arXiv subjects

Huishuai Zhang

Publications and source records attributed to Huishuai Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2023

Stabilize Deep ResNet with A Sharp Scaling Factor $τ$

We study the stability and convergence of training deep ResNets with gradient descent. Specifically, we show that the parametric branch in the residual block should be scaled down by a factor $τ=O(1/\sqrt{L})$ to guarantee stable forward/backward process, where $L$ is the number of residual blocks. Moreover, we establish a converse result that the forward process is unbounded when $τ>L^{-\frac{1}{2}+c}$, for any positive constant $c$. The above two results together establish a sharp value of the scaling factor in determining the stability of deep ResNet. Based on the stability result, we further show that gradient descent finds the global minima if the ResNet is properly over-parameterized, which significantly improves over the previous work with a much larger range of $τ$ that admits global convergence. Moreover, we show that the convergence rate is independent of the depth, theoretically justifying the advantage of ResNet over vanilla feedforward network. Empirically, with such a factor $τ$, one can train deep ResNet without normalization layer. Moreover, for ResNets with normalization layer, adding such a factor $τ$ also stabilizes the training and obtains significant performance gain for deep ResNet.

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arXiv2022

Exploring the Limits of Differentially Private Deep Learning with Group-wise Clipping

Differentially private deep learning has recently witnessed advances in computational efficiency and privacy-utility trade-off. We explore whether further improvements along the two axes are possible and provide affirmative answers leveraging two instantiations of \emph{group-wise clipping}. To reduce the compute time overhead of private learning, we show that \emph{per-layer clipping}, where the gradient of each neural network layer is clipped separately, allows clipping to be performed in conjunction with backpropagation in differentially private optimization. This results in private learning that is as memory-efficient and almost as fast per training update as non-private learning for many workflows of interest. While per-layer clipping with constant thresholds tends to underperform standard flat clipping, per-layer clipping with adaptive thresholds matches or outperforms flat clipping under given training epoch constraints, hence attaining similar or better task performance within less wall time. To explore the limits of scaling (pretrained) models in differentially private deep learning, we privately fine-tune the 175 billion-parameter GPT-3. We bypass scaling challenges associated with clipping gradients that are distributed across multiple devices with \emph{per-device clipping} that clips the gradient of each model piece separately on its host device. Privately fine-tuning GPT-3 with per-device clipping achieves a task performance at $ε=1$ better than what is attainable by non-privately fine-tuning the largest GPT-2 on a summarization task.

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arXiv2022

Similarity Distribution based Membership Inference Attack on Person Re-identification

While person Re-identification (Re-ID) has progressed rapidly due to its wide real-world applications, it also causes severe risks of leaking personal information from training data. Thus, this paper focuses on quantifying this risk by membership inference (MI) attack. Most of the existing MI attack algorithms focus on classification models, while Re-ID follows a totally different training and inference paradigm. Re-ID is a fine-grained recognition task with complex feature embedding, and model outputs commonly used by existing MI like logits and losses are not accessible during inference. Since Re-ID focuses on modelling the relative relationship between image pairs instead of individual semantics, we conduct a formal and empirical analysis which validates that the distribution shift of the inter-sample similarity between training and test set is a critical criterion for Re-ID membership inference. As a result, we propose a novel membership inference attack method based on the inter-sample similarity distribution. Specifically, a set of anchor images are sampled to represent the similarity distribution conditioned on a target image, and a neural network with a novel anchor selection module is proposed to predict the membership of the target image. Our experiments validate the effectiveness of the proposed approach on both the Re-ID task and conventional classification task.

