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]: 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]: Understanding the optimization trajectory is critical to understand training of deep neural networks. We show how the hyperparameters of stochastic gradient descent influence the covariance of the gradients (K) and the Hessian of the training loss (H) along this trajectory. Based on a theoretical model, we predict that using a high learning rate or a small batch size in the early phase of training leads SGD to regions of the parameter space with (1) reduced spectral norm of K, and (2) improved conditioning of K and H. We show that the point on the trajectory after which these effects hold, which we refer to as the break-even point, is reached early during training. We demonstrate these effects empirically for a range of deep neural networks applied to multiple different tasks. Finally, we apply our analysis to networks with batch normalization (BN) layers and find that it is necessary to use a high learning rate to achieve loss smoothing effects attributed previously to BN alone.
[A]: In the early phase of training of deep neural networks there exists a "break-even point" which determines properties of the entire optimization trajectory.

[Q]: The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms.
[A]:
Attention based model trained with REINFORCE with greedy rollout baseline to learn heuristics with competitive results on TSP and other routing problems