Robustness to adversarial attacks was shown to require a larger model capacity, and thus a larger memory footprint. In this paper, we introduce an approach to obtain robust yet compact models by pruning randomly-initialized binary networks. Unlike adversarial training, which learns the model parameters, we initialize the model parameters as either +1 or -1, keep them fixed, and find a subnetwork structure that is robust to attacks. Our method confirms the Strong Lottery Ticket Hypothesis in the presence of adversarial attacks, and extends this to binary networks. Furthermore, it yields more compact networks with competitive performance than existing works by 1) adaptively pruning different network layers; 2) exploiting an effective binary initialization scheme; 3) incorporating a last batch normalization layer to improve training stability. Our experiments demonstrate that our approach not only always outperforms the state-of-the-art robust binary networks, but also can achieve accuracy better than full-precision ones on some datasets. Finally, we show the structured patterns of our pruned binary networks.
Google Research（谷歌研究院）；Poznan University of Technology（波兹南理工大学）
We present the surprising result that randomly initialized neural networks are good feature extractors in expectation. These random features correspond to finite-sample realizations of what we call Neural Network Prior Kernel (NNPK), which is inherently infinite-dimensional. We conduct ablations across multiple architectures of varying sizes as well as initializations and activation functions. Our analysis suggests that certain structures that manifest in a trained model are already present at initialization. Therefore, NNPK may provide further insight into why neural networks are so effective…
Before training a neural net, a classic rule of thumb is to randomly initialize the weights so the variance of activations is preserved across layers. This is traditionally interpreted using the total variance due to randomness in both weights \emph{and} samples. Alternatively, one can interpret the rule of thumb as preservation of the variance over samples for a fixed network. The two interpretations differ little for a shallow net, but the difference is shown to grow with depth for a deep ReLU net by decomposing the total variance into the network-averaged sum of the sample variance and squa…
University of California, Santa Cruz（加州大学圣克鲁兹分校）；University of California, Irvine（加州大学欧文分校）；Columbia University（哥伦比亚大学）
Recurrent Neural Networks (RNNs) frequently exhibit complicated dynamics, and their sensitivity to the initialization process often renders them notoriously hard to train. Recent works have shed light on such phenomena analyzing when exploding or vanishing gradients may occur, either of which is detrimental for training dynamics. In this paper, we point to a formal connection between RNNs and chaotic dynamical systems and prove a qualitatively stronger phenomenon about RNNs than what exploding gradients seem to suggest. Our main result proves that under standard initialization (e.g., He, Xavie…
As a deep learning model typically contains millions of trainable weights, there has been a growing demand for a more efficient network structure with reduced storage space and improved run-time efficiency. Pruning is one of the most popular network compression techniques. In this paper, we propose a novel unstructured pruning pipeline, Attention-based Simultaneous sparse structure and Weight Learning (ASWL). Unlike traditional channel-wise or weight-wise attention mechanism, ASWL proposed an efficient algorithm to calculate the pruning ratio through layer-wise attention for each layer, and bo…
École Normale Supérieure, PSL（巴黎高等师范学院（PSL大学））；Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；McGill University（麦吉尔大学）
The Strong Lottery Ticket Hypothesis (SLTH) stipulates the existence of a subnetwork within a sufficiently overparameterized (dense) neural network that -- when initialized randomly and without any training -- achieves the accuracy of a fully trained target network. Recent works by Da Cunha et. al 2022; Burkholz 2022 demonstrate that the SLTH can be extended to translation equivariant networks -- i.e. CNNs -- with the same level of overparametrization as needed for the SLTs in dense networks. However, modern neural networks are capable of incorporating more than just translation symmetry, and …
This paper revisits the so-called vanishing gradient phenomenon, which commonly occurs in deep randomly initialized neural networks. Leveraging an in-depth analysis of neural chains, we first show that vanishing gradients cannot be circumvented when the network width scales with less than O(depth), even when initialized with the popular Xavier and He initializations. Second, we extend the analysis to second-order derivatives and show that random i.i.d. initialization also gives rise to Hessian matrices with eigenspectra that vanish as networks grow in depth. Whenever this happens, optimizers a…
Evaluation of generative models is mostly based on the comparison between the estimated distribution and the ground truth distribution in a certain feature space. To embed samples into informative features, previous works often use convolutional neural networks optimized for classification, which is criticized by recent studies. Therefore, various feature spaces have been explored to discover alternatives. Among them, a surprising approach is to use a randomly initialized neural network for feature embedding. However, the fundamental basis to employ the random features has not been sufficientl…
