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.

[Q]: 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.
[A]: We combine differentiable decision trees with supervised variational autoencoders to enhance interpretability of classification. 


[Q]: A distinct commonality between HMMs and RNNs is that they both learn hidden representations for sequential data. In addition, it has been noted that the backward computation of the Baum-Welch algorithm for HMMs is a special case of the back-propagation algorithm used for neural networks (Eisner (2016)). Do these observations suggest that, despite their many apparent differences, HMMs are a special case of RNNs? In this paper, we show that that is indeed the case, and investigate a series of architectural transformations between HMMs and RNNs, both through theoretical derivations and empirical hybridization. In particular, we investigate three key design factors—independence assumptions between the hidden states and the observation, the placement of softmaxes, and the use of non-linearities—in order to pin down their empirical effects. We present a comprehensive empirical study to provide insights into the interplay between expressivity and interpretability in this model family with respect to language modeling and parts-of-speech induction.
[A]: Are HMMs a special case of RNNs? We investigate a series of architectural transformations between HMMs and RNNs, both through theoretical derivations and empirical hybridization and provide new insights.


[Q]: We present a method for translating music across musical instruments and styles. This method is based on unsupervised training of a multi-domain wavenet autoencoder, with a shared encoder and a domain-independent latent space that is trained end-to-end on waveforms. Employing a diverse training dataset and large net capacity, the single encoder allows us to translate also from musical domains that were not seen during training. We evaluate our method on a dataset collected from professional musicians, and achieve convincing translations. We also study the properties of the obtained translation and demonstrate translating even from a whistle, potentially enabling the creation of instrumental music by untrained humans.
[A]:
An automatic method for converting music between instruments and styles