2,700 research outputs found
A Variational Perspective on Accelerated Methods in Optimization
Accelerated gradient methods play a central role in optimization, achieving
optimal rates in many settings. While many generalizations and extensions of
Nesterov's original acceleration method have been proposed, it is not yet clear
what is the natural scope of the acceleration concept. In this paper, we study
accelerated methods from a continuous-time perspective. We show that there is a
Lagrangian functional that we call the \emph{Bregman Lagrangian} which
generates a large class of accelerated methods in continuous time, including
(but not limited to) accelerated gradient descent, its non-Euclidean extension,
and accelerated higher-order gradient methods. We show that the continuous-time
limit of all of these methods correspond to traveling the same curve in
spacetime at different speeds. From this perspective, Nesterov's technique and
many of its generalizations can be viewed as a systematic way to go from the
continuous-time curves generated by the Bregman Lagrangian to a family of
discrete-time accelerated algorithms.Comment: 38 pages. Subsumes an earlier working draft arXiv:1509.0361
Non-classical behavior in multimode and disordered transverse structures in OPO. Use of the Q representation
We employ the Q representation to study the non-classical correlations that
are present from below to above-threshold in the degenerate optical parametric
oscillator. Our study shows that such correlations are present just above
threshold, in the regime in which stripe patterns are formed, but that they
also persist further above threshold in the presence of spatially disordered
structures
Adam through a Second-Order Lens
Research into optimisation for deep learning is characterised by a tension
between the computational efficiency of first-order, gradient-based methods
(such as SGD and Adam) and the theoretical efficiency of second-order,
curvature-based methods (such as quasi-Newton methods and K-FAC). We seek to
combine the benefits of both approaches into a single computationally-efficient
algorithm. Noting that second-order methods often depend on stabilising
heuristics (such as Levenberg-Marquardt damping), we propose AdamQLR: an
optimiser combining damping and learning rate selection techniques from K-FAC
(Martens and Grosse, 2015) with the update directions proposed by Adam,
inspired by considering Adam through a second-order lens. We evaluate AdamQLR
on a range of regression and classification tasks at various scales, achieving
competitive generalisation performance vs runtime.Comment: 28 pages, 15 figures, 4 tables. Submitted to ICLR 202
Detecting gravitational waves from highly eccentric compact binaries
In dense stellar regions, highly eccentric binaries of black holes and
neutron stars can form through various n-body interactions. Such a binary could
emit a significant fraction of its binding energy in a sequence of largely
isolated gravitational wave bursts prior to merger. Given expected black hole
and neutron star masses, many such systems will emit these repeated bursts at
frequencies within the sensitive band of contemporary ground-based
gravitational wave detectors. Unfortunately, existing gravitational wave
searches are ill-suited to detect these signals. In this work, we adapt a
"power stacking" method to the detection of gravitational wave signals from
highly eccentric binaries. We implement this method as an extension of the
Q-transform, a projection onto a multiresolution basis of windowed complex
exponentials that has previously been used to analyze data from the network of
LIGO/Virgo detectors. Our method searches for excess power over an ensemble of
time-frequency tiles. We characterize the performance of our method using Monte
Carlo experiments with signals injected in simulated detector noise. Our
results indicate that the power stacking method achieves substantially better
sensitivity to eccentric binary signals than existing localized burst searches.Comment: 17 pages, 20 figure
Head-on collisions of boson stars
We study head-on collisions of boson stars in three dimensions. We consider
evolutions of two boson stars which may differ in their phase or have opposite
frequencies but are otherwise identical. Our studies show that these phase
differences result in different late time behavior and gravitational wave
output
Shape Animation with Combined Captured and Simulated Dynamics
We present a novel volumetric animation generation framework to create new
types of animations from raw 3D surface or point cloud sequence of captured
real performances. The framework considers as input time incoherent 3D
observations of a moving shape, and is thus particularly suitable for the
output of performance capture platforms. In our system, a suitable virtual
representation of the actor is built from real captures that allows seamless
combination and simulation with virtual external forces and objects, in which
the original captured actor can be reshaped, disassembled or reassembled from
user-specified virtual physics. Instead of using the dominant surface-based
geometric representation of the capture, which is less suitable for volumetric
effects, our pipeline exploits Centroidal Voronoi tessellation decompositions
as unified volumetric representation of the real captured actor, which we show
can be used seamlessly as a building block for all processing stages, from
capture and tracking to virtual physic simulation. The representation makes no
human specific assumption and can be used to capture and re-simulate the actor
with props or other moving scenery elements. We demonstrate the potential of
this pipeline for virtual reanimation of a real captured event with various
unprecedented volumetric visual effects, such as volumetric distortion,
erosion, morphing, gravity pull, or collisions
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