ETH Zurich（苏黎世联邦理工学院）；INRIA Paris（法国国家信息与自动化研究所巴黎分部）
Randomly initialized neural networks are known to become harder to train with increasing depth, unless architectural enhancements like residual connections and batch normalization are used. We here investigate this phenomenon by revisiting the connection between random initialization in deep networks and spectral instabilities in products of random matrices. Given the rich literature on random matrices, it is not surprising to find that the rank of the intermediate representations in unnormalized networks collapses quickly with depth. In this work we highlight the fact that batch normalization…
NTT Computer and Data Science Laboratories, NTT Corporation（NTT公司NTT计算机与数据科学实验室）；NTT Social Informatics Laboratories, NTT Corporation（NTT公司NTT社会信息学实验室）
Pruning the weights of randomly initialized neural networks plays an important role in the context of lottery ticket hypothesis. Ramanujan et al. (2020) empirically showed that only pruning the weights can achieve remarkable performance instead of optimizing the weight values. However, to achieve the same level of performance as the weight optimization, the pruning approach requires more parameters in the networks before pruning and thus more memory space. To overcome this parameter inefficiency, we introduce a novel framework to prune randomly initialized neural networks with iteratively rand…
The Multi-Prize Lottery Ticket Hypothesis posits that randomly initialized neural networks contain several subnetworks that achieve comparable accuracy to fully trained models of the same architecture. However, current methods require that the network is sufficiently overparameterized. In this work, we propose a modification to two state-of-the-art algorithms (Edge-Popup and Biprop) that finds high-accuracy subnetworks with no additional storage cost or scaling. The algorithm, Iterative Weight Recycling, identifies subsets of important weights within a randomly initialized network for intra-la…
the University of Texas, Austin（得克萨斯大学奥斯汀分校）；the University of Chicago（芝加哥大学）；Google Research（谷歌研究院）
Recent empirical works show that large deep neural networks are often highly redundant and one can find much smaller subnetworks without a significant drop of accuracy. However, most existing methods of network pruning are empirical and heuristic, leaving it open whether good subnetworks provably exist, how to find them efficiently, and if network pruning can be provably better than direct training using gradient descent. We answer these problems positively by proposing a simple greedy selection approach for finding good subnetworks, which starts from an empty network and greedily adds importa…
We study random embeddings produced by untrained neural set functions, and show that they are powerful representations which well capture the input features for downstream tasks such as classification, and are often linearly separable. We obtain surprising results that show that random set functions can often obtain close to or even better accuracy than fully trained models. We investigate factors that affect the representative power of such embeddings quantitatively and qualitatively.
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…
In this paper, we first introduce batch normalization to the edRVFL network. This re-normalization method can help the network avoid divergence of the hidden features. Then we propose novel variants of Ensemble Deep Random Vector Functional Link (edRVFL). Weighted edRVFL (WedRVFL) uses weighting methods to give training samples different weights in different layers according to how the samples were classified confidently in the previous layer thereby increasing the ensemble's diversity and accuracy. Furthermore, a pruning-based edRVFL (PedRVFL) has also been proposed. We prune some inferior ne…
Learned optimizers are increasingly effective, with performance exceeding that of hand designed optimizers such as Adam~\citep{kingma2014adam} on specific tasks \citep{metz2019understanding}. Despite the potential gains available, in current work the meta-training (or `outer-training') of the learned optimizer is performed by a hand-designed optimizer, or by an optimizer trained by a hand-designed optimizer \citep{metz2020tasks}. We show that a population of randomly initialized learned optimizers can be used to train themselves from scratch in an online fashion, without resorting to a hand de…
RaPA: Enhancing Transferable Targeted Attacks via Random Parameter Pruning
State Key Lab of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所人工智能安全国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
The strong lottery ticket hypothesis has highlighted the potential for training deep neural networks by pruning, which has inspired interesting practical and theoretical insights into how neural networks can represent functions. For networks with ReLU activation functions, it has been proven that a target network with depth $L$ can be approximated by the subnetwork of a randomly initialized neural network that has double the target's depth $2L$ and is wider by a logarithmic factor. We show that a depth $L+1$ network is sufficient. This result indicates that we can expect to find lottery ticket…
University of Manouba（马努巴大学）；Taibah University（塔伊巴大学）；Prince Sultan University（苏丹王子大学）；Arab Open University（阿拉伯开放大学）；University of Sfax（斯法克斯大学）
