Related papers: Symmetric Ternary Logic and Its Systematic Logic C…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

Modern integrated circuits are essentially two-dimensional (2D). Partial three-dimensional (3D) integration and 3D-transistor-level integrated circuits have long been anticipated as routes to improve the performance, cost and size of…

The multi-pumping resource sharing technique can overcome the limitations commonly found in single-clocked FPGA designs by allowing hardware components to operate at a higher clock frequency than the surrounding system. However, this…

We consider a problem of decomposition of a ternary function into a composition of binary ones from the viewpoint of communication complexity and algorithmic information theory as well as some applications to cellular automata.

Current evaluations of synthetic tabular data mainly focus on how well joint distributions are modeled, often overlooking the assessment of their effectiveness in preserving realistic event sequences and coherent entity relationships across…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

Deep neural networks (DNNs) have been widely and successfully applied to various applications, but they require large amounts of memory and computational power. This severely restricts their deployment on resource-limited devices. To…

We propose a set of compositional design patterns to describe a large variety of systems that combine statistical techniques from machine learning with symbolic techniques from knowledge representation. As in other areas of computer science…

The task of logic synthesis is to map a technology-independent representation of an application to hardware-specific operations, taking into account various constraints and trading off different costs associated with the implementation.…

Tensor algebra is a crucial component for data-intensive workloads such as machine learning and scientific computing. As the complexity of data grows, scientists often encounter a dilemma between the highly specialized dense tensor algebra…

We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex…

Tensor programs often need to process large tensors (vectors, matrices, or higher order tensors) that require a specialized storage format for their memory layout. Several such layouts have been proposed in the literature, such as the…

The increasing advancement of emerging device technologies that provide alternative basis logic sets necessitates the exploration of innovative logic design automation methodologies. Specifically, emerging computing architectures based on…

New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or…

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…

Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However,…

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

Monolithic three-dimensional integration of memory and logic circuits could dramatically improve performance and energy efficiency of computing systems. Some conventional and emerging memories are suitable for vertical integration,…

This paper shows how to optimize sparse tensor algebraic expressions by introducing temporary tensors, called workspaces, into the resulting loop nests. We develop a new intermediate language for tensor operations called concrete index…