1,634 research outputs found
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Many critical EDA problems suffer from the curse of dimensionality, i.e. the
very fast-scaling computational burden produced by large number of parameters
and/or unknown variables. This phenomenon may be caused by multiple spatial or
temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit
simulation), nonlinearity of devices and circuits, large number of design or
optimization parameters (e.g. full-chip routing/placement and circuit sizing),
or extensive process variations (e.g. variability/reliability analysis and
design for manufacturability). The computational challenges generated by such
high dimensional problems are generally hard to handle efficiently with
traditional EDA core algorithms that are based on matrix and vector
computation. This paper presents "tensor computation" as an alternative general
framework for the development of efficient EDA algorithms and tools. A tensor
is a high-dimensional generalization of a matrix and a vector, and is a natural
choice for both storing and solving efficiently high-dimensional EDA problems.
This paper gives a basic tutorial on tensors, demonstrates some recent examples
of EDA applications (e.g., nonlinear circuit modeling and high-dimensional
uncertainty quantification), and suggests further open EDA problems where the
use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and
System
Bayesian Robust Tensor Ring Model for Incomplete Multiway Data
Robust tensor completion (RTC) aims to recover a low-rank tensor from its
incomplete observation with outlier corruption. The recently proposed tensor
ring (TR) model has demonstrated superiority in solving the RTC problem.
However, the existing methods either require a pre-assigned TR rank or
aggressively pursue the minimum TR rank, thereby often leading to biased
solutions in the presence of noise. In this paper, a Bayesian robust tensor
ring decomposition (BRTR) method is proposed to give more accurate solutions to
the RTC problem, which can avoid exquisite selection of the TR rank and penalty
parameters. A variational Bayesian (VB) algorithm is developed to infer the
probability distribution of posteriors. During the learning process, BRTR can
prune off slices of core tensor with marginal components, resulting in
automatic TR rank detection. Extensive experiments show that BRTR can achieve
significantly improved performance than other state-of-the-art methods
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