2,937 research outputs found
Throughput-Distortion Computation Of Generic Matrix Multiplication: Toward A Computation Channel For Digital Signal Processing Systems
The generic matrix multiply (GEMM) function is the core element of
high-performance linear algebra libraries used in many
computationally-demanding digital signal processing (DSP) systems. We propose
an acceleration technique for GEMM based on dynamically adjusting the
imprecision (distortion) of computation. Our technique employs adaptive scalar
companding and rounding to input matrix blocks followed by two forms of packing
in floating-point that allow for concurrent calculation of multiple results.
Since the adaptive companding process controls the increase of concurrency (via
packing), the increase in processing throughput (and the corresponding increase
in distortion) depends on the input data statistics. To demonstrate this, we
derive the optimal throughput-distortion control framework for GEMM for the
broad class of zero-mean, independent identically distributed, input sources.
Our approach converts matrix multiplication in programmable processors into a
computation channel: when increasing the processing throughput, the output
noise (error) increases due to (i) coarser quantization and (ii) computational
errors caused by exceeding the machine-precision limitations. We show that,
under certain distortion in the GEMM computation, the proposed framework can
significantly surpass 100% of the peak performance of a given processor. The
practical benefits of our proposal are shown in a face recognition system and a
multi-layer perceptron system trained for metadata learning from a large music
feature database.Comment: IEEE Transactions on Signal Processing (vol. 60, 2012
Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation
Random sequential addition (RSA) time-dependent packing process, in which
congruent hard hyperspheres are randomly and sequentially placed into a system
without interparticle overlap, is a useful packing model to study disorder in
high dimensions. Of particular interest is the infinite-time {\it saturation}
limit in which the available space for another sphere tends to zero. However,
the associated saturation density has been determined in all previous
investigations by extrapolating the density results for near-saturation
configurations to the saturation limit, which necessarily introduces numerical
uncertainties. We have refined an algorithm devised by us [S. Torquato, O.
Uche, and F.~H. Stillinger, Phys. Rev. E {\bf 74}, 061308 (2006)] to generate
RSA packings of identical hyperspheres. The improved algorithm produce such
packings that are guaranteed to contain no available space using finite
computational time with heretofore unattained precision and across the widest
range of dimensions (). We have also calculated the packing and
covering densities, pair correlation function and structure factor
of the saturated RSA configurations. As the space dimension increases,
we find that pair correlations markedly diminish, consistent with a recently
proposed "decorrelation" principle, and the degree of "hyperuniformity"
(suppression of infinite-wavelength density fluctuations) increases. We have
also calculated the void exclusion probability in order to compute the
so-called quantizer error of the RSA packings, which is related to the second
moment of inertia of the average Voronoi cell. Our algorithm is easily
generalizable to generate saturated RSA packings of nonspherical particles
Optimization Modulo Theories with Linear Rational Costs
In the contexts of automated reasoning (AR) and formal verification (FV),
important decision problems are effectively encoded into Satisfiability Modulo
Theories (SMT). In the last decade efficient SMT solvers have been developed
for several theories of practical interest (e.g., linear arithmetic, arrays,
bit-vectors). Surprisingly, little work has been done to extend SMT to deal
with optimization problems; in particular, we are not aware of any previous
work on SMT solvers able to produce solutions which minimize cost functions
over arithmetical variables. This is unfortunate, since some problems of
interest require this functionality.
In the work described in this paper we start filling this gap. We present and
discuss two general procedures for leveraging SMT to handle the minimization of
linear rational cost functions, combining SMT with standard minimization
techniques. We have implemented the procedures within the MathSAT SMT solver.
Due to the absence of competitors in the AR, FV and SMT domains, we have
experimentally evaluated our implementation against state-of-the-art tools for
the domain of linear generalized disjunctive programming (LGDP), which is
closest in spirit to our domain, on sets of problems which have been previously
proposed as benchmarks for the latter tools. The results show that our tool is
very competitive with, and often outperforms, these tools on these problems,
clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic,
currently under revision. arXiv admin note: text overlap with arXiv:1202.140
Shapes for maximal coverage for two-dimensional random sequential adsorption
The random sequential adsorption of various particle shapes is studied in
order to determine the influence of particle anisotropy on the saturated random
packing. For all tested particles there is an optimal level of anisotropy which
maximizes the saturated packing fraction. It is found that a concave shape
derived from a dimer of disks gives a packing fraction of 0.5833, which is
comparable to the maximum packing fraction of ellipsoids and spherocylinders
and higher than any other studied shape. Discussion why this shape is so
beneficial for random sequential adsorption is given.Comment: 6 pages, 8 figures, 3 table
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
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