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arXiv2022

Differentially Private Fine-tuning of Language Models

We give simpler, sparser, and faster algorithms for differentially private fine-tuning of large-scale pre-trained language models, which achieve the state-of-the-art privacy versus utility tradeoffs on many standard NLP tasks. We propose a meta-framework for this problem, inspired by the recent success of highly parameter-efficient methods for fine-tuning. Our experiments show that differentially private adaptations of these approaches outperform previous private algorithms in three important dimensions: utility, privacy, and the computational and memory cost of private training. On many commonly studied datasets, the utility of private models approaches that of non-private models. For example, on the MNLI dataset we achieve an accuracy of $87.8\%$ using RoBERTa-Large and $83.5\%$ using RoBERTa-Base with a privacy budget of $ε= 6.7$. In comparison, absent privacy constraints, RoBERTa-Large achieves an accuracy of $90.2\%$. Our findings are similar for natural language generation tasks. Privately fine-tuning with DART, GPT-2-Small, GPT-2-Medium, GPT-2-Large, and GPT-2-XL achieve BLEU scores of 38.5, 42.0, 43.1, and 43.8 respectively (privacy budget of $ε= 6.8,δ=$ 1e-5) whereas the non-private baseline is $48.1$. All our experiments suggest that larger models are better suited for private fine-tuning: while they are well known to achieve superior accuracy non-privately, we find that they also better maintain their accuracy when privacy is introduced.

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arXiv2022

Normalized/Clipped SGD with Perturbation for Differentially Private Non-Convex Optimization

By ensuring differential privacy in the learning algorithms, one can rigorously mitigate the risk of large models memorizing sensitive training data. In this paper, we study two algorithms for this purpose, i.e., DP-SGD and DP-NSGD, which first clip or normalize \textit{per-sample} gradients to bound the sensitivity and then add noise to obfuscate the exact information. We analyze the convergence behavior of these two algorithms in the non-convex optimization setting with two common assumptions and achieve a rate $\mathcal{O}\left(\sqrt[4]{\frac{d\log(1/δ)}{N^2ε^2}}\right)$ of the gradient norm for a $d$-dimensional model, $N$ samples and $(ε,δ)$-DP, which improves over previous bounds under much weaker assumptions. Specifically, we introduce a regularizing factor in DP-NSGD and show that it is crucial in the convergence proof and subtly controls the bias and noise trade-off. Our proof deliberately handles the per-sample gradient clipping and normalization that are specified for the private setting. Empirically, we demonstrate that these two algorithms achieve similar best accuracy while DP-NSGD is comparatively easier to tune than DP-SGD and hence may help further save the privacy budget when accounting the tuning effort.

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arXiv2022

Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum

Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often generalizes worse than Stochastic Gradient Descent (SGD). The purpose of this paper is to unveil the mystery of this behavior in the diffusion theoretical framework. Specifically, we disentangle the effects of Adaptive Learning Rate and Momentum of the Adam dynamics on saddle-point escaping and flat minima selection. We prove that Adaptive Learning Rate can escape saddle points efficiently, but cannot select flat minima as SGD does. In contrast, Momentum provides a drift effect to help the training process pass through saddle points, and almost does not affect flat minima selection. This partly explains why SGD (with Momentum) generalizes better, while Adam generalizes worse but converges faster. Furthermore, motivated by the analysis, we design a novel adaptive optimization framework named Adaptive Inertia, which uses parameter-wise adaptive inertia to accelerate the training and provably favors flat minima as well as SGD. Our extensive experiments demonstrate that the proposed adaptive inertia method can generalize significantly better than SGD and conventional adaptive gradient methods.

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arXiv2022

Adversarial Noises Are Linearly Separable for (Nearly) Random Neural Networks

Adversarial examples, which are usually generated for specific inputs with a specific model, are ubiquitous for neural networks. In this paper we unveil a surprising property of adversarial noises when they are put together, i.e., adversarial noises crafted by one-step gradient methods are linearly separable if equipped with the corresponding labels. We theoretically prove this property for a two-layer network with randomly initialized entries and the neural tangent kernel setup where the parameters are not far from initialization. The proof idea is to show the label information can be efficiently backpropagated to the input while keeping the linear separability. Our theory and experimental evidence further show that the linear classifier trained with the adversarial noises of the training data can well classify the adversarial noises of the test data, indicating that adversarial noises actually inject a distributional perturbation to the original data distribution. Furthermore, we empirically demonstrate that the adversarial noises may become less linearly separable when the above conditions are compromised while they are still much easier to classify than original features.

