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.
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Question: Weight pruning has proven to be an effective method in reducing the model size and computation cost while not sacrificing the model accuracy. Conventional sparse matrix formats, however, involve irregular index structures with large storage requirement and sequential reconstruction process, resulting in inefficient use of highly parallel computing resources. Hence, pruning is usually restricted to inference with a batch size of one, for which an efficient parallel matrix-vector multiplication method exists. In this paper, a new class of sparse matrix representation utilizing Viterbi algorithm that has a high, and more importantly, fixed index compression ratio regardless of the pruning rate, is proposed. In this approach, numerous sparse matrix candidates are first generated by the Viterbi encoder, and then the one that aims to minimize the model accuracy degradation is selected by the Viterbi algorithm. The model pruning process based on the proposed Viterbi encoder and Viterbi algorithm is highly parallelizable, and can be implemented efficiently in hardware to achieve low-energy, high-performance index decoding process. Compared with the existing magnitude-based pruning methods, index data storage requirement can be further compressed by 85.2% in MNIST and 83.9% in AlexNet while achieving similar pruning rate. Even compared with the relative index compression technique, our method can still reduce the index storage requirement by 52.7% in MNIST and 35.5% in AlexNet.

Answer: We present a new pruning method and sparse matrix format to enable high index compression ratio and parallel index decoding process.

Question: We extend the recent results of (Arora et al., 2019) by a spectral analysis of representations corresponding to kernel and neural embeddings. They showed that in a simple single layer network, the alignment of the labels to the eigenvectors of the corresponding Gram matrix determines both the convergence of the optimization during training as well as the generalization properties. We generalize their result to kernel and neural representations and show that these extensions improve both optimization and generalization of the basic setup studied in (Arora et al., 2019).

Answer: Spectral analysis for understanding how different representations can improve optimization and generalization.

Question: Auto-encoders are commonly used for unsupervised representation learning and for pre-training deeper neural networks.
When its activation function is linear and the encoding dimension (width of hidden layer) is smaller than the input dimension, it is well known that auto-encoder is optimized to learn the principal components of the data distribution (Oja1982).
However, when the activation is nonlinear and when the width is larger than the input dimension (overcomplete), auto-encoder behaves differently from PCA, and in fact is known to perform well empirically for sparse coding problems.

We provide a theoretical explanation for this empirically observed phenomenon, when rectified-linear unit (ReLu) is adopted as the activation function and the hidden-layer width is set to be large.
In this case, we show that, with significant probability, initializing the weight matrix of an auto-encoder by sampling from a spherical Gaussian distribution followed by stochastic gradient descent (SGD) training converges towards the ground-truth representation for a class of sparse dictionary learning models.
In addition, we can show that, conditioning on convergence, the expected convergence rate is O(1/t), where t is the number of updates.
Our analysis quantifies how increasing hidden layer width helps the training performance when random initialization is used, and how the norm of network weights influence the speed of SGD convergence.

Answer:
theoretical analysis of nonlinear wide autoencoder