Related papers: Comparing ternary and binary adders and multiplier…

We propose non-binary LDPC codes concatenated with multiplicative repetition codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9,…

Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.

Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier…

Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we…

Bit addition arises virtually everywhere in digital circuits: arithmetic operations, increment/decrement operators, computing addresses and table indices, and so on. Since bit addition is such a basic task in Boolean circuit synthesis, a…

The history of ternary adders goes back to more than six decades ago. Since then, a multitude of ternary full adders (TFAs) have been presented in the literature. This paper conducts a review of TFAs so that one can be familiar with the…

Network binarization exhibits great potential for deployment on resource-constrained devices due to its low computational cost. Despite the critical importance, the security of binarized neural networks (BNNs) is rarely investigated. In…

Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes whose coefficients are restricted to the set $\{-1, 0, 1\}$…

Transformer models have revolutionized AI tasks, but their large size hinders real-world deployment on resource-constrained and latency-critical edge devices. While binarized Transformers offer a promising solution by significantly reducing…

Binary neural networks (BNN) have been studied extensively since they run dramatically faster at lower memory and power consumption than floating-point networks, thanks to the efficiency of bit operations. However, contemporary BNNs whose…

We give an explicit algorithm and source code for computing optimal weights for combining a large number N of alphas. This algorithm does not cost O(N^3) or even O(N^2) operations but is much cheaper, in fact, the number of required…

In Carry Propagate Adders, carry propagation is the critical delay. For the 1-digit adders that they use, the most efficient scheme is to generate two intermediate carries: C$_{out0}$ ($C_{in}$=0) and $C_{out1}$($C_{in}$=1). Then multiplex…

Inference efficiency is the predominant consideration in designing deep learning accelerators. Previous work mainly focuses on skipping zero values to deal with remarkable ineffectual computation, while zero bits in non-zero values, as…

We study general properties of multipliers and weak multipliers of algebras. We apply the results to determine the (weak) multipliers of associative algebras and zeropotent algebras of dimension 3 over an algebraically closed field.

Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we…

Deep neural networks have demonstrated their superior performance in almost every Natural Language Processing task, however, their increasing complexity raises concerns. In particular, these networks require high expenses on computational…

Binary Neural Networks (BNNs) use 1-bit weights and activations to efficiently execute deep convolutional neural networks on edge devices. Nevertheless, the binarization of the first layer is conventionally excluded, as it leads to a large…

Algebraic matrix multiplication algorithms are designed by bounding the rank of matrix multiplication tensors, and then using a recursive method. However, designing algorithms in this way quickly leads to large constant factors: if one…

Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success…

This paper presents a design for test (DFT)architecture for fast and scalable testing of array multipliers (MULTs). Regardless of the MULT size, our proposed testable architecture, without major changes in the original architecture,…