In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[Q]: We show that information about whether a neural network's output will be correct or incorrect is present in the outputs of the network's intermediate layers. To demonstrate this effect, we train a new "meta" network to predict from either the final output of the underlying "base" network or the output of one of the base network's intermediate layers whether the base network will be correct or incorrect for a particular input. We find that, over a wide range of tasks and base networks, the meta network can achieve accuracies ranging from 65% - 85% in making this determination.

[A]: Information about whether a neural network's output will be correct or incorrect is somewhat present in the outputs of the network's intermediate layers.

[Q]: Neural networks with low-precision weights and activations offer compelling
efficiency advantages over their full-precision equivalents. The two most
frequently discussed benefits of quantization are reduced memory consumption,
and a faster forward pass when implemented with efficient bitwise
operations. We propose a third benefit of very low-precision neural networks:
improved robustness against some adversarial attacks, and in the worst case,
performance that is on par with full-precision models. We focus on the very
low-precision case where weights and activations are both quantized to $\pm$1,
and note that stochastically quantizing weights in just one layer can sharply
reduce the impact of iterative attacks. We observe that non-scaled binary neural
networks exhibit a similar effect to the original \emph{defensive distillation}
procedure that led to \emph{gradient masking}, and a false notion of security.
We address this by conducting both black-box and white-box experiments with
binary models that do not artificially mask gradients.
[A]: We conduct adversarial attacks against binarized neural networks and show that we reduce the impact of the strongest attacks, while maintaining comparable accuracy in a black-box setting

[Q]: In this paper, we propose a new loss function for performing principal component analysis (PCA) using linear autoencoders (LAEs). Optimizing the standard L2 loss results in a decoder matrix that spans the principal subspace of the sample covariance of the data, but fails to identify the exact eigenvectors. This downside originates from an invariance that cancels out in the global map. Here, we prove that our loss function eliminates this issue, i.e. the decoder converges to the exact ordered unnormalized eigenvectors of the sample covariance matrix. For this new loss, we establish that all local minima are global optima and also show that computing the new loss (and also its gradients) has the same order of complexity as the classical loss. We report numerical results on both synthetic simulations, and a real-data PCA experiment on MNIST (i.e., a 60,000 x784 matrix), demonstrating our approach to be practically applicable and rectify previous LAEs' downsides.
[A]:
A new loss function for PCA with linear autoencoders that provably yields ordered exact eigenvectors