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Title: The Secret Revealer: Generative Model Inversion Attacks Against Deep Neural Networks

Paper content:
This paper studies \emph{model inversion attacks}, in which the access to a model is abused to infer information about the training data.
Since its first introduction by~\citet{fredrikson2014privacy}, such attacks have raised serious concerns given that training data usually contain sensitive information.
Thus far, successful model inversion attacks have only been demonstrated on simple models, such as linear regression and logistic regression.
Previous attempts to invert neural networks, even the ones with simple architectures, have failed to produce convincing results.
We present a novel attack method, termed the \emph{generative model inversion attack}, which can invert deep neural networks with high success rates.
Rather than reconstructing private training data from scratch, we leverage partial public information, which can be very generic, to learn a distributional prior via generative adversarial networks (GANs) and use it to guide the inversion process.
Moreover, we theoretically prove that a model's predictive power and its vulnerability to inversion attacks are indeed two sides of the same coin---highly predictive models are able to establish a strong correlation between features and labels, which coincides exactly with what an adversary exploits to mount the attacks.
Our experiments demonstrate that the proposed attack improves identification accuracy over the existing work by about $75\%$ for reconstructing face images from a state-of-the-art face recognition classifier.
We also show that differential privacy, in its canonical form, is of little avail to protect against our attacks.
Deep neural networks (DNNs) have been adopted in a wide range of applications, including computer vision, speech recognition, healthcare, among others.
The fact that many compelling applications of DNNs involve processing sensitive and proprietary datasets raised great concerns about privacy.
In particular, when machine learning (ML) algorithms are applied to private training data, the resulting models may unintentionally leak information about training data through their output (i.e., black-box attack) or their parameters (i.e., white-box attack).
A concrete example of privacy attacks is model inversion (MI) attacks, which aim to reconstruct sensitive features of training data by taking advantage of their correlation with the model output.
Algorithmically, MI attacks are implemented as an optimization problem seeking for the sensitive feature value that achieves the maximum likelihood under the target model.
The first MI attack was proposed in the context of genomic privacy (Fredrikson et al., 2014) , where the authors showed that adversarial access to a linear regression model for personalized medicine can be abused to infer private genomic attributes about individuals in the training dataset.
Recent work (Fredrikson et al., 2015) extended MI attacks to other settings, e.g., recovering an image of a person from a face recognition model given just their name, and other target models, e.g., logistic regression and decision trees.
Thus far, effective MI attacks have only been demonstrated on the aforementioned simple models.
It remains an open question whether it is possible to launch the attacks against a DNN and reconstruct its private training data.
The challenges of inverting DNNs arise from the intractability and ill-posedness of the underlying attack optimization problem.
For neural networks, even the ones with one hidden layer, the corresponding attack optimization becomes a non-convex problem; solving it via gradient descent methods may easily stuck in local minima, which leads to poor attack performance.
Moreover, in the attack scenarios where the target model is a DNN (e.g., attacking face recognition models), the sensitive features (face images) to be recovered often lie in a high-dimensional, continuous data space.
Directly optimizing over the high-dimensional space without any constraints may generate unrealistic features lacking semantic information (See Figure 1) .
Figure 1 : Reconstruction of the individual on the left by attacking three face recognition models (logistic regression, one-hidden-layer and twohidden-layer neural network) using the existing attack algorithm in (Fredrikson et al., 2015) In this paper, we focus on image data and propose a simple yet effective attack method, termed the generative model inversion (GMI) attack, which can invert DNNs and synthesize private training data with high fidelity.
The key observation supporting our approach is that it is arguably easy to obtain information about the general data distribution, especially for the image case.
For example, against a face recognition classifier, the adversary could randomly crawl facial images from the Internet without knowing the private training data.
We find these datasets, although may not contain the target individuals, still provide rich knowledge about how a face image might be structured; extraction and proper formulation of such prior knowledge will help regularize the originally ill-posed inversion problem.
We also move beyond specific attack algorithms and explore the fundamental reasons for a model's susceptibility to inversion attacks.
We show that the vulnerability is unavoidable for highly predictive models, since these models are able to establish a strong correlation between features and labels, which coincides exactly with what an adversary exploits to mount MI attacks.
Our contributions can be summarized as follows: (1) We propose to use generative models to learn an informative prior from public datasets so as to regularize the ill-posed inversion problem.
(2) We propose an end-to-end GMI attack algorithm based on GANs, which can reveal private training data of DNNs with high fidelity.
(3) We present a theoretical result that uncovers the fundamental connection between a model's predictive power and its susceptibility to general MI attacks and empirically validate it.
(4) We conduct extensive experiments to demonstrate the performance of the proposed attack.
Experiment code is publicly available at https://tinyurl.com/yxbnjk4s.
Related Work Privacy attacks against ML models consist of methods that aim to reveal some aspects of training data.
Of particular interest are membership attacks and MI attacks.
Membership attacks aim to determine whether a given individual's data is used in training the model (Shokri et al., 2017) .
MI attacks, on the other hand, aim to reconstruct the features corresponding to specific target labels.
In parallel to the emergence of various privacy attack methods, there is a line work that formalizes the privacy notion and develops defenses with formal and provable privacy guarantees.
One dominate definition of privacy is differential privacy (DP), which carefully randomizes an algorithm so that its output does not to depend too much on any individuals' data (Dwork et al., 2014) .
In the context of ML algorithms, DP guarantees protect against attempts to infer whether a data record is included in the training set from the trained model (Abadi et al., 2016) .
