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In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of…
Byte Pair Encoding (BPE) serves as a foundation method for text tokenization in the Natural Language Processing (NLP) field. Despite its wide adoption, the original BPE algorithm harbors an inherent flaw: it inadvertently introduces a…
We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
Ensemble methods in machine learning aim to improve prediction accuracy by combining multiple models. This is achieved by ensuring diversity among predictors to capture different data aspects. Homogeneous ensembles use identical models,…
Language models can largely benefit from efficient tokenization. However, they still mostly utilize the classical BPE algorithm, a simple and reliable method. This has been shown to cause such issues as under-trained tokens and sub-optimal…
There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally there are…
In multimedia, text or bioinformatics databases, applications query sequences of n consecutive symbols called n-grams. Estimating the number of distinct n-grams is a view-size estimation problem. While view sizes can be estimated by…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
The synchronisation of Tree Parity Machines (TPMs), has proven to provide a valuable alternative concept for secure symmetric key exchange. Yet, from a cryptographer's point of view, authentication is at least as important as a secure…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
This paper describes a method for estimating conditional probability distributions over the parses of ``unification-based'' grammars which can utilize auxiliary distributions that are estimated by other means. We show how this can be used…
In the paper, we investigate two problems on strings. The first one is the String matching problem, and the second one is the String comparing problem. We provide a quantum algorithm for the String matching problem that uses exponentially…
Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…
An algorithm is presented which implements a probabilistic attack on the key-exchange protocol based on permutation parity machines. Instead of imitating the synchronization of the communicating partners, the strategy consists of a Monte…
Discrimination of unitary operations is a fundamental quantum information processing task. Assisted with linear optical elements, we experimentally demonstrate perfect discrimination between single-bit unitary operations using two…
We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms {\it super greedy algorithms}. The…
The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a research carrier for anti-quantum cryptographic algorithms. This…
The ability to cheaply train text classifiers is critical to their use in information retrieval, content analysis, natural language processing, and other tasks involving data which is partly or fully textual. An algorithm for sequential…
We consider a somehow peculiar Token/Bucket problem which at first sight looks confusing and difficult to solve. The winning approach to solve the problem consists in going back to the simple and traditional methods to solve computer…