The recent lottery ticket hypothesis proposes that there is one sub-network that matches the accuracy of the original network when trained in isolation. We show that instead each network contains several winning tickets, even if the initial weights are fixed. The resulting winning sub-networks are not instances of the same network under weight space symmetry, and show no overlap or correlation significantly larger than expected by chance. If randomness during training is decreased, overlaps higher than chance occur, even if the networks are trained on different tasks. We conclude that there is rather a distribution over capable sub-networks, as opposed to a single winning ticket.
The success of lottery ticket initializations (Frankle and Carbin, 2019) suggests that small, sparsified networks can be trained so long as the network is initialized appropriately. Unfortunately, finding these "winning ticket" initializations is computationally expensive. One potential solution is to reuse the same winning tickets across a variety of datasets and optimizers. However, the generality of winning ticket initializations remains unclear. Here, we attempt to answer this question by generating winning tickets for one training configuration (optimizer and dataset) and evaluating their…
Eötvös Loránd University（厄特沃什·罗兰大学）；Alfréd Rényi Institute of Mathematics（阿尔弗雷德·雷尼数学研究所）
The Lottery Ticket Hypothesis postulates that a freshly initialized neural network contains a small subnetwork that can be trained in isolation to achieve similar performance as the full network. Our paper examines several alternatives to search for such subnetworks. We conclude that incorporating a data dependent component into the pruning criterion in the form of the gradient of the training loss -- as done in the SNIP method -- consistently improves the performance of existing pruning algorithms.
The lottery ticket hypothesis (LTH) has attracted attention because it can explain why over-parameterized models often show high generalization ability. It is known that when we use iterative magnitude pruning (IMP), which is an algorithm to find sparse networks with high generalization ability that can be trained from the initial weights independently, called winning tickets, the initial large learning rate does not work well in deep neural networks such as ResNet. However, since the initial large learning rate generally helps the optimizer to converge to flatter minima, we hypothesize that t…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
The lottery ticket hypothesis has sparked the rapid development of pruning algorithms that aim to reduce the computational costs associated with deep learning during training and model deployment. Currently, such algorithms are primarily evaluated on imaging data, for which we lack ground truth information and thus the understanding of how sparse lottery tickets could be. To fill this gap, we develop a framework that allows us to plant and hide winning tickets with desirable properties in randomly initialized neural networks. To analyze the ability of state-of-the-art pruning to identify ticke…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Microsoft Corporation（微软公司）；Tsinghua University（清华大学）
Lottery Ticket Hypothesis (LTH) raises keen attention to identifying sparse trainable subnetworks, or winning tickets, which can be trained in isolation to achieve similar or even better performance compared to the full models. Despite many efforts being made, the most effective method to identify such winning tickets is still Iterative Magnitude-based Pruning (IMP), which is computationally expensive and has to be run thoroughly for every different network. A natural question that comes in is: can we "transform" the winning ticket found in one network to another with a different architecture,…
The lottery ticket hypothesis suggests that sparse, sub-networks of a given neural network, if initialized properly, can be trained to reach comparable or even better performance to that of the original network. Prior works in lottery tickets have primarily focused on the supervised learning setup, with several papers proposing effective ways of finding "winning tickets" in classification problems. In this paper, we confirm the existence of winning tickets in deep generative models such as GANs and VAEs. We show that the popular iterative magnitude pruning approach (with late rewinding) can be…
The recently proposed Lottery Ticket Hypothesis of Frankle and Carbin (2019) suggests that the performance of over-parameterized deep networks is due to the random initialization seeding the network with a small fraction of favorable weights. These weights retain their dominant status throughout training -- in a very real sense, this sub-network "won the lottery" during initialization. The authors find sub-networks via unstructured magnitude pruning with 85-95% of parameters removed that train to the same accuracy as the original network at a similar speed, which they call winning tickets. In …
Northeastern University（东北大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Midea Group（美的集团）；Michigan State University（密歇根州立大学）
There have been long-standing controversies and inconsistencies over the experiment setup and criteria for identifying the "winning ticket" in literature. To reconcile such, we revisit the definition of lottery ticket hypothesis, with comprehensive and more rigorous conditions. Under our new definition, we show concrete evidence to clarify whether the winning ticket exists across the major DNN architectures and/or applications. Through extensive experiments, we perform quantitative analysis on the correlations between winning tickets and various experimental factors, and empirically study the …
The underlying loss landscapes of deep neural networks have a great impact on their training, but they have mainly been studied theoretically due to computational constraints. This work vastly reduces the time required to compute such loss landscapes, and uses them to study winning lottery tickets found via iterative magnitude pruning. We also share results that contradict previously claimed correlations between certain loss landscape projection methods and model trainability and generalization error.