By definition, DP limits the success rate of membership attacks.
However, it does not explicitly protect attribute privacy, which is the target of MI attacks (Fredrikson et al., 2014) .
The first MI attack was demonstrated in (Fredrikson et al., 2014) , where the authors presented an algorithm to recover genetic markers given the linear regression that uses them as input features, the response of the model, as well as other non-sensitive features of the input.
Hidano et al. (2017) proposed a algorithm that allows MI attacks to be carried out without the knowledge of non-sensitive features by poisoning training data properly.
Despite the generality of the algorithmic frameworks proposed in the above two papers, the evaluation of the attacks is only limited to linear models.
Fredrikson et al. (2015) discussed the application of MI attacks to more complex models including some shallow neural networks in the context of face recognition.
Although the attack can reconstruct face images with identification rates much higher than random guessing, the recovered faces are indeed blurry and hardly recognizable.
Moreover, the quality of reconstruction tends to degrade for more complex architectures.
Yang et al. (2019b) proposed to train a separate network that swaps the input and output of the target network to perform MI attacks.
The inversion model can be trained with black-box accesses to the target model.
However, their approach cannot directly be benefited from the white-box setting.
Moreover, several recent papers started to formalize MI attacks and study the factors that affect a model's vulnerability from a theoretical viewpoint.
For instance, Wu et al. (2016) characterized model invertibility for Boolean functions using the concept of influence from Boolean analysis; Yeom et al. (2018) formalized the risk that the model poses specifically to individuals in the training data and shows that the risk increases with the degree of overfitting of the model.
However, their theory assumed that the adversary has access to the join distribution of private feature and label, which is overly strong for many attack scenarios.
Our theory does not rely on this assumption and better supports the experimental findings.
In this paper, we present a generative approach to MI attacks, which can achieve the-state-of-the-art success rates for attacking the DNNs with high-dimensional input data.
The idea of our approach is to extract generic knowledge from public datasets via GAN and use it to regularize the inversion problem.
Our experimental results show that our proposed attack is highly performant even when the public datasets (1) do not include the identities that the adversary aims to recover, (2) are unlabeled, (3) have small sizes, (4) come from a different distribution from the private data.
We also provide theoretical analysis showing the fundamental connection between a model's predictive power and its vulnerability to inversion attacks.
For future work, we are interested in extending the attack to the black-box setting and studying effective defenses against MI attacks.
A PROOF OF THEOREM 1 Theorem 2.
Let f 1 and f 2 are two models such that for any fixed label y ∈ Y, U f1 (x ns , y) ≥ U f2 (x ns , y).
Then, S KL (p(X s |y, x ns )||p f1 (X s |y, x ns )) ≥ S KL (p(X s |y, x ns )||p f2 (X s |y, x ns )).
Proof.
We can expand the KL divergence D KL (p(X s |y, x ns )||p f1 (X s |y, x ns ) as follows.
Thus,
B EXPERIMENTAL DETAILS B.1
NETWORK ARCHITECTURE
The detailed architectures for the two encoders, the decoder of the generator, the local discriminator, and the global discriminator are presented in Table 6, Table 7, Table 8 , Table 9 , and Table 10 , respectively.
(1) LeNet adapted from (Lecun et al., 1998) , which has three convolutional layers, two max pooling layers and one FC layer; (2) SimpleCNN, which has five convolutional layers, each followed by a batch normalization layer and a leaky ReLU layer; (3) SoftmaxNet, which has only one FC layer.
We split the MNIST dataset into the private set used for training target networks with digits 0 ∼ 4 and the public set used for distilling prior knowledge with digits 5 ∼ 9.
The target network is implemented as a Multilayer Perceptron with 2 hidden layers, which have 512 and 256 neurons, respectively.
The evaluation classifier is a convulutional neural network with three convolution layers, followed by two fully-connected layers.
It is trained on the entire MNIST training set and can achieve 99.2% accuracy on the MNIST test set.
Differential privacy of target networks is guaranteed by adding Gaussian noise to each stochastic gradient descent step.
We use the moment accounting technique to keep track of the privacy budget spent during training (Abadi et al., 2016) .
During the training of the target networks, we set the batch size to be 256.
We fix the number of epochs to be 40 and clip the L2 norm of per-sample gradient to be bounded by 1.5.
We set the ratio between the noise scale and the gradient clipping threshold to be 0, 0.694, 0.92, 3, 28, respectively, to obtain the target networks with ε = ∞, 9.89, 4.94, 0.98, 0.10 when δ = 10 −5 .
For model with ε = 0.1, we use the SGD with a small learning rate 0.01 to ensure stable convergence; otherwise, we set the learning rate to be 0.1.
The architecture of the generator in Section B.1 is tailored to the MNIST dataset.
We reduce the number of input channels, change the size of kernels, and modify the layers of discriminators to be compatible with the shape of the MNIST data.
To train the GAN in the first stage of our GMI attack, we set the batch size to be 64 and use the Adam optimizer with the learning rate 0.004, β 1 = 0.5, and β 2 = 0.999 (Kingma and Ba, 2014) .
For the second stage, we set the batch size to be 64 and use the SGD with the Nesterov momentum that has the learning rate 0.01 and momentum 0.9.
The optimization is performed for 1500 iterations.
The center mask depicted in the main text is used to block the central part of digits.
We report the attack accuracy averaged across 640 randomly sampled images from the private set and 5 random initializations of the latent vector for each sampled image.

assistant: text: We develop a privacy attack that can recover the sensitive input data of a deep net from its output