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:
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.

Ex 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.

Ex Input:
The Variational Auto Encoder (VAE) is a popular generative
latent variable model that is often
applied for representation learning.
Standard VAEs assume continuous valued
latent variables and are trained by maximization
of the evidence lower bound (ELBO). Conventional methods obtain a
differentiable estimate of the ELBO with reparametrized sampling and
optimize it with Stochastic Gradient Descend (SGD). However, this is not possible if
we want to train VAEs with discrete valued latent variables,
since reparametrized sampling is not possible. Till now, there
exist no simple solutions to circumvent this problem.
In this paper, we propose an easy method to train VAEs
with binary or categorically valued latent representations. Therefore, we use a differentiable
estimator for the ELBO which is based on importance sampling. In experiments, we verify the approach and
train two different VAEs architectures with Bernoulli and
Categorically distributed latent representations on two different benchmark
datasets.

Ex Output:
We propose an easy method to train Variational Auto Encoders (VAE) with discrete latent representations, using importance sampling

Ex Input:
In this paper, we consider the problem of detecting object under occlusion. Most object detectors formulate bounding box regression as a unimodal task (i.e., regressing a single set of bounding box coordinates independently). However, we observe that the bounding box borders of an occluded object can have multiple plausible configurations. Also, the occluded bounding box borders have correlations with visible ones. Motivated by these two observations, we propose a deep multivariate mixture of Gaussians model for bounding box regression under occlusion. The mixture components potentially learn different configurations of an occluded part, and the covariances between variates help to learn the relationship between the occluded parts and the visible ones. Quantitatively, our model improves the AP of the baselines by 3.9% and 1.2% on CrowdHuman and MS-COCO respectively with almost no computational or memory overhead. Qualitatively, our model enjoys explainability since we can interpret the resulting bounding boxes via the covariance matrices and the mixture components.

Ex Output:
a deep multivariate mixture of Gaussians model for bounding box regression under occlusion