Recently, Convolutional Neural Networks (CNNs) have made a great performance for remote sensing image classification. Plant recognition using CNNs is one of the active deep learning research topics due to its added-value in different related fields, especially environmental conservation and natural areas preservation. Automatic recognition of plants in protected areas helps in the surveillance process of these zones and ensures the sustainability of their ecosystems. In this work, we propose an Enhanced Randomly Initialized Convolutional Neural Network (ERI-CNN) for the recognition of columnar…
Department of EECS, Oregon State University（俄勒冈州立大学电子工程与计算机科学系）
Training a neural network (NN) depends on multiple factors, including but not limited to the initial weights. In this paper, we focus on initializing deep NN parameters such that it performs better, comparing to random or zero initialization. We do this by reducing the process of initialization into an SMT solver. Previous works consider certain activation functions on small NNs, however the studied NN is a deep network with different activation functions. Our experiments show that the proposed approach for parameter initialization achieves better performance comparing to randomly initialized …
Technische Universität Dresden（德累斯顿工业大学）；Ghent University（根特大学）；Princeton University（普林斯顿大学）
Echo State Networks (ESNs) are a special type of recurrent neural networks (RNNs), in which the input and recurrent connections are traditionally generated randomly, and only the output weights are trained. Despite the recent success of ESNs in various tasks of audio, image and radar recognition, we postulate that a purely random initialization is not the ideal way of initializing ESNs. The aim of this work is to propose an unsupervised initialization of the input connections using the $K$-Means algorithm on the training data. We show that for a large variety of datasets this initialization pe…
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 pru…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Tel Aviv University（特拉维夫大学）
How does the geometric representation of a dataset change after the application of each randomly initialized layer of a neural network? The celebrated Johnson--Lindenstrauss lemma answers this question for linear fully-connected neural networks (FNNs), stating that the geometry is essentially preserved. For FNNs with the ReLU activation, the angle between two inputs contracts according to a known mapping. The question for non-linear convolutional neural networks (CNNs) becomes much more intricate. To answer this question, we introduce a geometric framework. For linear CNNs, we show that the Jo…
Romanian Institute of Science and Technology（罗马尼亚科学与技术研究院）
We present some novel, straightforward methods for training the connection graph of a randomly initialized neural network without training the weights. These methods do not use hyperparameters defining cutoff thresholds and therefore remove the need for iteratively searching optimal values of such hyperparameters. We can achieve similar or higher performances than in the case of training all weights, with a similar computational cost as for standard training techniques. Besides switching connections on and off, we introduce a novel way of training a network by flipping the signs of the weights…
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.
Southern University of Science and Technology（南方科技大学）；The University of Hong Kong（香港大学）；The University of Waikato（怀卡托大学）
White matter hyperintensity (WMH) is commonly found in elder individuals and appears to be associated with brain diseases. U-net is a convolutional network that has been widely used for biomedical image segmentation. Recently, U-net has been successfully applied to WMH segmentation. Random initialization is usally used to initialize the model weights in the U-net. However, the model may coverage to different local optima with different randomly initialized weights. We find a combination of thresholding and averaging the outputs of U-nets with different random initializations can largely improv…
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…
NTT Computer and Data Science Laboratories, NTT Corporation（NTT公司NTT计算机与数据科学实验室）；Kyoto University（京都大学）
Few-shot learning for neural networks (NNs) is an important problem that aims to train NNs with a few data. The main challenge is how to avoid overfitting since over-parameterized NNs can easily overfit to such small dataset. Previous work (e.g. MAML by Finn et al. 2017) tackles this challenge by meta-learning, which learns how to learn from a few data by using various tasks. On the other hand, one conventional approach to avoid overfitting is restricting hypothesis spaces by endowing sparse NN structures like convolution layers in computer vision. However, although such manually-designed spar…
the Ohio State University（俄亥俄州立大学）；KU Eichstätt-Ingolstadt（艾希施泰特-英戈尔施塔特天主教大学）
We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating Least Squares (ALS) method. While this algorithm has been studied in a number of previous works, most of them only show convergence from an initialization close to the true solution and thus require a carefully designed initialization scheme. However, random initialization has often been preferred by practitioners as it is model-agnostic. In this paper, we show…
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.