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arXiv2022

Availability Attacks Create Shortcuts

Availability attacks, which poison the training data with imperceptible perturbations, can make the data \emph{not exploitable} by machine learning algorithms so as to prevent unauthorized use of data. In this work, we investigate why these perturbations work in principle. We are the first to unveil an important population property of the perturbations of these attacks: they are almost \textbf{linearly separable} when assigned with the target labels of the corresponding samples, which hence can work as \emph{shortcuts} for the learning objective. We further verify that linear separability is indeed the workhorse for availability attacks. We synthesize linearly-separable perturbations as attacks and show that they are as powerful as the deliberately crafted attacks. Moreover, such synthetic perturbations are much easier to generate. For example, previous attacks need dozens of hours to generate perturbations for ImageNet while our algorithm only needs several seconds. Our finding also suggests that the \emph{shortcut learning} is more widely present than previously believed as deep models would rely on shortcuts even if they are of an imperceptible scale and mixed together with the normal features. Our source code is published at \url{https://github.com/dayu11/Availability-Attacks-Create-Shortcuts}.

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arXiv2022

Does Momentum Change the Implicit Regularization on Separable Data?

The momentum acceleration technique is widely adopted in many optimization algorithms. However, there is no theoretical answer on how the momentum affects the generalization performance of the optimization algorithms. This paper studies this problem by analyzing the implicit regularization of momentum-based optimization. We prove that on the linear classification problem with separable data and exponential-tailed loss, gradient descent with momentum (GDM) converges to the L2 max-margin solution, which is the same as vanilla gradient descent. That means gradient descent with momentum acceleration still converges to a low-complexity model, which guarantees their generalization. We then analyze the stochastic and adaptive variants of GDM (i.e., SGDM and deterministic Adam) and show they also converge to the L2 max-margin solution. Technically, to overcome the difficulty of the error accumulation in analyzing the momentum, we construct new potential functions to analyze the gap between the model parameter and the max-margin solution. Numerical experiments are conducted and support our theoretical results.

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arXiv2022

Two Coupled Rejection Metrics Can Tell Adversarial Examples Apart

Correctly classifying adversarial examples is an essential but challenging requirement for safely deploying machine learning models. As reported in RobustBench, even the state-of-the-art adversarially trained models struggle to exceed 67% robust test accuracy on CIFAR-10, which is far from practical. A complementary way towards robustness is to introduce a rejection option, allowing the model to not return predictions on uncertain inputs, where confidence is a commonly used certainty proxy. Along with this routine, we find that confidence and a rectified confidence (R-Con) can form two coupled rejection metrics, which could provably distinguish wrongly classified inputs from correctly classified ones. This intriguing property sheds light on using coupling strategies to better detect and reject adversarial examples. We evaluate our rectified rejection (RR) module on CIFAR-10, CIFAR-10-C, and CIFAR-100 under several attacks including adaptive ones, and demonstrate that the RR module is compatible with different adversarial training frameworks on improving robustness, with little extra computation. The code is available at https://github.com/P2333/Rectified-Rejection.

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arXiv2021

Large Scale Private Learning via Low-rank Reparametrization

We propose a reparametrization scheme to address the challenges of applying differentially private SGD on large neural networks, which are 1) the huge memory cost of storing individual gradients, 2) the added noise suffering notorious dimensional dependence. Specifically, we reparametrize each weight matrix with two \emph{gradient-carrier} matrices of small dimension and a \emph{residual weight} matrix. We argue that such reparametrization keeps the forward/backward process unchanged while enabling us to compute the projected gradient without computing the gradient itself. To learn with differential privacy, we design \emph{reparametrized gradient perturbation (RGP)} that perturbs the gradients on gradient-carrier matrices and reconstructs an update for the original weight from the noisy gradients. Importantly, we use historical updates to find the gradient-carrier matrices, whose optimality is rigorously justified under linear regression and empirically verified with deep learning tasks. RGP significantly reduces the memory cost and improves the utility. For example, we are the first able to apply differential privacy on the BERT model and achieve an average accuracy of $83.9\%$ on four downstream tasks with $ε=8$, which is within $5\%$ loss compared to the non-private baseline but enjoys much lower privacy leakage risk.

