Huan Zhang

Huan Zhang, Shiqi Wang, Kaidi Xu et al. · amazon-science

Bound propagation methods, when combined with branch and bound, are among the most effective methods to formally verify properties of deep neural networks such as correctness, robustness, and safety. However, existing works cannot handle the general form of cutting plane constraints widely accepted in traditional solvers, which are crucial for strengthening verifiers with tightened convex relaxations. In this paper, we generalize the bound propagation procedure to allow the addition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations. Our generalized bound propagation method, GCP-CROWN, opens up the opportunity to apply general cutting plane methods for neural network verification while benefiting from the efficiency and GPU acceleration of bound propagation methods. As a case study, we investigate the use of cutting planes generated by off-the-shelf mixed integer programming (MIP) solver. We find that MIP solvers can generate high-quality cutting planes for strengthening bound-propagation-based verifiers using our new formulation. Since the branching-focused bound propagation procedure and the cutting-plane-focused MIP solver can run in parallel utilizing different types of hardware (GPUs and CPUs), their combination can quickly explore a large number of branches with strong cutting planes, leading to strong verification performance. Experiments demonstrate that our method is the first verifier that can completely solve the oval20 benchmark and verify twice as many instances on the oval21 benchmark compared to the best tool in VNN-COMP 2021, and also noticeably outperforms state-of-the-art verifiers on a wide range of benchmarks. GCP-CROWN is part of the $α,\!β$-CROWN verifier, the VNN-COMP 2022 winner. Code is available at http://PaperCode.cc/GCP-CROWN

Jiawei Zhang, Zhongzhu Chen, Huan Zhang et al.

Diffusion models have been leveraged to perform adversarial purification and thus provide both empirical and certified robustness for a standard model. On the other hand, different robustly trained smoothed models have been studied to improve the certified robustness. Thus, it raises a natural question: Can diffusion model be used to achieve improved certified robustness on those robustly trained smoothed models? In this work, we first theoretically show that recovered instances by diffusion models are in the bounded neighborhood of the original instance with high probability; and the "one-shot" denoising diffusion probabilistic models (DDPM) can approximate the mean of the generated distribution of a continuous-time diffusion model, which approximates the original instance under mild conditions. Inspired by our analysis, we propose a certifiably robust pipeline DiffSmooth, which first performs adversarial purification via diffusion models and then maps the purified instances to a common region via a simple yet effective local smoothing strategy. We conduct extensive experiments on different datasets and show that DiffSmooth achieves SOTA-certified robustness compared with eight baselines. For instance, DiffSmooth improves the SOTA-certified accuracy from $36.0\%$ to $53.0\%$ under $\ell_2$ radius $1.5$ on ImageNet. The code is available at [https://github.com/javyduck/DiffSmooth].

Li-Cheng Lan, Huan Zhang, Cho-Jui Hsieh

In this paper, we define, evaluate, and improve the ``relay-generalization'' performance of reinforcement learning (RL) agents on the out-of-distribution ``controllable'' states. Ideally, an RL agent that generally masters a task should reach its goal starting from any controllable state of the environment instead of memorizing a small set of trajectories. For example, a self-driving system should be able to take over the control from humans in the middle of driving and must continue to drive the car safely. To practically evaluate this type of generalization, we start the test agent from the middle of other independently well-trained \emph{stranger} agents' trajectories. With extensive experimental evaluation, we show the prevalence of \emph{generalization failure} on controllable states from stranger agents. For example, in the Humanoid environment, we observed that a well-trained Proximal Policy Optimization (PPO) agent, with only 3.9\% failure rate during regular testing, failed on 81.6\% of the states generated by well-trained stranger PPO agents. To improve "relay generalization," we propose a novel method called Self-Trajectory Augmentation (STA), which will reset the environment to the agent's old states according to the Q function during training. After applying STA to the Soft Actor Critic's (SAC) training procedure, we reduced the failure rate of SAC under relay-evaluation by more than three times in most settings without impacting agent performance and increasing the needed number of environment interactions. Our code is available at https://github.com/lan-lc/STA.

Huan Ma. Qingyang Zhang, Changqing Zhang, Bingzhe Wu et al.

