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.

Ex Input:
Many imaging tasks require global information about all pixels in an image. Conventional bottom-up classification networks globalize information by decreasing resolution; features are pooled and down-sampled into a single output. But for semantic segmentation and object detection tasks, a network must provide higher-resolution pixel-level outputs. To globalize information while preserving resolution, many researchers propose the inclusion of sophisticated auxiliary blocks, but these come at the cost of a considerable increase in network size and computational cost. This paper proposes stacked u-nets (SUNets), which iteratively combine features from different resolution scales while maintaining resolution. SUNets leverage the information globalization power of u-nets in a deeper net- work architectures that is capable of handling the complexity of natural images. SUNets perform extremely well on semantic segmentation tasks using a small number of parameters.

Ex Output:
Presents new architecture which leverages information globalization power of u-nets in a deeper networks and performs well across tasks without any bells and whistles.

Ex 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.

Ex Output:
An adversarial defense method bridging robustness of deep neural nets with Lyapunov stability

Ex Input:
We propose a new notion of 'non-linearity' of a network layer with respect to an input batch that is based on its proximity to a linear system, which is reflected in the non-negative rank of the activation matrix.
We measure this non-linearity by applying non-negative factorization to the activation matrix.
Considering batches of similar samples, we find that high non-linearity in deep layers is indicative of memorization. Furthermore, by applying our approach layer-by-layer, we find that the mechanism for memorization consists of distinct phases. We perform experiments on fully-connected and convolutional neural networks trained on several image and audio datasets. Our results demonstrate that as an indicator for memorization, our technique can be used to perform early stopping.

Ex Output:
We use the non-negative rank of ReLU activation matrices as a complexity measure and show it (negatively) correlates with good generalization.