Related papers: Comparing ternary and binary adders and multiplier…
The purpose of this paper is to investigate ternary multiplications constructed from a binary multiplication, linear twisting maps and a trace function. We provide a construction of ternary Hom-Nambu and Hom-Nambu-Lie algebras starting from…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
In this work, we propose an ensemble of classification trees (CT) and artificial neural networks (ANN). Several statistical properties including universal consistency and upper bound of an important parameter of the proposed classifier are…
Block-encoding is a critical subroutine in quantum computing, enabling the transformation of classical data into a matrix representation within a quantum circuit. The resource trade-offs in simulating a block-encoding can be quantified by…
Binary neural networks utilize 1-bit quantized weights and activations to reduce both the model's storage demands and computational burden. However, advanced binary architectures still incorporate millions of inefficient and…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…
A concise study of ternary and cubic algebras with $Z_3$ grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, $S_3$, and its abelian subgroup…
While it is trivial to multiply two C-finite sequences (just like integers), it is not quite so trivial to "factorize" them, or to decide whether they are "prime". The former is plain linear algebra, while the latter is heavy-duty…
To construct ternary "quaternions" following Hamilton we must introduce two "imaginary "units, $q_1$ and $q_2$ with propeties $q_1^n=1$ and $q_2^m=1$. The general is enough difficult, and we consider the $m=n=3$. This case gives us the…
Binarization is an extreme network compression approach that provides large computational speedups along with energy and memory savings, albeit at significant accuracy costs. We investigate the question of where to binarize inputs at…
The unit cost model is both convenient and largely realistic for describing integer decision algorithms over (+,*). Additional operations like division with remainder or bitwise conjunction, although equally supported by computing hardware,…
(NxN)-matrix is called additive when its elements are pair-wise sums of N real numbers. For a quadratic binary functional with an additive connection matrix we succeeded in finding the global minimum expressing it through external…
Conventional neural accelerators rely on isolated self-sufficient functional units that perform an atomic operation while communicating the results through an operand delivery-aggregation logic. Each single unit processes all the bits of…
Chen and Cheng [Ann. Statist. 34 (2006) 546--558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for $9N/32\le n\le 5N/16$, all minimum aberration designs with $N$ runs and $n$…
Primary motivation for this work was the need to implement hardware accelerators for a newly proposed ANN structure called Auto Resonance Network (ARN) for robotic motion planning. ARN is an approximating feed-forward hierarchical and…
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.
Binary multipliers have long been a staple component in digital circuitry, serving crucial roles in microprocessor design, digital signal processing units and many more applications. This work presents a unique design for a multiplier that…
Bitmap indexes are routinely used to speed up simple aggregate queries in databases. Set operations such as intersections, unions and complements can be represented as logical operations (AND, OR, NOT). However, less is known about the…
The technique for hardware multiplication based upon Fourier transformation has been introduced. The technique has the highest efficiency on multiplication units with up to 8 bit range. Each multiplication unit is realized on base of the…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…