Multimodal machine learning has achieved remarkable progress in a wide range of scenarios. However, the reliability of multimodal learning remains largely unexplored. In this paper, through extensive empirical studies, we identify current multimodal classification methods suffer from unreliable predictive confidence that tend to rely on partial modalities when estimating confidence. Specifically, we find that the confidence estimated by current models could even increase when some modalities are corrupted. To address the issue, we introduce an intuitive principle for multimodal learning, i.e., the confidence should not increase when one modality is removed. Accordingly, we propose a novel regularization technique, i.e., Calibrating Multimodal Learning (CML) regularization, to calibrate the predictive confidence of previous methods. This technique could be flexibly equipped by existing models and improve the performance in terms of confidence calibration, classification accuracy, and model robustness.

Fan Wu, Linyi Li, Chejian Xu et al.

As reinforcement learning (RL) has achieved near human-level performance in a variety of tasks, its robustness has raised great attention. While a vast body of research has explored test-time (evasion) attacks in RL and corresponding defenses, its robustness against training-time (poisoning) attacks remains largely unanswered. In this work, we focus on certifying the robustness of offline RL in the presence of poisoning attacks, where a subset of training trajectories could be arbitrarily manipulated. We propose the first certification framework, COPA, to certify the number of poisoning trajectories that can be tolerated regarding different certification criteria. Given the complex structure of RL, we propose two certification criteria: per-state action stability and cumulative reward bound. To further improve the certification, we propose new partition and aggregation protocols to train robust policies. We further prove that some of the proposed certification methods are theoretically tight and some are NP-Complete problems. We leverage COPA to certify three RL environments trained with different algorithms and conclude: (1) The proposed robust aggregation protocols such as temporal aggregation can significantly improve the certifications; (2) Our certification for both per-state action stability and cumulative reward bound are efficient and tight; (3) The certification for different training algorithms and environments are different, implying their intrinsic robustness properties. All experimental results are available at https://copa-leaderboard.github.io.

Qiusi Zhan, Hyeonjeong Ha, Rui Yang et al.

Multimodal large language models (MLLMs) have advanced embodied agents by enabling direct perception, reasoning, and planning task-oriented actions from visual inputs. However, such vision driven embodied agents open a new attack surface: visual backdoor attacks, where the agent behaves normally until a visual trigger appears in the scene, then persistently executes an attacker-specified multi-step policy. We introduce BEAT, the first framework to inject such visual backdoors into MLLM-based embodied agents using objects in the environments as triggers. Unlike textual triggers, object triggers exhibit wide variation across viewpoints and lighting, making them difficult to implant reliably. BEAT addresses this challenge by (1) constructing a training set that spans diverse scenes, tasks, and trigger placements to expose agents to trigger variability, and (2) introducing a two-stage training scheme that first applies supervised fine-tuning (SFT) and then our novel Contrastive Trigger Learning (CTL). CTL formulates trigger discrimination as preference learning between trigger-present and trigger-free inputs, explicitly sharpening the decision boundaries to ensure precise backdoor activation. Across various embodied agent benchmarks and MLLMs, BEAT achieves attack success rates up to 80%, while maintaining strong benign task performance, and generalizes reliably to out-of-distribution trigger placements. Notably, compared to naive SFT, CTL boosts backdoor activation accuracy up to 39% under limited backdoor data. These findings expose a critical yet unexplored security risk in MLLM-based embodied agents, underscoring the need for robust defenses before real-world deployment.

Chong Zhang, Jieyu Zhao, Huan Zhang et al.

Robustness and counterfactual bias are usually evaluated on a test dataset. However, are these evaluations robust? If the test dataset is perturbed slightly, will the evaluation results keep the same? In this paper, we propose a "double perturbation" framework to uncover model weaknesses beyond the test dataset. The framework first perturbs the test dataset to construct abundant natural sentences similar to the test data, and then diagnoses the prediction change regarding a single-word substitution. We apply this framework to study two perturbation-based approaches that are used to analyze models' robustness and counterfactual bias in English. (1) For robustness, we focus on synonym substitutions and identify vulnerable examples where prediction can be altered. Our proposed attack attains high success rates (96.0%-99.8%) in finding vulnerable examples on both original and robustly trained CNNs and Transformers. (2) For counterfactual bias, we focus on substituting demographic tokens (e.g., gender, race) and measure the shift of the expected prediction among constructed sentences. Our method is able to reveal the hidden model biases not directly shown in the test dataset. Our code is available at https://github.com/chong-z/nlp-second-order-attack.

