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.

Example Input: In this paper, we introduce a novel method to interpret recurrent neural networks (RNNs), particularly long short-term memory networks (LSTMs) at the cellular level. We propose a systematic pipeline for interpreting individual hidden state dynamics within the network using response characterization methods. The ranked contribution of individual cells to the network's output is computed by analyzing a set of interpretable metrics of their decoupled step and sinusoidal responses. As a result, our method is able to uniquely identify neurons with insightful dynamics, quantify relationships between dynamical properties and test accuracy through ablation analysis, and interpret the impact of network capacity on a network's dynamical distribution. Finally, we demonstrate generalizability and scalability of our method by evaluating a series of different benchmark sequential datasets.
Example Output: Introducing the response charactrization method for interpreting cell dynamics in learned long short-term memory (LSTM) networks. 

Example 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.
Example 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.

Example Input: We provide a novel perspective on the forward pass through a block of layers in a deep network. In particular, we show that a forward pass through a standard dropout layer followed by a linear layer and a non-linear activation is equivalent to optimizing a convex objective with a single iteration of a $\tau$-nice Proximal Stochastic Gradient method. We further show that replacing standard Bernoulli dropout with additive dropout is equivalent to optimizing the same convex objective with a variance-reduced proximal method. By expressing both fully-connected and convolutional layers as special cases of a high-order tensor product, we unify the underlying convex optimization problem in the tensor setting and derive a formula for the Lipschitz constant $L$ used to determine the optimal step size of the above proximal methods. We conduct experiments with standard convolutional networks applied to the CIFAR-10 and CIFAR-100 datasets and show that replacing a block of layers with multiple iterations of the corresponding solver, with step size set via $L$, consistently improves classification accuracy.
Example Output:
A framework that links deep network layers to stochastic optimization algorithms; can be used to improve model accuracy and inform network design.