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: Sometimes SRS (Stereotactic Radio Surgery) requires using sphere packing on a Region of Interest (ROI) such as cancer to determine a treatment plan.   We have developed a sphere packing algorithm which packs non-intersecting spheres inside the ROI.   The region of interest in our case are those voxels which are identified as cancer tissues.   In this paper, we analyze the rotational invariant properties of  our sphere-packing algorithm which is based on distance transformations. Epsilon-Rotation invariant means the ability to arbitrary rotate the 3D ROI while keeping the volume properties remaining (almost) same within some limit of epsilon. The applied rotations produce spherical packing which remains highly correlated as we analyze the geometrically properties of sphere packing before and after the rotation of the volume data for the ROI. Our novel sphere packing algorithm has high degree of rotation invariance within the range of +/- epsilon. Our method used a shape descriptor derived from the values of the disjoint set of spheres form the distance-based sphere packing algorithm to extract the invariant descriptor from the ROI. We demonstrated by implementing these ideas using Slicer3D platform available for our research.   The data is based on sing MRI Stereotactic images. We presented several performance results on different benchmarks data of over 30 patients in Slicer3D platform.
Example Output: Packing region of Interest (ROI) such as cancerous regions identified in 3D Volume Data, Packing spheres inside the ROI, rotating the ROI , measures of difference in sphere packing before and after the rotation.

Example Input: Determining the optimal order in which data examples are presented to Deep Neural Networks during training is a non-trivial problem. However, choosing a non-trivial scheduling method may drastically improve convergence. In this paper, we propose a Self-Paced Learning (SPL)-fused Deep Metric Learning (DML) framework, which we call Learning Embeddings for Adaptive Pace (LEAP). Our method parameterizes mini-batches dynamically based on the \textit{easiness} and \textit{true diverseness} of the sample within a salient feature representation space. In LEAP, we train an \textit{embedding} Convolutional Neural Network (CNN) to learn an expressive representation space by adaptive density discrimination using the Magnet Loss. The \textit{student} CNN classifier dynamically selects samples to form a mini-batch based on the \textit{easiness} from cross-entropy losses and \textit{true diverseness} of examples from the representation space sculpted by the \textit{embedding} CNN. We evaluate LEAP using deep CNN architectures for the task of supervised image classification on MNIST, FashionMNIST, CIFAR-10, CIFAR-100, and SVHN. We show that the LEAP framework converges faster with respect to the number of mini-batch updates required to achieve a comparable or better test performance on each of the datasets.
Example Output: LEAP combines the strength of adaptive sampling with that of mini-batch online learning and adaptive representation learning to formulate a representative self-paced strategy in an end-to-end DNN training protocol. 

Example Input: The existence of adversarial examples, or intentional mis-predictions constructed from small changes to correctly predicted examples, is one of the most significant challenges in neural network research today. Ironically, many new defenses are based on a simple observation - the adversarial inputs themselves are not robust and small perturbations to the attacking input often recover the desired prediction. While the intuition is somewhat clear, a detailed understanding of this phenomenon is missing from the research literature. This paper presents a comprehensive experimental analysis of when and why perturbation defenses work and potential mechanisms that could explain their effectiveness (or ineffectiveness) in different settings.
Example Output:
We identify a family of defense techniques and show that both deterministic lossy compression and randomized perturbations to the input lead to similar gains in robustness.