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1. Pruning neural networks without any data by iteratively conserving synaptic flow

   Tanaka, H.; Kunin, D.; Yamins, Y.; Ganguli, S (December 2020, Advances in neural information processing systems)

   null (Ed.)

   Pruning the parameters of deep neural networks has generated intense interest due to potential savings in time, memory and energy both during training and at test time. Recent works have identified, through an expensive sequence of training and pruning cycles, the existence of winning lottery tickets or sparse trainable subnetworks at initialization. This raises a foundational question: can we identify highly sparse trainable subnetworks at initialization, without ever training, or indeed without ever looking at the data? We provide an affirmative answer to this question through theory driven algorithm design. We first mathematically formulate and experimentally verify a conservation law that explains why existing gradient-based pruning algorithms at initialization suffer from layer-collapse, the premature pruning of an entire layer rendering a network untrainable. This theory also elucidates how layer-collapse can be entirely avoided, motivating a novel pruning algorithm Iterative Synaptic Flow Pruning (SynFlow). This algorithm can be interpreted as preserving the total flow of synaptic strengths through the network at initialization subject to a sparsity constraint. Notably, this algorithm makes no reference to the training data and consistently competes with or outperforms existing state-of-the-art pruning algorithms at initialization over a range of models (VGG and ResNet), datasets (CIFAR-10/100 and Tiny ImageNet), and sparsity constraints (up to 99.99 percent). Thus our data-agnostic pruning algorithm challenges the existing paradigm that, at initialization, data must be used to quantify which synapses are important. 

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2. TPrune: Efficient Transformer Pruning for Mobile Devices

   https://doi.org/10.1145/3446640  

   Mao, Jiachen; Yang, Huanrui; Li, Ang; Li, Hai; Chen, Yiran (July 2021, ACM Transactions on Cyber-Physical Systems)

   null (Ed.)

   The invention of Transformer model structure boosts the performance of Neural Machine Translation (NMT) tasks to an unprecedented level. Many previous works have been done to make the Transformer model more execution-friendly on resource-constrained platforms. These researches can be categorized into three key fields: Model Pruning, Transfer Learning, and Efficient Transformer Variants. The family of model pruning methods are popular for their simplicity in practice and promising compression rate and have achieved great success in the field of convolution neural networks (CNNs) for many vision tasks. Nonetheless, previous Transformer pruning works did not perform a thorough model analysis and evaluation on each Transformer component on off-the-shelf mobile devices. In this work, we analyze and prune transformer models at the line-wise granularity and also implement our pruning method on real mobile platforms. We explore the properties of all Transformer components as well as their sparsity features, which are leveraged to guide Transformer model pruning. We name our whole Transformer analysis and pruning pipeline as TPrune. In TPrune, we first propose Block-wise Structured Sparsity Learning (BSSL) to analyze Transformer model property. Then, based on the characters derived from BSSL, we apply Structured Hoyer Square (SHS) to derive the final pruned models. Comparing with the state-of-the-art Transformer pruning methods, TPrune is able to achieve a higher model compression rate with less performance degradation. Experimental results show that our pruned models achieve 1.16×–1.92× speedup on mobile devices with 0%–8% BLEU score degradation compared with the original Transformer model. 

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3. On the Neural Tangent Kernel Analysis of Randomly Pruned Neural Networks

   Yang, Hongru; Wang, Zhangyang (April 2023, International Conference on Artificial Intelligence and Statistics)

   Motivated by both theory and practice, we study how random pruning of the weights affects a neural network's neural tangent kernel (NTK). In particular, this work establishes an equivalence of the NTKs between a fully-connected neural network and its randomly pruned version. The equivalence is established under two cases. The first main result studies the infinite-width asymptotic. It is shown that given a pruning probability, for fully-connected neural networks with the weights randomly pruned at the initialization, as the width of each layer grows to infinity sequentially, the NTK of the pruned neural network converges to the limiting NTK of the original network with some extra scaling. If the network weights are rescaled appropriately after pruning, this extra scaling can be removed. The second main result considers the finite-width case. It is shown that to ensure the NTK's closeness to the limit, the dependence of width on the sparsity parameter is asymptotically linear, as the NTK's gap to its limit goes down to zero. Moreover, if the pruning probability is set to zero (i.e., no pruning), the bound on the required width matches the bound for fully-connected neural networks in previous works up to logarithmic factors. The proof of this result requires developing a novel analysis of a network structure which we called mask-induced pseudo-networks. Experiments are provided to evaluate our results. 

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4. Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions

   Cai, Junyang; Nguyen, Khai-Nguyen; Shrestha, Nishant; Good, Aidan; Tu, Ruisen; Yu, Xin; Zhe, Shandian; Serra, Thiago (January 2023, International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research)

   One surprising trait of neural networks is the extent to which their connections can be pruned with little to no effect on accuracy. But when we cross a critical level of parameter sparsity, pruning any further leads to a sudden drop in accuracy. This drop plausibly reflects a loss in model complexity, which we aim to avoid. In this work, we explore how sparsity also affects the geometry of the linear regions defined by a neural network, and consequently reduces the expected maximum number of linear regions based on the architecture. We observe that pruning affects accuracy similarly to how sparsity affects the number of linear regions and our proposed bound for the maximum number. Conversely, we find out that selecting the sparsity across layers to maximize our bound very often improves accuracy in comparison to pruning as much with the same sparsity in all layers, thereby providing us guidance on where to prune. 

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5. Rare Gems: Finding Lottery Tickets at Initialization

   Sreenivasan, Kartik; Sohn, Jy-yong; Yang, Liu; Grinde, Matthew; Nagle, Alliot; Wang, Hongyi; Xing, Eric; Lee, Kangwook; Papailiopoulos, Dimitris (January 2022, Advances in neural information processing systems)

   Large neural networks can be pruned to a small fraction of their original size, with little loss in accuracy, by following a time-consuming "train, prune, re-train" approach. Frankle & Carbin conjecture that we can avoid this by training lottery tickets, i.e., special sparse subnetworks found at initialization, that can be trained to high accuracy. However, a subsequent line of work presents concrete evidence that current algorithms for finding trainable networks at initialization, fail simple baseline comparisons, e.g., against training random sparse subnetworks. Finding lottery tickets that train to better accuracy compared to simple baselines remains an open problem. In this work, we resolve this open problem by proposing Gem-Miner which finds lottery tickets at initialization that beat current baselines. Gem-Miner finds lottery tickets trainable to accuracy competitive or better than Iterative Magnitude Pruning (IMP), and does so up to 19x faster. 

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