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:
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.

Ex Output:
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.


Ex Input:
Training methods for deep networks are primarily variants on stochastic gradient descent.   Techniques that use (approximate) second-order information are rarely used because of the computational cost and noise associated with those approaches in deep learning contexts.   However, in this paper, we show how feedforward deep networks exhibit a low-rank derivative structure.   This low-rank structure makes it possible to use second-order information without needing approximations and without incurring a significantly greater computational cost than gradient descent.   To demonstrate this capability, we implement Cubic Regularization (CR) on a feedforward deep network with stochastic gradient descent and two of its variants.   There, we use CR to calculate learning rates on a per-iteration basis while training on the MNIST and CIFAR-10 datasets.   CR proved particularly successful in escaping plateau regions of the objective function.   We also found that this approach requires less problem-specific information (e.g. an optimal initial learning rate) than other first-order methods in order to perform well.

Ex Output:
We show that deep learning network derivatives have a low-rank structure, and this structure allows us to use second-order derivative information to calculate learning rates adaptively and in a computationally feasible manner.


Ex Input:
In high dimensions, the performance of nearest neighbor algorithms depends crucially on structure in the data.
 While traditional nearest neighbor datasets consisted mostly of hand-crafted feature vectors, an increasing number of datasets comes from representations learned with neural networks.
 We study the interaction between nearest neighbor algorithms and neural networks in more detail.
 We find that the network architecture can significantly influence the efficacy of nearest neighbor algorithms even when the classification accuracy is unchanged.
 Based on our experiments, we propose a number of training modifications that lead to significantly better datasets for nearest neighbor algorithms.
 Our modifications lead to learned representations that can accelerate nearest neighbor queries by 5x.

Ex Output:

We show how to get good representations from the point of view of Simiarity Search.