2,079 research outputs found
Analysis of Natural Gradient Descent for Multilayer Neural Networks
Natural gradient descent is a principled method for adapting the parameters
of a statistical model on-line using an underlying Riemannian parameter space
to redefine the direction of steepest descent. The algorithm is examined via
methods of statistical physics which accurately characterize both transient and
asymptotic behavior. A solution of the learning dynamics is obtained for the
case of multilayer neural network training in the limit of large input
dimension. We find that natural gradient learning leads to optimal asymptotic
performance and outperforms gradient descent in the transient, significantly
shortening or even removing plateaus in the transient generalization
performance which typically hamper gradient descent training.Comment: 14 pages including figures. To appear in Physical Review
The Competition for Shortest Paths on Sparse Graphs
Optimal paths connecting randomly selected network nodes and fixed routers
are studied analytically in the presence of non-linear overlap cost that
penalizes congestion. Routing becomes increasingly more difficult as the number
of selected nodes increases and exhibits ergodicity breaking in the case of
multiple routers. A distributed linearly-scalable routing algorithm is devised.
The ground state of such systems reveals non-monotonic complex behaviors in
both average path-length and algorithmic convergence, depending on the network
topology, and densities of communicating nodes and routers.Comment: 4 pages, 4 figure
Sustainable Competitive Advantage Through Servitization: An Investigation Into Servitization Strategy In the Real Estate Development Sector
Achieving sustainable competitive advantage, based upon services provision, is often claimed to be viable for businesses. There has, however, been little evidence captured on the application of aspects of servitization within the real estate development. By applying the RVB theory, the research propositions of this study include understanding how superior performance is driven from organization capabilities and how different organizations develop and position those capabilities to gain competitive advantage. This research was conducted using an exploratory research and in-depth case study. The study suggests that more strategic alignment between servitization decisions and operations management is required to create competitive advantage
Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields
A variation of low density parity check (LDPC) error correcting codes defined
over Galois fields () is investigated using statistical physics. A code
of this type is characterised by a sparse random parity check matrix composed
of nonzero elements per column. We examine the dependence of the code
performance on the value of , for finite and infinite values, both in
terms of the thermodynamical transition point and the practical decoding phase
characterised by the existence of a unique (ferromagnetic) solution. We find
different -dependencies in the cases of C=2 and ; the analytical
solutions are in agreement with simulation results, providing a quantitative
measure to the improvement in performance obtained using non-binary alphabets.Comment: 7 pages, 1 figur
Public key cryptography and error correcting codes as Ising models
We employ the methods of statistical physics to study the performance of
Gallager type error-correcting codes. In this approach, the transmitted
codeword comprises Boolean sums of the original message bits selected by two
randomly-constructed sparse matrices. We show that a broad range of these codes
potentially saturate Shannon's bound but are limited due to the decoding
dynamics used. Other codes show sub-optimal performance but are not restricted
by the decoding dynamics. We show how these codes may also be employed as a
practical public-key cryptosystem and are of competitive performance to modern
cyptographical methods.Comment: 6 page
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