University of California, Santa Barbara（加州大学圣巴巴拉分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Imperial College London（伦敦帝国理工学院）
Foundational work on the Lottery Ticket Hypothesis has suggested an exciting corollary: winning tickets found in the context of one task can be transferred to similar tasks, possibly even across different architectures. This has generated broad interest, but methods to study this universality are lacking. We make use of renormalization group theory, a powerful tool from theoretical physics, to address this need. We find that iterative magnitude pruning, the principal algorithm used for discovering winning tickets, is a renormalization group scheme, and can be viewed as inducing a flow in param…
Meta AI；MosaicML（MosaicML公司）；Google Research（谷歌研究院）；Mila（米拉人工智能研究所）
Modern deep learning involves training costly, highly overparameterized networks, thus motivating the search for sparser networks that can still be trained to the same accuracy as the full network (i.e. matching). Iterative magnitude pruning (IMP) is a state of the art algorithm that can find such highly sparse matching subnetworks, known as winning tickets. IMP operates by iterative cycles of training, masking smallest magnitude weights, rewinding back to an early training point, and repeating. Despite its simplicity, the underlying principles for when and how IMP finds winning tickets remain…
Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL（巴黎高等师范学院物理实验室，巴黎高等师范学院，巴黎文理研究大学）；CNRS（法国国家科学研究中心）；Sorbonne Université（索邦大学）；Université de Paris（巴黎大学）
Pruning methods can considerably reduce the size of artificial neural networks without harming their performance. In some cases, they can even uncover sub-networks that, when trained in isolation, match or surpass the test accuracy of their dense counterparts. Here we study the inductive bias that pruning imprints in such "winning lottery tickets". Focusing on visual tasks, we analyze the architecture resulting from iterative magnitude pruning of a simple fully connected network (FCN). We show that the surviving node connectivity is local in input space, and organized in patterns reminiscent o…
University of Science and Technology of China（中国科学技术大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Despite tremendous success in many application scenarios, the training and inference costs of using deep learning are also rapidly increasing over time. The lottery ticket hypothesis (LTH) emerges as a promising framework to leverage a special sparse subnetwork (i.e., winning ticket) instead of a full model for both training and inference, that can lower both costs without sacrificing the performance. The main resource bottleneck of LTH is however the extraordinary cost to find the sparse mask of the winning ticket. That makes the found winning ticket become a valuable asset to the owners, hig…
Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network given a specified tolerance of accuracy drop is still open. This paper provides one answer to this question by proposing a greedy optimization based pruning method. The proposed method has the guarantee that the discrepancy between the pruned network and the original network decays with exponentially fast rate w.r.t. the size of the pruned network, under weak…
TTI-Chicago（芝加哥丰田技术研究院）；University of Alberta（阿尔伯塔大学）；University of Chicago（芝加哥大学）
The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and…
Neural network pruning techniques can reduce the parameter counts of trained networks by over 90%, decreasing storage requirements and improving computational performance of inference without compromising accuracy. However, contemporary experience is that the sparse architectures produced by pruning are difficult to train from the start, which would similarly improve training performance. We find that a standard pruning technique naturally uncovers subnetworks whose initializations made them capable of training effectively. Based on these results, we articulate the "lottery ticket hypothesis:"…
University of Science and Technology of China（中国科学技术大学）
The proposition of lottery ticket hypothesis revealed the relationship between network structure and initialization parameters and the learning potential of neural networks. The original lottery ticket hypothesis performs pruning and weight resetting after training convergence, exposing it to the problem of forgotten learning knowledge and potential high cost of training. Therefore, we propose a strategy that combines the idea of neural network structure search with a pruning algorithm to alleviate this problem. This algorithm searches and extends the network structure on existing winning tick…
Nanjing University（南京大学）；Tencent AI Lab（腾讯人工智能实验室）；Hongkong University of Science and Technology（香港科技大学）
