Related papers: Adaptive Base Representation Theorem: An Alternati…
In this paper we use ternary representation of numbers for compressing text data. We use a binary map for ternary digits and introduce a way to use the binary 11-pair, which has never been use for coding data before, and we futher use…
This article deals with the adaptive and approximative computation of the Lam\'e equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM).…
The symbolic representation of a number should be considered as a data structure, and the choice of data structure depends on the arithmetic operations that are to be performed. Numbers are almost universally represented using position…
The dynamic ensemble selection of classifiers is an effective approach for processing label-imbalanced data classifications. However, such a technique is prone to overfitting, owing to the lack of regularization methods and the dependence…
While transformer models have been highly successful, they are computationally inefficient. We observe that for each layer, the full width of the layer may be needed only for a small subset of tokens inside a batch and that the "effective"…
Minimum Bayes-Risk (MBR) decoding is shown to be a powerful alternative to beam search decoding for a wide range of text generation tasks. However, MBR requires a huge amount of time for inference to compute the MBR objective, which makes…
A new system of hexadecimal and base-256 numerals is proposed whose digit shapes are based on binary numerals. The proposed numerals are implemented in open source fonts and integrated into popular editors (Notepad++ and Eclipse) to prove…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases,…
Case-based Reasoning (CBR) on high-dimensional and heterogeneous data is a trending yet challenging and computationally expensive task in the real world. A promising approach is to obtain low-dimensional hash codes representing cases and…
The knowledge discovery algorithms have become ineffective at the abundance of data and the need for fast algorithms or optimizing methods is required. To address this limitation, the objective of this work is to adapt a new method for…
Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.
Binarized neural networks, or BNNs, show great promise in edge-side applications with resource limited hardware, but raise the concerns of reduced accuracy. Motivated by the complex neural networks, in this paper we introduce complex…
We propose a novel approach to optimizing a byte-level representation for end-to-end automatic speech recognition (ASR). Byte-level representation is often used by large scale multilingual ASR systems when the character set of the supported…
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…
In this paper, we present ASPEN, an answer set programming (ASP) implementation of a recently proposed declarative framework for collective entity resolution (ER). While an ASP encoding had been previously suggested, several practical…
In this paper, we present a novel algorithm to address the Network Alignment problem. It is inspired from a previous message passing framework of Bayati et al. [2] and includes several modifications designed to significantly speed up the…
This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming…
Any system that is used for naming or representing numbers is a number system, also known as numeral system. The modern civilization is familiar with decimal number system using ten digits. However digital devices and computers use binary…