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…
A novel method to identify salient computational paths within randomly wired neural networks before training is proposed. The computational graph is pruned based on a node mass probability function defined by local graph measures and weighted by hyperparameters produced by a reinforcement learning-based controller neural network. We use the definition of Ricci curvature to remove edges of low importance before mapping the computational graph to a neural network. We show a reduction of almost $35\%$ in the number of floating-point operations (FLOPs) per pass, with no degradation in performance.…
Mathematical Institute, University of Oxford（牛津大学数学研究所）；The Alan Turing Institute（艾伦图灵研究所）
That neural networks may be pruned to high sparsities and retain high accuracy is well established. Recent research efforts focus on pruning immediately after initialization so as to allow the computational savings afforded by sparsity to extend to the training process. In this work, we introduce a new `DCT plus Sparse' layer architecture, which maintains information propagation and trainability even with as little as 0.01% trainable kernel parameters remaining. We show that standard training of networks built with these layers, and pruned at initialization, achieves state-of-the-art accuracy …
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…
Eindhoven University of Technology（埃因霍温理工大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；JD Explore Academy（京东探索研究院）；University of Twente（特文特大学）
Random pruning is arguably the most naive way to attain sparsity in neural networks, but has been deemed uncompetitive by either post-training pruning or sparse training. In this paper, we focus on sparse training and highlight a perhaps counter-intuitive finding, that random pruning at initialization can be quite powerful for the sparse training of modern neural networks. Without any delicate pruning criteria or carefully pursued sparsity structures, we empirically demonstrate that sparsely training a randomly pruned network from scratch can match the performance of its dense equivalent. Ther…
Yuanpei College, Peking University（北京大学元培学院）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）；Zhongguancun Haihua Institute for Frontier Information Technology（中关村海华前沿信息技术研究院）；Key Laboratory of Machine Perception, MOE, School of EECS, Peking University（北京大学信息科学技术学院机器感知教育部重点实验室）
Network pruning is a method for reducing test-time computational resource requirements with minimal performance degradation. Conventional wisdom of pruning algorithms suggests that: (1) Pruning methods exploit information from training data to find good subnetworks; (2) The architecture of the pruned network is crucial for good performance. In this paper, we conduct sanity checks for the above beliefs on several recent unstructured pruning methods and surprisingly find that: (1) A set of methods which aims to find good subnetworks of the randomly-initialized network (which we call "initial tic…
Neural network pruning typically removes connections or neurons from a pretrained converged model; while a new pruning paradigm, pruning at initialization (PaI), attempts to prune a randomly initialized network. This paper offers the first survey concentrated on this emerging pruning fashion. We first introduce a generic formulation of neural network pruning, followed by the major classic pruning topics. Then, as the main body of this paper, a thorough and structured literature review of PaI methods is presented, consisting of two major tracks (sparse training and sparse selection). Finally, w…
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…
Application of discrete Ricci curvature in pruning randomly wired neural networks: A case study with chest x-ray classification of COVID-19
The Institute of Mathematical Sciences (IMSc), Chennai 600113, India（数学科学研究所）；Institute of Computer Science（计算机科学研究所）；Homi Bhabha National Institute (HBNI), Mumbai 400094, India（霍米·巴哈瓦国家研究所）
University of Oxford（牛津大学）；Australian National University（澳大利亚国立大学）
Network pruning is a promising avenue for compressing deep neural networks. A typical approach to pruning starts by training a model and then removing redundant parameters while minimizing the impact on what is learned. Alternatively, a recent approach shows that pruning can be done at initialization prior to training, based on a saliency criterion called connection sensitivity. However, it remains unclear exactly why pruning an untrained, randomly initialized neural network is effective. In this work, by noting connection sensitivity as a form of gradient, we formally characterize initializat…
