17,824 research outputs found
Data-Dependent Stability of Stochastic Gradient Descent
We establish a data-dependent notion of algorithmic stability for Stochastic
Gradient Descent (SGD), and employ it to develop novel generalization bounds.
This is in contrast to previous distribution-free algorithmic stability results
for SGD which depend on the worst-case constants. By virtue of the
data-dependent argument, our bounds provide new insights into learning with SGD
on convex and non-convex problems. In the convex case, we show that the bound
on the generalization error depends on the risk at the initialization point. In
the non-convex case, we prove that the expected curvature of the objective
function around the initialization point has crucial influence on the
generalization error. In both cases, our results suggest a simple data-driven
strategy to stabilize SGD by pre-screening its initialization. As a corollary,
our results allow us to show optimistic generalization bounds that exhibit fast
convergence rates for SGD subject to a vanishing empirical risk and low noise
of stochastic gradient
Quantum dynamics of a two-level emitter with modulated transition frequency
The resonant quantum dynamics of an excited two-level emitter is investigated
via classical modulation of its transition frequency while simultaneously the
radiator interacts with a broadband electromagnetic field reservoir. The
frequency of modulation is selected to be of the order of the bare-state
spontaneous decay rate. In this way, one can induce quantum interference
effects and, consequently, quantum coherences among multiple decaying
transition pathways. Depending on the modulation depth and its absolute phase,
both the spontaneous emission and the frequency shift may be conveniently
modified and controlled.Comment: 8 pages, 6 figure
Accelerating the Fourier split operator method via graphics processing units
Current generations of graphics processing units have turned into highly
parallel devices with general computing capabilities. Thus, graphics processing
units may be utilized, for example, to solve time dependent partial
differential equations by the Fourier split operator method. In this
contribution, we demonstrate that graphics processing units are capable to
calculate fast Fourier transforms much more efficiently than traditional
central processing units. Thus, graphics processing units render efficient
implementations of the Fourier split operator method possible. Performance
gains of more than an order of magnitude as compared to implementations for
traditional central processing units are reached in the solution of the time
dependent Schr\"odinger equation and the time dependent Dirac equation
Diamond Integrated Optomechanical Circuits
Diamond offers unique material advantages for the realization of micro- and
nanomechanical resonators due to its high Young's modulus, compatibility with
harsh environments and superior thermal properties. At the same time, the wide
electronic bandgap of 5.45eV makes diamond a suitable material for integrated
optics because of broadband transparency and the absence of free-carrier
absorption commonly encountered in silicon photonics. Here we take advantage of
both to engineer full-scale optomechanical circuits in diamond thin films. We
show that polycrystalline diamond films fabricated by chemical vapour
deposition provide a convenient waferscale substrate for the realization of
high quality nanophotonic devices. Using free-standing nanomechanical
resonators embedded in on-chip Mach-Zehnder interferometers, we demonstrate
efficient optomechanical transduction via gradient optical forces. Fabricated
diamond resonators reproducibly show high mechanical quality factors up to
11,200. Our low cost, wideband, carrier-free photonic circuits hold promise for
all-optical sensing and optomechanical signal processing at ultra-high
frequencies
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