You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Pruning neural network parameters to reduce model size is an area of much interest, but the original motivation for pruning was the prevention of overfitting rather than the improvement of computational efficiency. This motivation is particularly relevant given the perhaps surprising observation that a wide variety of pruning approaches confer increases in test accuracy, even when parameter counts are drastically reduced. To better understand this phenomenon, we analyze the behavior of pruning over the course of training, finding that pruning's effect on generalization relies more on the instability generated by pruning than the final size of the pruned model. We demonstrate that even pruning of seemingly unimportant parameters can lead to such instability, allowing our finding to account for the generalization benefits of modern pruning techniques. Our results ultimately suggest that, counter-intuitively, pruning regularizes through instability and mechanisms unrelated to parameter counts.

Cited Abstract(s):
[1]: We have used information-theoretic ideas to derive a class of practical and nearly optimal schemes for adapting the size of a neural network. By removing unimportant weights from a network, several improvements can be expected: better generalization, fewer training examples required, and improved speed of learning and or classification. The basic idea is to use second-derivative information to make a tradeoff between network complexity and training set error. Experiments confirm the usefulness of the methods on a real-world application.

[2]: The deployment of deep convolutional neural networks (CNNs) in many real world applications is largely hindered by their high computational cost. In this paper, we propose a novel learning scheme for CNNs to simultaneously 1) reduce the model size; 2) decrease the run-time memory footprint; and 3) lower the number of computing operations, without compromising accuracy. This is achieved by enforcing channel-level sparsity in the network in a simple but effective way. Different from many existing approaches, the proposed method directly applies to modern CNN architectures, introduces minimum overhead to the training process, and requires no special software hardware accelerators for the resulting models. We call our approach network slimming, which takes wide and large networks as input models, but during training insignificant channels are automatically identified and pruned afterwards, yielding thin and compact models with comparable accuracy. We empirically demonstrate the effectiveness of our approach with several state-of-the-art CNN models, including VGGNet, ResNet and DenseNet, on various image classification datasets. For VGGNet, a multi-pass version of network slimming gives a 20× reduction in model size and a 5× reduction in computing operations.

[3]: 

[4]: Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems. Also, conventional networks fix the architecture before training starts; as a result, training cannot improve the architecture. To address these limitations, we describe a method to reduce the storage and computation required by neural networks by an order of magnitude without affecting their accuracy by learning only the important connections. Our method prunes redundant connections using a three-step method. First, we train the network to learn which connections are important. Next, we prune the unimportant connections. Finally, we retrain the network to fine tune the weights of the remaining connections. On the ImageNet dataset, our method reduced the number of parameters of AlexNet by a factor of 9x, from 61 million to 6.7 million, without incurring accuracy loss. Similar experiments with VGG-16 found that the total number of parameters can be reduced by 13x, from 138 million to 10.3 million, again with no loss of accuracy.

[5]: 

[6]: We rigorously evaluate three state-of-the-art techniques for inducing sparsity in deep neural networks on two large-scale learning tasks: Transformer trained on WMT 2014 English-to-German, and ResNet-50 trained on ImageNet. Across thousands of experiments, we demonstrate that complex techniques (, 2017; , 2017b) shown to yield high compression rates on smaller datasets perform inconsistently, and that simple magnitude pruning approaches achieve comparable or better results. Additionally, we replicate the experiments performed by (Frankle & Carbin, 2018) and (, 2018) at scale and show that unstructured sparse architectures learned through pruning cannot be trained from scratch to the same test set performance as a model trained with joint sparsification and optimization. Together, these results highlight the need for large-scale benchmarks in the field of model compression. We open-source our code, top performing model checkpoints, and results of all hyperparameter configurations to establish rigorous baselines for future work on compression and sparsification.

[7]: 

[8]: We investigate the use of information from all second order derivatives of the error function to perform network pruning (i.e., removing unimportant weights from a trained network) in order to improve generalization, simplify networks, reduce hardware or storage requirements, increase the speed of further training, and in some cases enable rule extraction. Our method, Optimal Brain Surgeon (OBS), is Significantly better than magnitude-based methods and Optimal Brain Damage [Le Cun, Denker and Solla, 1990], which often remove the wrong weights. OBS permits the pruning of more weights than other methods (for the same error on the training set), and thus yields better generalization on test data. Crucial to OBS is a recursion relation for calculating the inverse Hessian matrix H-1 from training data and structural information of the net. OBS permits a 90 , a 76 , and a 62 reduction in weights over backpropagation with weight decay on three benchmark MONK's problems [, 1991]. Of OBS, Optimal Brain Damage, and magnitude-based methods, only OBS deletes the correct weights from a trained XOR network in every case. Finally, whereas Sejnowski and Rosenberg [1987] used 18,000 weights in their NETtalk network, we used OBS to prune a network to just 1560 weights, yielding better generalization.
There are various approaches to pruning neural networks. Pruning may be performed after training a model to convergence [1] [8] [4] [2] , or throughout the training process such that there are multiple pruning events as the model trains [7] [3] [5] . While these methods share the goal of pruning parameters that appear unimportant to the function computed by the neural network, they differ greatly in their execution. For instance, magnitude pruning uses small-magnitude to indicate unimportance. Despite its simplicity, magnitude pruning has been shown to perform competitively with more sophisticated approaches to pruning [6] .