Related papers: Comparing ternary and binary adders and multiplier…

This paper proposes ReBNet, an end-to-end framework for training reconfigurable binary neural networks on software and developing efficient accelerators for execution on FPGA. Binary neural networks offer an intriguing opportunity for…

In this work, we propose extreme compression techniques like binarization, ternarization for Neural Decoders such as TurboAE. These methods reduce memory and computation by a factor of 64 with a performance better than the quantized (with…

Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…

This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n \lg n - 1.4427n + O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to…

This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations…

Edge computing must be capable of executing computationally intensive algorithms, such as Deep Neural Networks (DNNs) while operating within a constrained computational resource budget. Such computations involve Matrix Vector…

Modern pre-trained transformers have rapidly advanced the state-of-the-art in machine learning, but have also grown in parameters and computational complexity, making them increasingly difficult to deploy in resource-constrained…

We define and study the ternary analogues of Clifford algebras. It is proved that the ternary Clifford algebra with $N$ generators is isomorphic to the subalgebra of the elements of grade zero of the ternary Clifford algebra with $N+1$…

This paper shows that, for matrix multiplications and convolutions, it is possible to asymptotically replace each real multiplication with a single squaring operation. Similarly, a single complex multiplication can be replaced with 3…

Network binarization is a promising hardware-aware direction for creating efficient deep models. Despite its memory and computational advantages, reducing the accuracy gap between binary models and their real-valued counterparts remains an…

Tensor computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the…

As quantum computers continue to become more capable, the possibilities of their applications increase. For example, quantum techniques are being integrated with classical neural networks to perform machine learning. In order to be used in…

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…

We propose an approach to extending the concept of a Lie algebra to ternary structures based on $\omega$-symmetry, where $\omega$ is a primitive cube root of unity. We give a definition of a corresponding structure, called a ternary Lie…

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…

Binary neural networks have great resource and computing efficiency, while suffer from long training procedure and non-negligible accuracy drops, when comparing to the full-precision counterparts. In this paper, we propose the composite…

This document provides a brief overview of different metrics and terminology that is used to measure the performance of binary classification systems.

Many scientific computing problems can be reduced to Matrix-Matrix Multiplications (MMM), making the General Matrix Multiply (GEMM) kernels in the Basic Linear Algebra Subroutine (BLAS) of interest to the high-performance computing…

In recent years, deep neural networks have had great success in machine learning and pattern recognition. Architecture size for a neural network contributes significantly to the success of any neural network. In this study, we optimize the…

We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given…