51 research outputs found
Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
We provide a scheme for efficient simulation of a broad class of quantum
optics experiments. Our efficient simulation extends the continuous variable
Gottesman-Knill theorem to a large class of non-Gaussian mixed states, thereby
identifying that these non-Gaussian states are not an enabling resource for
exponential quantum speed-up. Our results also provide an operationally
motivated interpretation of negativity as non-classicality. We apply our scheme
to the case of noisy single-photon-added-thermal-states to show that this class
admits states with positive Wigner function but negative P -function that are
not useful resource states for quantum computation.Comment: 14 pages, 1 figur
Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach
Modern neural networks are highly overparameterized, with capacity to
substantially overfit to training data. Nevertheless, these networks often
generalize well in practice. It has also been observed that trained networks
can often be "compressed" to much smaller representations. The purpose of this
paper is to connect these two empirical observations. Our main technical result
is a generalization bound for compressed networks based on the compressed size.
Combined with off-the-shelf compression algorithms, the bound leads to state of
the art generalization guarantees; in particular, we provide the first
non-vacuous generalization guarantees for realistic architectures applied to
the ImageNet classification problem. As additional evidence connecting
compression and generalization, we show that compressibility of models that
tend to overfit is limited: We establish an absolute limit on expected
compressibility as a function of expected generalization error, where the
expectations are over the random choice of training examples. The bounds are
complemented by empirical results that show an increase in overfitting implies
an increase in the number of bits required to describe a trained network.Comment: 16 pages, 1 figure. Accepted at ICLR 201
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