Shiqi Wang, Huan Zhang, Kaidi Xu et al.

Bound propagation based incomplete neural network verifiers such as CROWN are very efficient and can significantly accelerate branch-and-bound (BaB) based complete verification of neural networks. However, bound propagation cannot fully handle the neuron split constraints introduced by BaB commonly handled by expensive linear programming (LP) solvers, leading to loose bounds and hurting verification efficiency. In this work, we develop $β$-CROWN, a new bound propagation based method that can fully encode neuron splits via optimizable parameters $β$ constructed from either primal or dual space. When jointly optimized in intermediate layers, $β$-CROWN generally produces better bounds than typical LP verifiers with neuron split constraints, while being as efficient and parallelizable as CROWN on GPUs. Applied to complete robustness verification benchmarks, $β$-CROWN with BaB is up to three orders of magnitude faster than LP-based BaB methods, and is notably faster than all existing approaches while producing lower timeout rates. By terminating BaB early, our method can also be used for efficient incomplete verification. We consistently achieve higher verified accuracy in many settings compared to powerful incomplete verifiers, including those based on convex barrier breaking techniques. Compared to the typically tightest but very costly semidefinite programming (SDP) based incomplete verifiers, we obtain higher verified accuracy with three orders of magnitudes less verification time. Our algorithm empowered the $α,\!β$-CROWN (alpha-beta-CROWN) verifier, the winning tool in VNN-COMP 2021. Our code is available at http://PaperCode.cc/BetaCROWN

Huan Zhang, Hongge Chen, Duane Boning et al.

We study the robustness of reinforcement learning (RL) with adversarially perturbed state observations, which aligns with the setting of many adversarial attacks to deep reinforcement learning (DRL) and is also important for rolling out real-world RL agent under unpredictable sensing noise. With a fixed agent policy, we demonstrate that an optimal adversary to perturb state observations can be found, which is guaranteed to obtain the worst case agent reward. For DRL settings, this leads to a novel empirical adversarial attack to RL agents via a learned adversary that is much stronger than previous ones. To enhance the robustness of an agent, we propose a framework of alternating training with learned adversaries (ATLA), which trains an adversary online together with the agent using policy gradient following the optimal adversarial attack framework. Additionally, inspired by the analysis of state-adversarial Markov decision process (SA-MDP), we show that past states and actions (history) can be useful for learning a robust agent, and we empirically find a LSTM based policy can be more robust under adversaries. Empirical evaluations on a few continuous control environments show that ATLA achieves state-of-the-art performance under strong adversaries. Our code is available at https://github.com/huanzhang12/ATLA_robust_RL.

Huan Zhang, Hongge Chen, Chaowei Xiao et al.

A deep reinforcement learning (DRL) agent observes its states through observations, which may contain natural measurement errors or adversarial noises. Since the observations deviate from the true states, they can mislead the agent into making suboptimal actions. Several works have shown this vulnerability via adversarial attacks, but existing approaches on improving the robustness of DRL under this setting have limited success and lack for theoretical principles. We show that naively applying existing techniques on improving robustness for classification tasks, like adversarial training, is ineffective for many RL tasks. We propose the state-adversarial Markov decision process (SA-MDP) to study the fundamental properties of this problem, and develop a theoretically principled policy regularization which can be applied to a large family of DRL algorithms, including proximal policy optimization (PPO), deep deterministic policy gradient (DDPG) and deep Q networks (DQN), for both discrete and continuous action control problems. We significantly improve the robustness of PPO, DDPG and DQN agents under a suite of strong white box adversarial attacks, including new attacks of our own. Additionally, we find that a robust policy noticeably improves DRL performance even without an adversary in a number of environments. Our code is available at https://github.com/chenhongge/StateAdvDRL.

Hadi Salman, Greg Yang, Jerry Li et al.

