3,041 research outputs found
Scalable Data Augmentation for Deep Learning
Scalable Data Augmentation (SDA) provides a framework for training deep
learning models using auxiliary hidden layers. Scalable MCMC is available for
network training and inference. SDA provides a number of computational
advantages over traditional algorithms, such as avoiding backtracking, local
modes and can perform optimization with stochastic gradient descent (SGD) in
TensorFlow. Standard deep neural networks with logit, ReLU and SVM activation
functions are straightforward to implement. To illustrate our architectures and
methodology, we use P\'{o}lya-Gamma logit data augmentation for a number of
standard datasets. Finally, we conclude with directions for future research
Paraelectric in a Strong High-Frequency Field
A change in the effective permittivity of a ferroelectric film in the
paraelectric phase under the action of a strong high-frequency field
(nonequilibrium soft mode heating) is considered. It is shown that this effect
must be most clearly pronounced far from the resonance (\omega_0 << \omega_sm),
rather than for the external field frequency \omega_0 close to the soft mode
frequency \omega_sm. The effective permittivity as a function of the
high-frequency field amplitude is calculated using the phenomenological
approach and within the microscopic theory based on the simple model of a
displacement-type ferroelectric.Comment: 3 two-column page
Quantum Resonances and Regularity Islands in Quantum Maps
We study analytically as well as numerically the dynamics of a quantum map
near a quantum resonance of an order q. The map is embedded into a continuous
unitary transformation generated by a time-independent quasi-Hamiltonian. Such
a Hamiltonian generates at the very point of the resonance a local gauge
transformation described the unitary unimodular group SU(q). The resonant
energy growth of is attributed to the zero Liouville eigenmodes of the
generator in the adjoint representation of the group while the non-zero modes
yield saturating with time contribution. In a vicinity of a given resonance,
the quasi-Hamiltonian is then found in the form of power expansion with respect
to the detuning from the resonance. The problem is related in this way to the
motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of
a quantum particle with intrinsic degrees of freedom described by the SU(q)
group. This motion is in parallel with the classical phase oscillations near a
non-linear resonance. The most important role is played by the resonances with
the orders much smaller than the typical localization length, q << l. Such
resonances master for exponentially long though finite times the motion in some
domains around them. Explicit analytical solution is possible for a few lowest
and strongest resonances.Comment: 28 pages (LaTeX), 11 ps figures, submitted to PR
How Well a Chaotic Quantum System Can Retain Memory of Its Initial State?
In classical mechanics the local exponential instability effaces the memory
of initial conditions and leads to practical irreversibility. In striking
contrast, quantum mechanics appears to exhibit strong memory of the initial
state. We relate the latter fact to the low (at most linear) rate with which
the system's Wigner function gets during evolution more and more complicated
structure and establish existence of a critical strength of external influence
below which such a memory still survives.Comment: 5 pages, 4 figure
Integrable quadratic Hamiltonians on so(4) and so(3,1)
We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1)
and describe Hamiltonians that have additional polynomial integrals. One of the
main results is a new integrable case with an integral of sixth degree.Comment: 16 page
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