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arXiv2021

Optimizing Information-theoretical Generalization Bounds via Anisotropic Noise in SGLD

Recently, the information-theoretical framework has been proven to be able to obtain non-vacuous generalization bounds for large models trained by Stochastic Gradient Langevin Dynamics (SGLD) with isotropic noise. In this paper, we optimize the information-theoretical generalization bound by manipulating the noise structure in SGLD. We prove that with constraint to guarantee low empirical risk, the optimal noise covariance is the square root of the expected gradient covariance if both the prior and the posterior are jointly optimized. This validates that the optimal noise is quite close to the empirical gradient covariance. Technically, we develop a new information-theoretical bound that enables such an optimization analysis. We then apply matrix analysis to derive the form of optimal noise covariance. Presented constraint and results are validated by the empirical observations.

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arXiv2021

Do Not Let Privacy Overbill Utility: Gradient Embedding Perturbation for Private Learning

The privacy leakage of the model about the training data can be bounded in the differential privacy mechanism. However, for meaningful privacy parameters, a differentially private model degrades the utility drastically when the model comprises a large number of trainable parameters. In this paper, we propose an algorithm \emph{Gradient Embedding Perturbation (GEP)} towards training differentially private deep models with decent accuracy. Specifically, in each gradient descent step, GEP first projects individual private gradient into a non-sensitive anchor subspace, producing a low-dimensional gradient embedding and a small-norm residual gradient. Then, GEP perturbs the low-dimensional embedding and the residual gradient separately according to the privacy budget. Such a decomposition permits a small perturbation variance, which greatly helps to break the dimensional barrier of private learning. With GEP, we achieve decent accuracy with reasonable computational cost and modest privacy guarantee for deep models. Especially, with privacy bound $ε=8$, we achieve $74.9\%$ test accuracy on CIFAR10 and $95.1\%$ test accuracy on SVHN, significantly improving over existing results.

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arXiv2021

Regularized OFU: an Efficient UCB Estimator forNon-linear Contextual Bandit

Balancing exploration and exploitation (EE) is a fundamental problem in contex-tual bandit. One powerful principle for EE trade-off isOptimism in Face of Uncer-tainty(OFU), in which the agent takes the action according to an upper confidencebound (UCB) of reward. OFU has achieved (near-)optimal regret bound for lin-ear/kernel contextual bandits. However, it is in general unknown how to deriveefficient and effective EE trade-off methods for non-linearcomplex tasks, suchas contextual bandit with deep neural network as the reward function. In thispaper, we propose a novel OFU algorithm namedregularized OFU(ROFU). InROFU, we measure the uncertainty of the reward by a differentiable function andcompute the upper confidence bound by solving a regularized optimization prob-lem. We prove that, for multi-armed bandit, kernel contextual bandit and neuraltangent kernel bandit, ROFU achieves (near-)optimal regret bounds with certainuncertainty measure, which theoretically justifies its effectiveness on EE trade-off.Importantly, ROFU admits a very efficient implementation with gradient-basedoptimizer, which easily extends to general deep neural network models beyondneural tangent kernel, in sharp contrast with previous OFU methods. The em-pirical evaluation demonstrates that ROFU works extremelywell for contextualbandits under various settings.

