Sifting out the features by pruning: Are convolutional networks the winning lottery ticket of fully connected ones?
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 of the ones found in convolutional networks (CNN). We investigate the role played by data and tasks in shaping the architecture of pruned sub-networks. Our results show that the winning lottery tickets of FCNs display the key features of CNNs. The ability of such automatic network-simplifying procedure to recover the key features "hand-crafted" in the design of CNNs suggests interesting applications to other datasets and tasks, in order to discover new and efficient architectural inductive biases.
National University of Defense Technology（国防科技大学）；Chinese Academy of Sciences（中国科学院）
Neural architecture search (NAS) has brought significant progress in recent image recognition tasks. Most existing NAS methods apply restricted search spaces, which limits the upper-bound performance of searched models. To address this issue, we propose a new search space named MobileNet3-MT. By reducing human-prior knowledge in omni dimensions of networks, MobileNet3-MT accommodates more potential candidates. For searching in this challenging search space, we present an efficient Multi-trial Evolution-based NAS method termed MENAS. Specifically, we accelerate the evolutionary search process b…
Center for Applied Scientific Computing（应用科学计算中心）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Recently, Frankle & Carbin (2019) demonstrated that randomly-initialized dense networks contain subnetworks that once found can be trained to reach test accuracy comparable to the trained dense network. However, finding these high performing trainable subnetworks is expensive, requiring iterative process of training and pruning weights. In this paper, we propose (and prove) a stronger Multi-Prize Lottery Ticket Hypothesis: A sufficiently over-parameterized neural network with random weights contains several subnetworks (winning tickets) that (a) have comparable accuracy to a dense target netwo…
MIT EECS（麻省理工学院电气工程与计算机科学系）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）
Magnitude pruning is a common, effective technique to identify sparse subnetworks at little cost to accuracy. In this work, we ask whether a particular architecture's accuracy-sparsity tradeoff can be improved by combining pruning information across multiple runs of training. From a shared ResNet-20 initialization, we train several network copies (\emph{siblings}) to completion using different SGD data orders on CIFAR-10. While the siblings' pruning masks are naively not much more similar than chance, starting sibling training after a few epochs of shared pretraining significantly increases pr…
Illinois Institute of Technology（伊利诺伊理工学院）；Texas State University（德克萨斯州立大学）；Shandong University（山东大学）
With the remarkable success of deep learning recently, efficient network compression algorithms are urgently demanded for releasing the potential computational power of edge devices, such as smartphones or tablets. However, optimal network pruning is a non-trivial task which mathematically is an NP-hard problem. Previous researchers explain training a pruned network as buying a lottery ticket. In this paper, we investigate the Magnitude-Based Pruning (MBP) scheme and analyze it from a novel perspective through Fourier analysis on the deep learning model to guide model designation. Besides expl…
The Lottery Ticket Hypothesis (LTH) showed that by iteratively training a model, removing connections with the lowest global weight magnitude and rewinding the remaining connections, sparse networks can be extracted. This global comparison removes context information between connections within a layer. Here we study means for recovering some of this layer distributional context and generalise the LTH to consider weight importance values rather than global weight magnitudes. We find that given a repeatable training procedure, applying different importance metrics leads to distinct performant lo…
We propose the differentially private lottery ticket mechanism (DPLTM). An end-to-end differentially private training paradigm based on the lottery ticket hypothesis. Using "high-quality winners", selected via our custom score function, DPLTM significantly improves the privacy-utility trade-off over the state-of-the-art. We show that DPLTM converges faster, allowing for early stopping with reduced privacy budget consumption. We further show that the tickets from DPLTM are transferable across datasets, domains, and architectures. Our extensive evaluation on several public datasets provides evid…
The recent "Lottery Ticket Hypothesis" paper by Frankle & Carbin showed that a simple approach to creating sparse networks (keeping the large weights) results in models that are trainable from scratch, but only when starting from the same initial weights. The performance of these networks often exceeds the performance of the non-sparse base model, but for reasons that were not well understood. In this paper we study the three critical components of the Lottery Ticket (LT) algorithm, showing that each may be varied significantly without impacting the overall results. Ablating these factors lead…
Facebook AI Research（Facebook人工智能研究院）；Brown University（布朗大学）
The observation of sparse trainable sub-networks within over-parametrized networks - also known as Lottery Tickets (LTs) - has prompted inquiries around their trainability, scaling, uniqueness, and generalization properties. Across 28 combinations of image classification tasks and architectures, we discover differences in the connectivity structure of LTs found through different iterative pruning techniques, thus disproving their uniqueness and connecting emergent mask structure to the choice of pruning. In addition, we propose a consensus-based method for generating refined lottery tickets. T…
We analyse the pruning procedure behind the lottery ticket hypothesis arXiv:1803.03635v5, iterative magnitude pruning (IMP), when applied to linear models trained by gradient flow. We begin by presenting sufficient conditions on the statistical structure of the features under which IMP prunes those features that have smallest projection onto the data. Following this, we explore IMP as a method for sparse estimation.
