Related papers: Pseudocodewords from Bethe Permanents
We define the AWGNC, BSC, and max-fractional pseudocodeword redundancy of a code as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance. We show that…
This papers presents a detailed analysis of pseudocodewords of Tanner graphs. Pseudocodewords arising on the iterative decoder's computation tree are distinguished from pseudocodewords arising on finite degree lifts. Lower bounds on the…
We present a method for exploring regions around individual points in a contextualized vector space (particularly, BERT space), as a way to investigate how these regions correspond to word senses. By inducing a contextualized "pseudoword"…
It is shown that, for the block matrices belonging to $M(nd,\mathbb{C})$ with commuting and normal block entries of dimension $d$, the separability of such a block matrices is equivalent to its semi-positive definity. The separability…
While important properties of word vector representations have been studied extensively, far less is known about the properties of sentence vector representations. Word vectors are often evaluated by assessing to what degree they exhibit…
We prove that the permanent of nonnegative matrices can be deterministically approximated within a factor of $\sqrt{2}^n$ in polynomial time, improving upon the previous deterministic approximations. We show this by proving that the Bethe…
This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.
Pseudocodewords of q-ary LDPC codes are examined and the weight of a pseudocodeword on the q-ary symmetric channel is defined. The weight definition of a pseudocodeword on the AWGN channel is also extended to two-dimensional q-ary…
Permanent Data Encoding (PDE) is a visual language framework designed for long-term, human-readable, and electrically independent knowledge preservation. By encoding semantic content into compact 2-3 character alphanumeric codes, paired…
The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming…
This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role can play the consideration of an…
Gender bias is highly impacting natural language processing applications. Word embeddings have clearly been proven both to keep and amplify gender biases that are present in current data sources. Recently, contextualized word embeddings…
Positional Encodings (PEs) are used to inject word-order information into transformer-based language models. While they can significantly enhance the quality of sentence representations, their specific contribution to language models is not…
Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…
A code is called solid if, roughly speaking, any correctly-transmitted codeword in an arbitrarily corrupted string of codewords can still be decoded correctly and unambiguously. So-called variable-length solid codes, in which codewords may…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
The positive effect of adding subword information to word embeddings has been demonstrated for predictive models. In this paper we investigate whether similar benefits can also be derived from incorporating subwords into counting models. We…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of…