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arXiv2021

$\mathcal{G}$-SGD: Optimizing ReLU Neural Networks in its Positively Scale-Invariant Space

It is well known that neural networks with rectified linear units (ReLU) activation functions are positively scale-invariant. Conventional algorithms like stochastic gradient descent optimize the neural networks in the vector space of weights, which is, however, not positively scale-invariant. This mismatch may lead to problems during the optimization process. Then, a natural question is: \emph{can we construct a new vector space that is positively scale-invariant and sufficient to represent ReLU neural networks so as to better facilitate the optimization process }? In this paper, we provide our positive answer to this question. First, we conduct a formal study on the positive scaling operators which forms a transformation group, denoted as $\mathcal{G}$. We show that the value of a path (i.e. the product of the weights along the path) in the neural network is invariant to positive scaling and prove that the value vector of all the paths is sufficient to represent the neural networks under mild conditions. Second, we show that one can identify some basis paths out of all the paths and prove that the linear span of their value vectors (denoted as $\mathcal{G}$-space) is an invariant space with lower dimension under the positive scaling group. Finally, we design stochastic gradient descent algorithm in $\mathcal{G}$-space (abbreviated as $\mathcal{G}$-SGD) to optimize the value vector of the basis paths of neural networks with little extra cost by leveraging back-propagation. Our experiments show that $\mathcal{G}$-SGD significantly outperforms the conventional SGD algorithm in optimizing ReLU networks on benchmark datasets.

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arXiv2021

How Does Data Augmentation Affect Privacy in Machine Learning?

It is observed in the literature that data augmentation can significantly mitigate membership inference (MI) attack. However, in this work, we challenge this observation by proposing new MI attacks to utilize the information of augmented data. MI attack is widely used to measure the model's information leakage of the training set. We establish the optimal membership inference when the model is trained with augmented data, which inspires us to formulate the MI attack as a set classification problem, i.e., classifying a set of augmented instances instead of a single data point, and design input permutation invariant features. Empirically, we demonstrate that the proposed approach universally outperforms original methods when the model is trained with data augmentation. Even further, we show that the proposed approach can achieve higher MI attack success rates on models trained with some data augmentation than the existing methods on models trained without data augmentation. Notably, we achieve a 70.1% MI attack success rate on CIFAR10 against a wide residual network while the previous best approach only attains 61.9%. This suggests the privacy risk of models trained with data augmentation could be largely underestimated.

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arXiv2021

BN-invariant sharpness regularizes the training model to better generalization

It is arguably believed that flatter minima can generalize better. However, it has been pointed out that the usual definitions of sharpness, which consider either the maxima or the integral of loss over a $δ$ ball of parameters around minima, cannot give consistent measurement for scale invariant neural networks, e.g., networks with batch normalization layer. In this paper, we first propose a measure of sharpness, BN-Sharpness, which gives consistent value for equivalent networks under BN. It achieves the property of scale invariance by connecting the integral diameter with the scale of parameter. Then we present a computation-efficient way to calculate the BN-sharpness approximately i.e., one dimensional integral along the "sharpest" direction. Furthermore, we use the BN-sharpness to regularize the training and design an algorithm to minimize the new regularized objective. Our algorithm achieves considerably better performance than vanilla SGD over various experiment settings.

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arXiv2020

Gradient Perturbation is Underrated for Differentially Private Convex Optimization

Gradient perturbation, widely used for differentially private optimization, injects noise at every iterative update to guarantee differential privacy. Previous work first determines the noise level that can satisfy the privacy requirement and then analyzes the utility of noisy gradient updates as in the non-private case. In contrast, we explore how privacy noise affects optimization property. We show that for differentially private convex optimization, the utility guarantee of differentially private (stochastic) gradient descent is determined by an \emph{expected curvature} rather than the minimum curvature. The \emph{expected curvature}, which represents the average curvature over the optimization path, is usually much larger than the minimum curvature. By using the \emph{expected curvature}, we show that gradient perturbation can achieve a significantly improved utility guarantee that can theoretically justify the advantage of gradient perturbation over other perturbation methods. Finally, our extensive experiments suggest that gradient perturbation with the advanced composition method indeed outperforms other perturbation approaches by a large margin, matching our theoretical findings.

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