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:
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective.

In this paper we introduce the building blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression.

Ex Output:
We introduce Spherical CNNs, a convolutional network for spherical signals, and apply it to 3D model recognition and molecular energy regression.

Ex Input:
As deep learning-based classifiers are increasingly adopted in real-world applications, the importance of understanding how a particular label is chosen grows. Single decision trees are an example of a simple, interpretable classifier, but are unsuitable for use with complex, high-dimensional data. On the other hand, the variational autoencoder (VAE) is designed to learn a factored, low-dimensional representation of data, but typically encodes high-likelihood data in an intrinsically non-separable way. We introduce the differentiable decision tree (DDT) as a modular component of deep networks and a simple, differentiable loss function that allows for end-to-end optimization of a deep network to compress high-dimensional data for classification by a single decision tree. We also explore the power of labeled data in a supervised VAE (SVAE) with a Gaussian mixture prior, which leverages label information to produce a high-quality generative model with improved bounds on log-likelihood. We combine the SVAE with the DDT to get our classifier+VAE (C+VAE), which is competitive in both classification error and log-likelihood, despite optimizing both simultaneously and using a very simple encoder/decoder architecture.

Ex Output:
We combine differentiable decision trees with supervised variational autoencoders to enhance interpretability of classification.

Ex Input:
Deep convolutional neural networks (CNNs) are known to be robust against label noise on extensive datasets. However, at the same time, CNNs are capable of memorizing all labels even if they are random, which means they can memorize corrupted labels. Are CNNs robust or fragile to label noise? Much of researches focusing on such memorization uses class-independent label noise to simulate label corruption, but this setting is simple and unrealistic. In this paper, we investigate the behavior of CNNs under class-dependently simulated label noise, which is generated based on the conceptual distance between classes of a large dataset (i.e., ImageNet-1k). Contrary to previous knowledge, we reveal CNNs are more robust to such class-dependent label noise than class-independent label noise. We also demonstrate the networks under class-dependent noise situations learn similar representation to the no noise situation, compared to class-independent noise situations.

Ex Output:
Are CNNs robust or fragile to label noise? Practically, robust.