Recent works have shown the effectiveness of randomized smoothing as a scalable technique for building neural network-based classifiers that are provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we employ adversarial training to improve the performance of randomized smoothing. We design an adapted attack for smoothed classifiers, and we show how this attack can be used in an adversarial training setting to boost the provable robustness of smoothed classifiers. We demonstrate through extensive experimentation that our method consistently outperforms all existing provably $\ell_2$-robust classifiers by a significant margin on ImageNet and CIFAR-10, establishing the state-of-the-art for provable $\ell_2$-defenses. Moreover, we find that pre-training and semi-supervised learning boost adversarially trained smoothed classifiers even further. Our code and trained models are available at http://github.com/Hadisalman/smoothing-adversarial .

Shaokai Ye, Kaidi Xu, Sijia Liu et al.

It is well known that deep neural networks (DNNs) are vulnerable to adversarial attacks, which are implemented by adding crafted perturbations onto benign examples. Min-max robust optimization based adversarial training can provide a notion of security against adversarial attacks. However, adversarial robustness requires a significantly larger capacity of the network than that for the natural training with only benign examples. This paper proposes a framework of concurrent adversarial training and weight pruning that enables model compression while still preserving the adversarial robustness and essentially tackles the dilemma of adversarial training. Furthermore, this work studies two hypotheses about weight pruning in the conventional setting and finds that weight pruning is essential for reducing the network model size in the adversarial setting, training a small model from scratch even with inherited initialization from the large model cannot achieve both adversarial robustness and high standard accuracy. Code is available at https://github.com/yeshaokai/Robustness-Aware-Pruning-ADMM.

Hadi Salman, Greg Yang, Huan Zhang et al.

Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but incomplete. In this paper, we unify all existing LP-relaxed verifiers, to the best of our knowledge, under a general convex relaxation framework. This framework works for neural networks with diverse architectures and nonlinearities and covers both primal and dual views of robustness verification. We further prove strong duality between the primal and dual problems under very mild conditions. Next, we perform large-scale experiments, amounting to more than 22 CPU-years, to obtain exact solution to the convex-relaxed problem that is optimal within our framework for ReLU networks. We find the exact solution does not significantly improve upon the gap between PGD and existing relaxed verifiers for various networks trained normally or robustly on MNIST and CIFAR datasets. Our results suggest there is an inherent barrier to tight verification for the large class of methods captured by our framework. We discuss possible causes of this barrier and potential future directions for bypassing it. Our code and trained models are available at http://github.com/Hadisalman/robust-verify-benchmark .

Dong Su, Huan Zhang, Hongge Chen et al.

The prediction accuracy has been the long-lasting and sole standard for comparing the performance of different image classification models, including the ImageNet competition. However, recent studies have highlighted the lack of robustness in well-trained deep neural networks to adversarial examples. Visually imperceptible perturbations to natural images can easily be crafted and mislead the image classifiers towards misclassification. To demystify the trade-offs between robustness and accuracy, in this paper we thoroughly benchmark 18 ImageNet models using multiple robustness metrics, including the distortion, success rate and transferability of adversarial examples between 306 pairs of models. Our extensive experimental results reveal several new insights: (1) linear scaling law - the empirical $\ell_2$ and $\ell_\infty$ distortion metrics scale linearly with the logarithm of classification error; (2) model architecture is a more critical factor to robustness than model size, and the disclosed accuracy-robustness Pareto frontier can be used as an evaluation criterion for ImageNet model designers; (3) for a similar network architecture, increasing network depth slightly improves robustness in $\ell_\infty$ distortion; (4) there exist models (in VGG family) that exhibit high adversarial transferability, while most adversarial examples crafted from one model can only be transferred within the same family. Experiment code is publicly available at \url{https://github.com/huanzhang12/Adversarial_Survey}.

Junyu Zhang, Yifan Sun, Tianang Leng et al.

Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper presents the Laws of Reasoning (LoRe), a unified framework that characterizes intrinsic reasoning patterns in LRMs. We first propose compute law with the hypothesis that the reasoning compute should scale linearly with question complexity. Beyond compute, we extend LoRe with a supplementary accuracy law. Since the question complexity is difficult to quantify in practice, we examine these hypotheses by two properties of the laws, monotonicity and compositionality. We therefore introduce LoRe-Bench, a benchmark that systematically measures these two tractable properties for large reasoning models. Evaluation shows that most reasoning models exhibit reasonable monotonicity but lack compositionality. In response, we develop an effective finetuning approach that enforces compute-law compositionality. Extensive empirical studies demonstrate that better compliance with compute laws yields consistently improved reasoning performance on multiple benchmarks, and uncovers synergistic effects across properties and laws. Project page: https://lore-project.github.io/

Junyu Zhang, Runpei Dong, Han Wang et al.

