instruction:
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.
question:
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.
answer:
We combine differentiable decision trees with supervised variational autoencoders to enhance interpretability of classification. 


question:
The vast majority of natural sensory data is temporally redundant. For instance, video frames or audio samples which are sampled at nearby points in time tend to have similar values.   Typically, deep learning algorithms take no advantage of this redundancy to reduce computations.   This can be an obscene waste of energy.   We present a variant on backpropagation for neural networks in which computation scales with the rate of change of the data - not the rate at which we process the data.   We do this by implementing a form of Predictive Coding wherein neurons communicate a combination of their state, and their temporal change in state, and quantize this signal using Sigma-Delta modulation.   Intriguingly, this simple communication rule give rise to units that resemble biologically-inspired leaky integrate-and-fire neurons, and to a spike-timing-dependent weight-update similar to Spike-Timing Dependent Plasticity (STDP), a synaptic learning rule observed in the brain.   We demonstrate that on MNIST, on a temporal variant of MNIST, and on Youtube-BB, a dataset with videos in the wild, our algorithm performs about as well as a standard deep network trained with backpropagation, despite only communicating discrete values between layers.  
answer:
An algorithm for training neural networks efficiently on temporally redundant data.


question:
Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.
answer:

We train in random subspaces of parameter space to measure how many dimensions are really needed to find a solution.