The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.. The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience -Albert Einstein, 1933 INTRODUCTIONDeep learning shows unparalleled promise for solving very complex real-world problems in areas such as computer vision, natural language processing, knowledge representation, recommendation systems, drug discovery, and many more. With this development, the field of machine learning is moving from traditional feature engineering to neural architecture engineering. However, still little is known about how to pick the right architecture to solve a specific task. Several methods such as translational equivariance in convolutional layers, recurrence, structured weight sharing, pooling, or locality are used to introduce strong inductive biases in the model design. Yet, the exact model size and capacity required for a task remain unknown and a common strategy is to train overparameterized models and compress them into smaller representations. Biological brains, especially the human brain, are hierarchical, sparse, and recurrent structures [Friston 2008] and one can draw some similarities with the inductive biases in today's artificial neural networks. Sparsity plays an important role in scaling biological brains-the more

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We examine the question of whether SGD-based optimization of deep neural networks (DNNs) can be adapted to produce models which are both highly-accurate and easily-compressible. We propose a new compression-aware minimizer dubbed CrAM, which modifies the SGD training iteration in a principled way, in order to produce models whose local loss behavior is stable under compression operations such as weight pruning or quantization. Experimental results on standard image classification tasks show that CrAM produces dense models that can be more accurate than standard SGD-type baselines, but which are surprisingly stable under weight pruning: for instance, for ResNet50 on ImageNet, CrAM-trained models can lose up to 70% of their weights in one shot with only minor accuracy loss.

Transfer learning is a classic paradigm by which models pretrained on large "upstream" datasets are adapted to yield good results on "downstream," specialized datasets. Generally, it is understood that more accurate models on the "upstream" dataset will provide better transfer accuracy "downstream". In this work, we perform an in-depth investigation of this phenomenon in the context of convolutional neural networks (CNNs) trained on the ImageNet dataset, which have been pruned-that is, compressed by sparsifiying their connections. Specifically, we consider transfer using unstructured pruned models obtained by applying several state-of-the-art pruning methods, including magnitude-based, second-order, re-growth and regularization approaches, in the context of twelve standard transfer tasks. In a nutshell, our study shows that sparse models can match or even outperform the transfer performance of dense models, even at high sparsities, and, while doing so, can lead to significant inference and even training speedups. At the same time, we observe and analyze significant differences in the behaviour of different pruning methods.