37,971 research outputs found
Comparison of the Worst and Best Sum-of-Products Expressions for Multiple-Valued Functions
Because most practical logic design algorithms produce irredundant sum-of-products (ISOP) expressions, the understanding of ISOPs is crucial. We show a class of functions for which Morreale-Minato's ISOP generation algorithm produces worst ISOPs (WSOP), ISOPs with the most product terms. We show this class has the property that the ratio of the number of products in the WSOP to the number in the minimum ISOP (MSOP) is arbitrarily large when the number of variables is unbounded. The ramifications of this are significant; care must be exercised in designing algorithms that produce ISOPs. We also show that 2/sup n-1/ is a firm upper bound on the number of product terms in any ISOP for switching functions on n variables, answering a question that has been open for 30 years. We show experimental data and extend our results to functions of multiple-valued variables
Multilevel Artificial Neural Network Training for Spatially Correlated Learning
Multigrid modeling algorithms are a technique used to accelerate relaxation
models running on a hierarchy of similar graphlike structures. We introduce and
demonstrate a new method for training neural networks which uses multilevel
methods. Using an objective function derived from a graph-distance metric, we
perform orthogonally-constrained optimization to find optimal prolongation and
restriction maps between graphs. We compare and contrast several methods for
performing this numerical optimization, and additionally present some new
theoretical results on upper bounds of this type of objective function. Once
calculated, these optimal maps between graphs form the core of Multiscale
Artificial Neural Network (MsANN) training, a new procedure we present which
simultaneously trains a hierarchy of neural network models of varying spatial
resolution. Parameter information is passed between members of this hierarchy
according to standard coarsening and refinement schedules from the multiscale
modelling literature. In our machine learning experiments, these models are
able to learn faster than default training, achieving a comparable level of
error in an order of magnitude fewer training examples.Comment: Manuscript (24 pages) and Supplementary Material (4 pages). Updated
January 2019 to reflect new formulation of MsANN structure and new training
procedur
Analysis of minimization algorithms for multiple-valued programmable logic arrays
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.Proceedings of the 18th International Symposium on Multiple-Valued Logic, May 1988, pp. 226-236We compare the performance of three heuristic algorithms [3,6,13] for the minimization of
sum-of-products expressions realized by the newly
developed multiplevalued programmable logic arrays [9]. Heuristic methods are important because exact minimization is extremely time consuming. We compare the heuristics to the exact solution, showing that heuristic methods are reasonably close to minimal. We use as a basis of comparison the average number of product terms over a set of randomly generated functions. All three heuristics produce nearly the same average number of product terms. Although the averages are close, there is surprisingly little overlap among the set of functions where the best realization is achieved. Thus, there is a benefit to applying different heuristics and then choosing the best realization
Gate-Level Simulation of Quantum Circuits
While thousands of experimental physicists and chemists are currently trying
to build scalable quantum computers, it appears that simulation of quantum
computation will be at least as critical as circuit simulation in classical
VLSI design. However, since the work of Richard Feynman in the early 1980s
little progress was made in practical quantum simulation. Most researchers
focused on polynomial-time simulation of restricted types of quantum circuits
that fall short of the full power of quantum computation. Simulating quantum
computing devices and useful quantum algorithms on classical hardware now
requires excessive computational resources, making many important simulation
tasks infeasible. In this work we propose a new technique for gate-level
simulation of quantum circuits which greatly reduces the difficulty and cost of
such simulations. The proposed technique is implemented in a simulation tool
called the Quantum Information Decision Diagram (QuIDD) and evaluated by
simulating Grover's quantum search algorithm. The back-end of our package,
QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability
to efficiently represent many seemingly intractable combinatorial structures.
This reliance on a well-established area of research allows us to take
advantage of existing software for BDD manipulation and achieve unparalleled
empirical results for quantum simulation
Coherence Optimization and Best Complex Antipodal Spherical Codes
Vector sets with optimal coherence according to the Welch bound cannot exist
for all pairs of dimension and cardinality. If such an optimal vector set
exists, it is an equiangular tight frame and represents the solution to a
Grassmannian line packing problem. Best Complex Antipodal Spherical Codes
(BCASCs) are the best vector sets with respect to the coherence. By extending
methods used to find best spherical codes in the real-valued Euclidean space,
the proposed approach aims to find BCASCs, and thereby, a complex-valued vector
set with minimal coherence. There are many applications demanding vector sets
with low coherence. Examples are not limited to several techniques in wireless
communication or to the field of compressed sensing. Within this contribution,
existing analytical and numerical approaches for coherence optimization of
complex-valued vector spaces are summarized and compared to the proposed
approach. The numerically obtained coherence values improve previously reported
results. The drawback of increased computational effort is addressed and a
faster approximation is proposed which may be an alternative for time critical
cases
LF-PPL: A Low-Level First Order Probabilistic Programming Language for Non-Differentiable Models
We develop a new Low-level, First-order Probabilistic Programming Language
(LF-PPL) suited for models containing a mix of continuous, discrete, and/or
piecewise-continuous variables. The key success of this language and its
compilation scheme is in its ability to automatically distinguish parameters
the density function is discontinuous with respect to, while further providing
runtime checks for boundary crossings. This enables the introduction of new
inference engines that are able to exploit gradient information, while
remaining efficient for models which are not everywhere differentiable. We
demonstrate this ability by incorporating a discontinuous Hamiltonian Monte
Carlo (DHMC) inference engine that is able to deliver automated and efficient
inference for non-differentiable models. Our system is backed up by a
mathematical formalism that ensures that any model expressed in this language
has a density with measure zero discontinuities to maintain the validity of the
inference engine.Comment: Published in the proceedings of the 22nd International Conference on
Artificial Intelligence and Statistics (AISTATS
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