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.
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.
We introduce a generalization to the lottery ticket hypothesis in which the notion of "sparsity" is relaxed by choosing an arbitrary basis in the space of parameters. We present evidence that the original results reported for the canonical basis continue to hold in this broader setting. We describe how structured pruning methods, including pruning units or factorizing fully-connected layers into products of low-rank matrices, can be cast as particular instances of this "generalized" lottery ticket hypothesis. The investigations reported here are preliminary and are provided to encourage furthe…
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…
Duke University（杜克大学）；Alibaba DAMO Academy（阿里巴巴达摩院）
Federated learning is a popular distributed machine learning paradigm with enhanced privacy. Its primary goal is learning a global model that offers good performance for the participants as many as possible. The technology is rapidly advancing with many unsolved challenges, among which statistical heterogeneity (i.e., non-IID) and communication efficiency are two critical ones that hinder the development of federated learning. In this work, we propose LotteryFL -- a personalized and communication-efficient federated learning framework via exploiting the Lottery Ticket hypothesis. In LotteryFL,…
School of Computer Science, Hebrew University（希伯来大学计算机科学学院）；Weizmann Institute of Science（魏茨曼科学研究所）
The lottery ticket hypothesis (Frankle and Carbin, 2018), states that a randomly-initialized network contains a small subnetwork such that, when trained in isolation, can compete with the performance of the original network. We prove an even stronger hypothesis (as was also conjectured in Ramanujan et al., 2019), showing that for every bounded distribution and every target network with bounded weights, a sufficiently over-parameterized neural network with random weights contains a subnetwork with roughly the same accuracy as the target network, without any further training.
Laboratory of Advanced Imaging Technology (LAIT), Ulsan National Institute of Science and Technology (UNIST)（先进成像技术实验室（LAIT），蔚山国立科学技术院（UNIST））；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Naver AI Lab（Naver AI 实验室）
Yes. In this paper, we investigate strong lottery tickets in generative models, the subnetworks that achieve good generative performance without any weight update. Neural network pruning is considered the main cornerstone of model compression for reducing the costs of computation and memory. Unfortunately, pruning a generative model has not been extensively explored, and all existing pruning algorithms suffer from excessive weight-training costs, performance degradation, limited generalizability, or complicated training. To address these problems, we propose to find a strong lottery ticket via…
Recognition tasks, such as object recognition and keypoint estimation, have seen widespread adoption in recent years. Most state-of-the-art methods for these tasks use deep networks that are computationally expensive and have huge memory footprints. This makes it exceedingly difficult to deploy these systems on low power embedded devices. Hence, the importance of decreasing the storage requirements and the amount of computation in such models is paramount. The recently proposed Lottery Ticket Hypothesis (LTH) states that deep neural networks trained on large datasets contain smaller subnetwork…
The lottery ticket hypothesis proposes that over-parameterization of deep neural networks (DNNs) aids training by increasing the probability of a "lucky" sub-network initialization being present rather than by helping the optimization process (Frankle & Carbin, 2019). Intriguingly, this phenomenon suggests that initialization strategies for DNNs can be improved substantially, but the lottery ticket hypothesis has only previously been tested in the context of supervised learning for natural image tasks. Here, we evaluate whether "winning ticket" initializations exist in two different domains: n…
Carnegie Mellon University（卡内基梅隆大学）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）；Petuum, Inc（Petuum公司）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
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 by Frankle et al. and Su et al. presents concrete evidence that current algorithms for finding trainable networks at initialization, fail simple baseline comparisons, e.g., against training random sparse subnetwo…
Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；MIT（麻省理工学院）
