566 research outputs found
New quantum-mechanical phenomenon in a model of electron-electron interaction in graphene
A quantum mechanical model of two interacting electrons in graphene is
considered. We concentrate on the case of zero total momentum of the pair. We
show that the dynamics of the system is very unusual. Both stationary and
time-dependent problems are considered. It is shown that the complete set of
the wave functions with definite energy includes the new functions, previously
overlooked. The time evolution of the wave packet, corresponding to the
scattering problem setup, leads to the appearance of the localized state at
large time. The asymptotics of this state is found analytically. We obtain the
lower bound of the life time of this state, which is connected with the
breakdown of the continuous model on the lattice scale. The estimate of this
bound gives one a hope to observe the localized states in the experiment.Comment: 10 pages, 2 figure
Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence
Incremental learning (IL) has received a lot of attention recently, however,
the literature lacks a precise problem definition, proper evaluation settings,
and metrics tailored specifically for the IL problem. One of the main
objectives of this work is to fill these gaps so as to provide a common ground
for better understanding of IL. The main challenge for an IL algorithm is to
update the classifier whilst preserving existing knowledge. We observe that, in
addition to forgetting, a known issue while preserving knowledge, IL also
suffers from a problem we call intransigence, inability of a model to update
its knowledge. We introduce two metrics to quantify forgetting and
intransigence that allow us to understand, analyse, and gain better insights
into the behaviour of IL algorithms. We present RWalk, a generalization of
EWC++ (our efficient version of EWC [Kirkpatrick2016EWC]) and Path Integral
[Zenke2017Continual] with a theoretically grounded KL-divergence based
perspective. We provide a thorough analysis of various IL algorithms on MNIST
and CIFAR-100 datasets. In these experiments, RWalk obtains superior results in
terms of accuracy, and also provides a better trade-off between forgetting and
intransigence
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