T$ of length $N$ asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding $\mathcal{G}$ of size $w = O(\min(z \log N…
As state of the art neural networks (NNs) continue to grow in size, their resource-efficient implementation becomes ever more important. In this paper, we introduce a compression scheme that reduces the number of computations required for…
In the field of biological research, it is essential to comprehend the characteristics and functions of molecular sequences. The classification of molecular sequences has seen widespread use of neural network-based techniques. Despite their…
Grammar compression is, next to Lempel-Ziv (LZ77) and run-length Burrows-Wheeler transform (RLBWT), one of the most flexible approaches to representing and processing highly compressible strings. The main idea is to represent a text as a…
It was recently proved that any Straight-Line Program (SLP) generating a given string can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We generalize this proof to a general class of grammars we…
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…
In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear measurements…
The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…
Let a text $T[1..n]$ be the only string generated by a context-free grammar with $g$ (terminal and nonterminal) symbols, and of size $G$ (measured as the sum of the lengths of the right-hand sides of the rules). Such a grammar, called a…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been…