Modern deep neural networks (DNNs) are vulnerable to adversarial attacks and adversarial training has been shown to be a promising method for improving the adversarial robustness of DNNs. Pruning methods have been considered in adversarial context to reduce model capacity and improve adversarial robustness simultaneously in training. Existing adversarial pruning methods generally mimic the classical pruning methods for natural training, which follow the three-stage 'training-pruning-fine-tuning' pipelines. We observe that such pruning methods do not necessarily preserve the dynamics of dense n…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Northeastern University（东北大学）
The lottery ticket hypothesis (LTH) has shown that dense models contain highly sparse subnetworks (i.e., winning tickets) that can be trained in isolation to match full accuracy. Despite many exciting efforts being made, there is one "commonsense" rarely challenged: a winning ticket is found by iterative magnitude pruning (IMP) and hence the resultant pruned subnetworks have only unstructured sparsity. That gap limits the appeal of winning tickets in practice, since the highly irregular sparse patterns are challenging to accelerate on hardware. Meanwhile, directly substituting structured pruni…
Skin cancer affects a large population every year -- automated skin cancer detection algorithms can thus greatly help clinicians. Prior efforts involving deep learning models have high detection accuracy. However, most of the models have a large number of parameters, with some works even using an ensemble of models to achieve good accuracy. In this paper, we investigate a recently proposed pruning technique called Lottery Ticket Hypothesis. We find that iterative pruning of the network resulted in improved accuracy, compared to that of the unpruned network, implying that -- the lottery ticket …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Overparameterization has been shown to benefit both the optimization and generalization of neural networks, but large networks are resource hungry at both training and test time. Network pruning can reduce test-time resource requirements, but is typically applied to trained networks and therefore cannot avoid the expensive training process. We aim to prune networks at initialization, thereby saving resources at training time as well. Specifically, we argue that efficient training requires preserving the gradient flow through the network. This leads to a simple but effective pruning criterion w…
Zoho Labs（Zoho实验室）；Zoho Corporation（Zoho公司）；Copenhagen University（哥本哈根大学）；Univ. of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）
Large Transformer-based models were shown to be reducible to a smaller number of self-attention heads and layers. We consider this phenomenon from the perspective of the lottery ticket hypothesis, using both structured and magnitude pruning. For fine-tuned BERT, we show that (a) it is possible to find subnetworks achieving performance that is comparable with that of the full model, and (b) similarly-sized subnetworks sampled from the rest of the model perform worse. Strikingly, with structured pruning even the worst possible subnetworks remain highly trainable, indicating that most pre-trained…
Georgia Institute of Technology（佐治亚理工学院）；Microsoft Research（微软研究院）；Microsoft Azure AI（微软Azure人工智能部门）
The Lottery Ticket Hypothesis suggests that an over-parametrized network consists of ``lottery tickets'', and training a certain collection of them (i.e., a subnetwork) can match the performance of the full model. In this paper, we study such a collection of tickets, which is referred to as ``winning tickets'', in extremely over-parametrized models, e.g., pre-trained language models. We observe that at certain compression ratios, the generalization performance of the winning tickets can not only match but also exceed that of the full model. In particular, we observe a phase transition phenomen…
University of Science and Technology of China（中国科学技术大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
The lottery ticket hypothesis (LTH) reveals the existence of winning tickets (sparse but critical subnetworks) for dense networks, that can be trained in isolation from random initialization to match the latter's accuracies. However, finding winning tickets requires burdensome computations in the train-prune-retrain process, especially on large-scale datasets (e.g., ImageNet), restricting their practical benefits. This paper explores a new perspective on finding lottery tickets more efficiently, by doing so only with a specially selected subset of data, called Pruning-Aware Critical set (PrAC …
Midea Group（美的集团）；Northeastern University（东北大学）；Didi Chuxing（滴滴出行）；Snap Inc.（Snap公司）；Michigan State University（密歇根州立大学）