The lottery ticket hypothesis conjectures the existence of sparse subnetworks of large randomly initialized deep neural networks that can be successfully trained in isolation. Recent work has experimentally observed that some of these tickets can be practically reused across a variety of tasks, hinting at some form of universality. We formalize this concept and theoretically prove that not only do such universal tickets exist but they also do not require further training. Our proofs introduce a couple of technical innovations related to pruning for strong lottery tickets, including extensions …
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,…
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 …
Arizona State University（亚利桑那州立大学）；Lawrence Livermore National Labs（劳伦斯利弗莫尔国家实验室）；IBM Research AI（IBM研究院人工智能部门）
The hypothesis that sub-network initializations (lottery) exist within the initializations of over-parameterized networks, which when trained in isolation produce highly generalizable models, has led to crucial insights into network initialization and has enabled efficient inferencing. Supervised models with uncalibrated confidences tend to be overconfident even when making wrong prediction. In this paper, for the first time, we study how explicit confidence calibration in the over-parameterized network impacts the quality of the resulting lottery tickets. More specifically, we incorporate a s…
The lottery ticket hypothesis states that sparse subnetworks exist in randomly initialized dense networks that can be trained to the same accuracy as the dense network they reside in. However, the subsequent work has failed to replicate this on large-scale models and required rewinding to an early stable state instead of initialization. We show that by using a training method that is stable with respect to linear mode connectivity, large networks can also be entirely rewound to initialization. Our subsequent experiments on common vision tasks give strong credence to the hypothesis in Evci et a…
CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
The Lottery Ticket Hypothesis continues to have a profound practical impact on the quest for small scale deep neural networks that solve modern deep learning tasks at competitive performance. These lottery tickets are identified by pruning large randomly initialized neural networks with architectures that are as diverse as their applications. Yet, theoretical insights that attest their existence have been mostly focused on deep fully-connected feed forward networks with ReLU activation functions. We prove that also modern architectures consisting of convolutional and residual layers that can b…
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…
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…
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 …
University of Michigan（密歇根大学）；Syracuse University（雪城大学）；Baidu USA（百度美国）；Duke University（杜克大学）；Columbia University（哥伦比亚大学）
Recent research has proposed the lottery ticket hypothesis, suggesting that for a deep neural network, there exist trainable sub-networks performing equally or better than the original model with commensurate training steps. While this discovery is insightful, finding proper sub-networks requires iterative training and pruning. The high cost incurred limits the applications of the lottery ticket hypothesis. We show there exists a subset of the aforementioned sub-networks that converge significantly faster during the training process and thus can mitigate the cost issue. We conduct extensive ex…
Recent work on the lottery ticket hypothesis has produced highly sparse Transformers for NMT while maintaining BLEU. However, it is unclear how such pruning techniques affect a model's learned representations. By probing Transformers with more and more low-magnitude weights pruned away, we find that complex semantic information is first to be degraded. Analysis of internal activations reveals that higher layers diverge most over the course of pruning, gradually becoming less complex than their dense counterparts. Meanwhile, early layers of sparse models begin to perform more encoding. Attentio…
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…
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…
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 …
The vulnerability of the Lottery Ticket Hypothesis has not been studied from the purview of Membership Inference Attacks. Through this work, we are the first to empirically show that the lottery ticket networks are equally vulnerable to membership inference attacks. A Membership Inference Attack (MIA) is the process of determining whether a data sample belongs to a training set of a trained model or not. Membership Inference Attacks could leak critical information about the training data that can be used for targeted attacks. Recent deep learning models often have very large memory footprints …