This paper presents AlphaOne ($α$1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. $α$1 first introduces $α$ moment, which represents the scaled thinking phase with a universal parameter $α$. Within this scaled pre-$α$ moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the $α$ moment, $α$1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation. This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate $α$1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/

Rui Yang, Ruomeng Ding, Yong Lin et al.

Reward models trained on human preference data have been proven to effectively align Large Language Models (LLMs) with human intent within the framework of reinforcement learning from human feedback (RLHF). However, current reward models have limited generalization capabilities to unseen prompts and responses, which can lead to an unexpected phenomenon known as reward over-optimization, resulting in a decline in actual performance due to excessive optimization of rewards. While previous research has advocated for constraining policy optimization, our study introduces a novel approach to enhance the reward model's generalization ability against distribution shifts by regularizing the hidden states. Specifically, we retain the base model's language model head and incorporate a suite of text-generation losses to preserve the hidden states' text-generation capabilities, while concurrently learning a reward head behind the same hidden states. Our experimental results demonstrate that the introduced regularization technique markedly improves the accuracy of learned reward models across a variety of out-of-distribution (OOD) tasks and effectively alleviates the over-optimization issue in RLHF, offering a more reliable and robust preference learning paradigm.

Zhiji Yang, Wanyi Chen, Huan Zhang et al.

Support vector machine (SVM) has achieved many successes in machine learning, especially for a small sample problem. As a famous extension of the traditional SVM, the $ν$ support vector machine ($ν$-SVM) has shown outstanding performance due to its great model interpretability. However, it still faces challenges in training overhead for large-scale problems. To address this issue, we propose a safe screening rule with bi-level optimization for $ν$-SVM (SRBO-$ν$-SVM) which can screen out inactive samples before training and reduce the computational cost without sacrificing the prediction accuracy. Our SRBO-$ν$-SVM is strictly deduced by integrating the Karush-Kuhn-Tucker (KKT) conditions, the variational inequalities of convex problems and the $ν$-property. Furthermore, we develop an efficient dual coordinate descent method (DCDM) to further improve computational speed. Finally, a unified framework for SRBO is proposed to accelerate many SVM-type models, and it is successfully applied to one-class SVM. Experimental results on 6 artificial data sets and 30 benchmark data sets have verified the effectiveness and safety of our proposed methods in supervised and unsupervised tasks.

Jaehui Hwang, Huan Zhang, Jun-Ho Choi et al.

Recently, video-based action recognition methods using convolutional neural networks (CNNs) achieve remarkable recognition performance. However, there is still lack of understanding about the generalization mechanism of action recognition models. In this paper, we suggest that action recognition models rely on the motion information less than expected, and thus they are robust to randomization of frame orders. Furthermore, we find that motion monotonicity remaining after randomization also contributes to such robustness. Based on this observation, we develop a novel defense method using temporal shuffling of input videos against adversarial attacks for action recognition models. Another observation enabling our defense method is that adversarial perturbations on videos are sensitive to temporal destruction. To the best of our knowledge, this is the first attempt to design a defense method without additional training for 3D CNN-based video action recognition models.

Jun-Ho Choi, Huan Zhang, Jun-Hyuk Kim et al.

Recently, the vulnerability of deep image classification models to adversarial attacks has been investigated. However, such an issue has not been thoroughly studied for image-to-image tasks that take an input image and generate an output image (e.g., colorization, denoising, deblurring, etc.) This paper presents comprehensive investigations into the vulnerability of deep image-to-image models to adversarial attacks. For five popular image-to-image tasks, 16 deep models are analyzed from various standpoints such as output quality degradation due to attacks, transferability of adversarial examples across different tasks, and characteristics of perturbations. We show that unlike image classification tasks, the performance degradation on image-to-image tasks largely differs depending on various factors, e.g., attack methods and task objectives. In addition, we analyze the effectiveness of conventional defense methods used for classification models in improving the robustness of the image-to-image models.

