Recent advances in neural network pruning have shown how it is possible to reduce the computational costs and memory demands of deep learning models before training. We focus on this framework and propose a new pruning at initialization algorithm that leverages the Neural Tangent Kernel (NTK) theory to align the training dynamics of the sparse network with that of the dense one. Specifically, we show how the usually neglected data-dependent component in the NTK's spectrum can be taken into account by providing an analytical upper bound to the NTK's trace obtained by decomposing neural networks into individual paths. This leads to our Path eXclusion (PX), a foresight pruning method designed to preserve the parameters that mostly influence the NTK's trace. PX is able to find lottery tickets (i.e. good paths) even at high sparsity levels and largely reduces the need for additional training. When applied to pre-trained models it extracts subnetworks directly usable for several downstream tasks, resulting in performance comparable to those of the dense counterpart but with substantial cost and computational savings. Code available at: https://github.com/iurada/px-ntk-pruning
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…
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…
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…
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…
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 …
Spiking Neural Networks (SNNs) have recently emerged as a new generation of low-power deep neural networks, which is suitable to be implemented on low-power mobile/edge devices. As such devices have limited memory storage, neural pruning on SNNs has been widely explored in recent years. Most existing SNN pruning works focus on shallow SNNs (2~6 layers), however, deeper SNNs (>16 layers) are proposed by state-of-the-art SNN works, which is difficult to be compatible with the current SNN pruning work. To scale up a pruning technique towards deep SNNs, we investigate Lottery Ticket Hypothesis (LT…
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…
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 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 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…
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…
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,…
PLA Strategy Support Force Information Engineering University（中国人民解放军战略支援部队信息工程大学）；University of Science and Technology of China（中国科学技术大学）
Adversarial attacks are considered the intrinsic vulnerability of CNNs. Defense strategies designed for attacks have been stuck in the adversarial attack-defense arms race, reflecting the imbalance between attack and defense. Dynamic Defense Framework (DDF) recently changed the passive safety status quo based on the stochastic ensemble model. The diversity of subnetworks, an essential concern in the DDF, can be effectively evaluated by the adversarial transferability between different networks. Inspired by the poor adversarial transferability between subnetworks of scratch tickets with various…
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…
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）
Deep generative adversarial networks (GANs) have gained growing popularity in numerous scenarios, while usually suffer from high parameter complexities for resource-constrained real-world applications. However, the compression of GANs has less been explored. A few works show that heuristically applying compression techniques normally leads to unsatisfactory results, due to the notorious training instability of GANs. In parallel, the lottery ticket hypothesis shows prevailing success on discriminative models, in locating sparse matching subnetworks capable of training in isolation to full model…
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 …
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…
Sun Yat-sen University（中山大学）；Purdue University（普渡大学）；Northwestern University（西北大学）；Nanyang Technological University（南洋理工大学）
Recently many plug-and-play self-attention modules (SAMs) are proposed to enhance the model generalization by exploiting the internal information of deep convolutional neural networks (CNNs). In general, previous works ignore where to plug in the SAMs since they connect the SAMs individually with each block of the entire CNN backbone for granted, leading to incremental computational cost and the number of parameters with the growth of network depth. However, we empirically find and verify some counterintuitive phenomena that: (a) Connecting the SAMs to all the blocks may not always bring the l…
Style transfer has achieved great success and attracted a wide range of attention from both academic and industrial communities due to its flexible application scenarios. However, the dependence on a pretty large VGG-based autoencoder leads to existing style transfer models having high parameter complexities, which limits their applications on resource-constrained devices. Compared with many other tasks, the compression of style transfer models has been less explored. Recently, the lottery ticket hypothesis (LTH) has shown great potential in finding extremely sparse matching subnetworks which …
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…
Texas A&M University（得克萨斯农工大学）；North Carolina State University（北卡罗来纳州立大学）；Purdue University（普渡大学）
Although sparse training has been successfully used in various resource-limited deep learning tasks to save memory, accelerate training, and reduce inference time, the reliability of the produced sparse models remains unexplored. Previous research has shown that deep neural networks tend to be over-confident, and we find that sparse training exacerbates this problem. Therefore, calibrating the sparse models is crucial for reliable prediction and decision-making. In this paper, we propose a new sparse training method to produce sparse models with improved confidence calibration. In contrast to …
Microsoft Corporation（微软公司）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Tsinghua University（清华大学）
Large-scale pre-training has recently revolutionized vision-and-language (VL) research. Models such as LXMERT and UNITER have significantly lifted the state of the art over a wide range of VL tasks. However, the large number of parameters in such models hinders their application in practice. In parallel, work on the lottery ticket hypothesis (LTH) has shown that deep neural networks contain small matching subnetworks that can achieve on par or even better performance than the dense networks when trained in isolation. In this work, we perform the first empirical study to assess whether such tra…
Université de Liège（列日大学）；Universiteit Antwerpen（安特卫普大学）
We study the generalization properties of pruned neural networks that are the winners of the lottery ticket hypothesis on datasets of natural images. We analyse their potential under conditions in which training data is scarce and comes from a non-natural domain. Specifically, we investigate whether pruned models that are found on the popular CIFAR-10/100 and Fashion-MNIST datasets, generalize to seven different datasets that come from the fields of digital pathology and digital heritage. Our results show that there are significant benefits in transferring and training sparse architectures ove…
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…
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 Wisconsin Madison（威斯康星大学麦迪逊分校）；Stanford University（斯坦福大学）
$\textit{RigL}$, a sparse training algorithm, claims to directly train sparse networks that match or exceed the performance of existing dense-to-sparse training techniques (such as pruning) for a fixed parameter count and compute budget. We implement $\textit{RigL}$ from scratch in Pytorch and reproduce its performance on CIFAR-10 within 0.1% of the reported value. On both CIFAR-10/100, the central claim holds -- given a fixed training budget, $\textit{RigL}$ surpasses existing dynamic-sparse training methods over a range of target sparsities. By training longer, the performance can match or e…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；Michigan State University（密歇根州立大学）
The computer vision world has been re-gaining enthusiasm in various pre-trained models, including both classical ImageNet supervised pre-training and recently emerged self-supervised pre-training such as simCLR and MoCo. Pre-trained weights often boost a wide range of downstream tasks including classification, detection, and segmentation. Latest studies suggest that pre-training benefits from gigantic model capacity. We are hereby curious and ask: after pre-training, does a pre-trained model indeed have to stay large for its downstream transferability? In this paper, we examine supervised and …
Many applications require sparse neural networks due to space or inference time restrictions. There is a large body of work on training dense networks to yield sparse networks for inference, but this limits the size of the largest trainable sparse model to that of the largest trainable dense model. In this paper we introduce a method to train sparse neural networks with a fixed parameter count and a fixed computational cost throughout training, without sacrificing accuracy relative to existing dense-to-sparse training methods. Our method updates the topology of the sparse network during traini…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of California, Irvine（加利福尼亚大学欧文分校）
Lottery Ticket Hypothesis (LTH) suggests that a dense neural network contains a sparse sub-network that can match the performance of the original dense network when trained in isolation from scratch. Most works retrain the sparse sub-network with the same training protocols as its dense network, such as initialization, architecture blocks, and training recipes. However, till now it is unclear that whether these training protocols are optimal for sparse networks. In this paper, we demonstrate that it is unnecessary for spare retraining to strictly inherit those properties from the dense network…
