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.

Example Input: Deep neural networks are known to be vulnerable to adversarial perturbations. In this paper, we bridge adversarial robustness of neural nets with Lyapunov stability of dynamical systems. From this viewpoint, training neural nets is equivalent to finding an optimal control of the discrete dynamical system, which allows one to utilize methods of successive approximations, an optimal control algorithm based on Pontryagin's maximum principle, to train neural nets. This decoupled training method allows us to add constraints to the optimization, which makes the deep model more robust. The constrained optimization problem can be formulated as a semi-definite programming problem and hence can be solved efficiently. Experiments show that our method effectively improves deep model's adversarial robustness.
Example Output: An adversarial defense method bridging robustness of deep neural nets with Lyapunov stability

Example Input: 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.

Example Output: 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.

Example Input: We present a representation for describing transition models in complex uncertain domains using relational rules.   For any action, a rule selects a set of relevant objects and computes a distribution over properties of just those objects in the resulting state given their properties in the previous state.   An iterative greedy algorithm is used to construct a set of deictic references that determine which objects are relevant in any given state.    Feed-forward neural networks are used to learn the transition distribution on the relevant objects' properties.   This strategy is demonstrated to be both more versatile and more sample efficient than learning a monolithic transition model in a simulated domain in which a robot pushes stacks of objects on a cluttered table.
Example Output:
A new approach that learns a representation for describing transition models in complex uncertaindomains using relational rules.