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…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；University of Cambridge（剑桥大学）；Element AI；University of Toronto（多伦多大学）；Vector Institute
Pruning is a well-established technique for removing unnecessary structure from neural networks after training to improve the performance of inference. Several recent results have explored the possibility of pruning at initialization time to provide similar benefits during training. In particular, the "lottery ticket hypothesis" conjectures that typical neural networks contain small subnetworks that can train to similar accuracy in a commensurate number of steps. The evidence for this claim is that a procedure based on iterative magnitude pruning (IMP) reliably finds such subnetworks retroacti…
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:"…
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 strong lottery ticket hypothesis holds the promise that pruning randomly initialized deep neural networks could offer a computationally efficient alternative to deep learning with stochastic gradient descent. Common parameter initialization schemes and existence proofs, however, are focused on networks with zero biases, thus foregoing the potential universal approximation property of pruning. To fill this gap, we extend multiple initialization schemes and existence proofs to nonzero biases, including explicit 'looks-linear' approaches for ReLU activation functions. These do not only enable…
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%, …
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）
Training generative adversarial networks (GANs) with limited real image data generally results in deteriorated performance and collapsed models. To conquer this challenge, we are inspired by the latest observation, that one can discover independently trainable and highly sparse subnetworks (a.k.a., lottery tickets) from GANs. Treating this as an inductive prior, we suggest a brand-new angle towards data-efficient GAN training: by first identifying the lottery ticket from the original GAN using the small training set of real images; and then focusing on training that sparse subnetwork by re-usi…
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…
In this paper, we explore the performance of different pruning methods in the context of the lottery ticket hypothesis. We compare the performance of L1 unstructured pruning, Fisher pruning, and random pruning on different network architectures and pruning scenarios. The experiments include an evaluation of one-shot and iterative pruning, an examination of weight movement in the network during pruning, a comparison of the pruning methods on networks of varying widths, and an analysis of the performance of the methods when the network becomes very sparse. Additionally, we propose and evaluate a…
Google（谷歌）；University of Calgary（卡尔加里大学）；Facebook（脸书）
Sparse Neural Networks (NNs) can match the generalization of dense NNs using a fraction of the compute/storage for inference, and also have the potential to enable efficient training. However, naively training unstructured sparse NNs from random initialization results in significantly worse generalization, with the notable exceptions of Lottery Tickets (LTs) and Dynamic Sparse Training (DST). Through our analysis of gradient flow during training we attempt to answer: (1) why training unstructured sparse networks from random initialization performs poorly and; (2) what makes LTs and DST the exc…
Beijing Institute of Technology（北京理工大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Over-parameterized models, typically pretrained language models (LMs), have shown an appealing expressive power due to their small learning bias. However, the huge learning capacity of LMs can also lead to large learning variance. In a pilot study, we find that, when faced with multiple domains, a critical portion of parameters behave unexpectedly in a domain-specific manner while others behave in a domain-general one. Motivated by this phenomenon, we for the first time posit that domain-general parameters can underpin a domain-general LM that can be derived from the original LM. To uncover th…
Huazhong University of Science and Technology（华中科技大学）
Edge devices in federated learning usually have much more limited computation and communication resources compared to servers in a data center. Recently, advanced model compression methods, like the Lottery Ticket Hypothesis, have already been implemented on federated learning to reduce the model size and communication cost. However, Backdoor Attack can compromise its implementation in the federated learning scenario. The malicious edge device trains the client model with poisoned private data and uploads parameters to the center, embedding a backdoor to the global shared model after unwitting…
