442 research outputs found
Emergent hydrodynamics in non-equilibrium quantum systems
A tremendous amount of recent attention has focused on characterizing the
dynamical properties of periodically driven many-body systems. Here, we use a
novel numerical tool termed `density matrix truncation' (DMT) to investigate
the late-time dynamics of large-scale Floquet systems. We find that DMT
accurately captures two essential pieces of Floquet physics, namely,
prethermalization and late-time heating to infinite temperature. Moreover, by
implementing a spatially inhomogeneous drive, we demonstrate that an interplay
between Floquet heating and diffusive transport is crucial to understanding the
system's dynamics. Finally, we show that DMT also provides a powerful method
for quantitatively capturing the emergence of hydrodynamics in static
(un-driven) Hamiltonians; in particular, by simulating the dynamics of generic,
large-scale quantum spin chains (up to L = 100), we are able to directly
extract the energy diffusion coefficient.Comment: 6+21 pages, 4+23 figure
Emergent Hydrodynamics in Nonequilibrium Quantum Systems
A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed “density matrix truncation” (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system’s dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (undriven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L=100), we are able to directly extract the energy diffusion coefficient
Efficient Sharpness-aware Minimization for Improved Training of Neural Networks
Overparametrized Deep Neural Networks (DNNs) often achieve astounding
performances, but may potentially result in severe generalization error.
Recently, the relation between the sharpness of the loss landscape and the
generalization error has been established by Foret et al. (2020), in which the
Sharpness Aware Minimizer (SAM) was proposed to mitigate the degradation of the
generalization. Unfortunately, SAM s computational cost is roughly double that
of base optimizers, such as Stochastic Gradient Descent (SGD). This paper thus
proposes Efficient Sharpness Aware Minimizer (ESAM), which boosts SAM s
efficiency at no cost to its generalization performance. ESAM includes two
novel and efficient training strategies-StochasticWeight Perturbation and
Sharpness-Sensitive Data Selection. In the former, the sharpness measure is
approximated by perturbing a stochastically chosen set of weights in each
iteration; in the latter, the SAM loss is optimized using only a judiciously
selected subset of data that is sensitive to the sharpness. We provide
theoretical explanations as to why these strategies perform well. We also show,
via extensive experiments on the CIFAR and ImageNet datasets, that ESAM
enhances the efficiency over SAM from requiring 100% extra computations to 40%
vis-a-vis base optimizers, while test accuracies are preserved or even
improved
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