9,982 research outputs found
Convergence Theory of Learning Over-parameterized ResNet: A Full Characterization
ResNet structure has achieved great empirical success since its debut. Recent
work established the convergence of learning over-parameterized ResNet with a
scaling factor on the residual branch where is the network
depth. However, it is not clear how learning ResNet behaves for other values of
. In this paper, we fully characterize the convergence theory of gradient
descent for learning over-parameterized ResNet with different values of .
Specifically, with hiding logarithmic factor and constant coefficients, we show
that for gradient descent is guaranteed to converge to the
global minma, and especially when the convergence is irrelevant
of the network depth. Conversely, we show that for ,
the forward output grows at least with rate in expectation and then the
learning fails because of gradient explosion for large . This means the
bound is sharp for learning ResNet with arbitrary depth.
To the best of our knowledge, this is the first work that studies learning
ResNet with full range of .Comment: 31 page
Assessment of density functional methods with correct asymptotic behavior
Long-range corrected (LC) hybrid functionals and asymptotically corrected
(AC) model potentials are two distinct density functional methods with correct
asymptotic behavior. They are known to be accurate for properties that are
sensitive to the asymptote of the exchange-correlation potential, such as the
highest occupied molecular orbital energies and Rydberg excitation energies of
molecules. To provide a comprehensive comparison, we investigate the
performance of the two schemes and others on a very wide range of applications,
including the asymptote problems, self-interaction-error problems, energy-gap
problems, charge-transfer problems, and many others. The LC hybrid scheme is
shown to consistently outperform the AC model potential scheme. In addition, to
be consistent with the molecules collected in the IP131 database [Y.-S. Lin,
C.-W. Tsai, G.-D. Li, and J.-D. Chai, J. Chem. Phys., 2012, 136, 154109], we
expand the EA115 and FG115 databases to include, respectively, the vertical
electron affinities and fundamental gaps of the additional 16 molecules, and
develop a new database AE113 (113 atomization energies), consisting of accurate
reference values for the atomization energies of the 113 molecules in IP131.
These databases will be useful for assessing the accuracy of density functional
methods.Comment: accepted for publication in Phys. Chem. Chem. Phys., 46 pages, 4
figures, supplementary material include
Controllable coupling between a nanomechanical resonator and a coplanar-waveguide resonator via a superconducting flux qubit
We study a tripartite quantum system consisting of a coplanar-waveguide (CPW)
resonator and a nanomechanical resonator (NAMR) connected by a flux qubit,
where the flux qubit has a large detuning from both resonators. By a unitray
transformation and a second-order approximation, we obtain a strong and
controllable (i.e., magnetic-field-dependent) effective coupling between the
NAMR and the CPW resonator. Due to the strong coupling, vacuum Rabi splitting
can be observed from the voltage-fluctuation spectrum of the CPW resonator. We
further study the properties of single photon transport as inferred from the
reflectance or equivalently the transmittance. We show that the reflectance and
the corresponding phase shift spectra both exhibit doublet of narrow spectral
features due to vacuum Rabi splitting. By tuning the external magnetic field,
the reflectance and the phase shift can be varied from 0 to 1 and to
, respectively. The results indicate that this hybrid quantum system can
act as a quantum router.Comment: 8 pages, 6 figure
A supra-massive magnetar central engine for short GRB 130603B
We show that the peculiar early optical and in particular X-ray afterglow
emission of the short duration burst GRB 130603B can be explained by continuous
energy injection into the blastwave from a supra-massive magnetar central
engine. The observed energetics and temporal/spectral properties of the late
infrared bump (i.e., the "kilonova") are also found consistent with emission
from the ejecta launched during an NS-NS merger and powered by a magnetar
central engine. The isotropic-equivalent kinetic energies of both the GRB
blastwave and the kilonova are about erg, consistent
with being powered by a near-isotropic magnetar wind. However, this relatively
small value demands that most of the initial rotational energy of the magnetar
is carried away by gravitational wave
radiation. Our results suggest that (i) the progenitor of GRB 130603B would be
a NS-NS binary system, whose merger product would be a supra-massive neutron
star that lasted for about seconds; (ii) the equation-of-state of
nuclear matter would be stiff enough to allow survival of a long-lived
supra-massive neutron star, so that it is promising to detect bright
electromagnetic counterparts of gravitational wave triggers without short GRB
associations in the upcoming Advanced LIGO/Virgo era.Comment: Five pages including 1 Figure, to appear in ApJ
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