In deep model compression, the recent finding "Lottery Ticket Hypothesis" (LTH) (Frankle & Carbin, 2018) pointed out that there could exist a winning ticket (i.e., a properly pruned sub-network together with original weight initialization) that can achieve competitive performance than the original dense network. However, it is not easy to observe such winning property in many scenarios, where for example, a relatively large learning rate is used even if it benefits training the original dense model. In this work, we investigate the underlying condition and rationale behind the winning property…
Northeastern University（东北大学）；Santa Clara University（圣克拉拉大学）；Meta Research（Meta研究院）
Fully exploiting the learning capacity of neural networks requires overparameterized dense networks. On the other side, directly training sparse neural networks typically results in unsatisfactory performance. Lottery Ticket Hypothesis (LTH) provides a novel view to investigate sparse network training and maintain its capacity. Concretely, it claims there exist winning tickets from a randomly initialized network found by iterative magnitude pruning and preserving promising trainability (or we say being in trainable condition). In this work, we regard the winning ticket from LTH as the subnetwo…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Michigan State University（密歇根州立大学）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；University at Buffalo（布法罗大学）
The \textit{lottery ticket hypothesis} (LTH) states that learning on a properly pruned network (the \textit{winning ticket}) improves test accuracy over the original unpruned network. Although LTH has been justified empirically in a broad range of deep neural network (DNN) involved applications like computer vision and natural language processing, the theoretical validation of the improved generalization of a winning ticket remains elusive. To the best of our knowledge, our work, for the first time, characterizes the performance of training a pruned neural network by analyzing the geometric st…
Recent work on the Lottery Ticket Hypothesis (LTH) shows that there exist ``\textit{winning tickets}'' in large neural networks. These tickets represent ``sparse'' versions of the full model that can be trained independently to achieve comparable accuracy with respect to the full model. However, finding the winning tickets requires one to \emph{pretrain} the large model for at least a number of epochs, which can be a burdensome task, especially when the original neural network gets larger. In this paper, we explore how one can efficiently identify the emergence of such winning tickets, and use…
Random Masking Finds Winning Tickets for Parameter Efficient Fine-tuning
Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Shanghai Qizhi Institute（上海期智研究院）；Shanghai AI Laboratory（上海人工智能实验室）
Yonsei University（延世大学）；Korea Maritime and Ocean University（韩国海洋大学）；Deakin University（迪肯大学）；University of Oulu（奥卢大学）
The lottery ticket hypothesis (LTH) claims that a deep neural network (i.e., ground network) contains a number of subnetworks (i.e., winning tickets), each of which exhibiting identically accurate inference capability as that of the ground network. Federated learning (FL) has recently been applied in LotteryFL to discover such winning tickets in a distributed way, showing higher accuracy multi-task learning than Vanilla FL. Nonetheless, LotteryFL relies on unicast transmission on the downlink, and ignores mitigating stragglers, questioning scalability. Motivated by this, in this article we pro…
Winning Prize Comes from Losing Tickets: Improve Invariant Learning by Exploring Variant Parameters for Out-of-Distribution Generalization
Sydney AI Centre, The University of Sydney（悉尼大学悉尼人工智能中心）；JD Explore Academy（京东探索研究院）；University of Science and Technology of China（中国科学技术大学）；Nanjing University of Science and Technology（南京理工大学）；Hong Kong Baptist University（香港浸会大学）
Inspired by Regularized Lottery Ticket Hypothesis (RLTH), which states that competitive smooth (non-binary) subnetworks exist within a dense network in continual learning tasks, we investigate two proposed architecture-based continual learning methods which sequentially learn and select adaptive binary- (WSN) and non-binary Soft-Subnetworks (SoftNet) for each task. WSN and SoftNet jointly learn the regularized model weights and task-adaptive non-binary masks of subnetworks associated with each task whilst attempting to select a small set of weights to be activated (winning ticket) by reusing w…
Sparse models require less memory for storage and enable a faster inference by reducing the necessary number of FLOPs. This is relevant both for time-critical and on-device computations using neural networks. The stabilized lottery ticket hypothesis states that networks can be pruned after none or few training iterations, using a mask computed based on the unpruned converged model. On the transformer architecture and the WMT 2014 English-to-German and English-to-French tasks, we show that stabilized lottery ticket pruning performs similar to magnitude pruning for sparsity levels of up to 85%, …
