TASK DEFINITION: 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.
PROBLEM: Whereas it is believed that techniques such as Adam, batch normalization and, more recently, SeLU nonlinearities ``solve'' the exploding gradient problem, we show that this is not the case and that in a range of popular MLP architectures, exploding gradients exist and that they limit the depth to which networks can be effectively trained, both in theory and in practice. We explain why exploding gradients occur and highlight the {\it collapsing domain problem}, which can arise in architectures that avoid exploding gradients. 

 ResNets have significantly lower gradients and thus can circumvent the exploding gradient problem, enabling the effective training of much deeper networks, which we show is a consequence of a surprising mathematical property. By noticing that {\it any neural network is a residual network}, we devise the {\it residual trick}, which reveals that introducing skip connections simplifies the network mathematically, and that this simplicity may be the major cause for their success.

SOLUTION: We show that in contras to popular wisdom, the exploding gradient problem has not been solved and that it limits the depth to which MLPs can be effectively trained. We show why gradients explode and how ResNet handles them.

PROBLEM: Recurrent neural networks (RNNs) can model natural language by sequentially ''reading'' input tokens and outputting a distributed representation of each token. Due to the sequential nature of RNNs, inference time is linearly dependent on the input length, and all inputs are read regardless of their importance. Efforts to speed up this inference, known as ''neural speed reading'', either ignore or skim over part of the input. We present Structural-Jump-LSTM: the first neural speed reading model to both skip and jump text during inference. The model consists of a standard LSTM and two agents: one capable of skipping single words when reading, and one capable of exploiting punctuation structure (sub-sentence separators (,:), sentence end symbols (.!?), or end of text markers) to jump ahead after reading a word.
 A comprehensive experimental evaluation of our model against all five state-of-the-art neural reading models shows that 
 Structural-Jump-LSTM achieves the best overall floating point operations (FLOP) reduction (hence is faster), while keeping the same accuracy or even improving it compared to a vanilla LSTM that reads the whole text.

SOLUTION: We propose a new model for neural speed reading that utilizes the inherent punctuation structure of a text to define effective jumping and skipping behavior.

PROBLEM: High-dimensional data often lie in or close to low-dimensional subspaces. Sparse subspace clustering methods with sparsity induced by L0-norm, such as L0-Sparse Subspace Clustering (L0-SSC), are demonstrated to be more effective than its L1 counterpart such as Sparse Subspace Clustering (SSC). However, these L0-norm based subspace clustering methods are restricted to clean data that lie exactly in subspaces. Real data often suffer from noise and they may lie close to subspaces. We propose noisy L0-SSC to handle noisy data so as to improve the robustness. We show that the optimal solution to the optimization problem of noisy L0-SSC achieves subspace detection property (SDP), a key element with which data from different subspaces are separated, under deterministic and randomized models. Our results provide theoretical guarantee on the correctness of noisy L0-SSC in terms of SDP on noisy data. We further propose Noisy-DR-L0-SSC which provably recovers the subspaces on dimensionality reduced data. Noisy-DR-L0-SSC first projects the data onto a lower dimensional space by linear transformation, then performs noisy L0-SSC on the dimensionality reduced data so as to improve the efficiency. The experimental results demonstrate the effectiveness of noisy L0-SSC and Noisy-DR-L0-SSC.

SOLUTION:
We propose Noisy-DR-L0-SSC (Noisy Dimension Reduction L0-Sparse Subspace Clustering) to efficiently partition noisy data in accordance to their underlying subspace structure.