Kaidi Xu, Huan Zhang, Shiqi Wang et al.

Formal verification of neural networks (NNs) is a challenging and important problem. Existing efficient complete solvers typically require the branch-and-bound (BaB) process, which splits the problem domain into sub-domains and solves each sub-domain using faster but weaker incomplete verifiers, such as Linear Programming (LP) on linearly relaxed sub-domains. In this paper, we propose to use the backward mode linear relaxation based perturbation analysis (LiRPA) to replace LP during the BaB process, which can be efficiently implemented on the typical machine learning accelerators such as GPUs and TPUs. However, unlike LP, LiRPA when applied naively can produce much weaker bounds and even cannot check certain conflicts of sub-domains during splitting, making the entire procedure incomplete after BaB. To address these challenges, we apply a fast gradient based bound tightening procedure combined with batch splits and the design of minimal usage of LP bound procedure, enabling us to effectively use LiRPA on the accelerator hardware for the challenging complete NN verification problem and significantly outperform LP-based approaches. On a single GPU, we demonstrate an order of magnitude speedup compared to existing LP-based approaches.

Yihan Wang, Huan Zhang, Hongge Chen et al.

Recent papers have demonstrated that ensemble stumps and trees could be vulnerable to small input perturbations, so robustness verification and defense for those models have become an important research problem. However, due to the structure of decision trees, where each node makes decision purely based on one feature value, all the previous works only consider the $\ell_\infty$ norm perturbation. To study robustness with respect to a general $\ell_p$ norm perturbation, one has to consider the correlation between perturbations on different features, which has not been handled by previous algorithms. In this paper, we study the problem of robustness verification and certified defense with respect to general $\ell_p$ norm perturbations for ensemble decision stumps and trees. For robustness verification of ensemble stumps, we prove that complete verification is NP-complete for $p\in(0, \infty)$ while polynomial time algorithms exist for $p=0$ or $\infty$. For $p\in(0, \infty)$ we develop an efficient dynamic programming based algorithm for sound verification of ensemble stumps. For ensemble trees, we generalize the previous multi-level robustness verification algorithm to $\ell_p$ norm. We demonstrate the first certified defense method for training ensemble stumps and trees with respect to $\ell_p$ norm perturbations, and verify its effectiveness empirically on real datasets.

Bowen Wu, Huan Zhang, Mengyuan Li et al.

Recently, BERT has become an essential ingredient of various NLP deep models due to its effectiveness and universal-usability. However, the online deployment of BERT is often blocked by its large-scale parameters and high computational cost. There are plenty of studies showing that the knowledge distillation is efficient in transferring the knowledge from BERT into the model with a smaller size of parameters. Nevertheless, current BERT distillation approaches mainly focus on task-specified distillation, such methodologies lead to the loss of the general semantic knowledge of BERT for universal-usability. In this paper, we propose a sentence representation approximating oriented distillation framework that can distill the pre-trained BERT into a simple LSTM based model without specifying tasks. Consistent with BERT, our distilled model is able to perform transfer learning via fine-tuning to adapt to any sentence-level downstream task. Besides, our model can further cooperate with task-specific distillation procedures. The experimental results on multiple NLP tasks from the GLUE benchmark show that our approach outperforms other task-specific distillation methods or even much larger models, i.e., ELMO, with efficiency well-improved.

Runtian Zhai, Chen Dan, Di He et al.

Adversarial training is one of the most popular ways to learn robust models but is usually attack-dependent and time costly. In this paper, we propose the MACER algorithm, which learns robust models without using adversarial training but performs better than all existing provable l2-defenses. Recent work shows that randomized smoothing can be used to provide a certified l2 radius to smoothed classifiers, and our algorithm trains provably robust smoothed classifiers via MAximizing the CErtified Radius (MACER). The attack-free characteristic makes MACER faster to train and easier to optimize. In our experiments, we show that our method can be applied to modern deep neural networks on a wide range of datasets, including Cifar-10, ImageNet, MNIST, and SVHN. For all tasks, MACER spends less training time than state-of-the-art adversarial training algorithms, and the learned models achieve larger average certified radius.

Po-Sen Huang, Huan Zhang, Ray Jiang et al.

Advances in language modeling architectures and the availability of large text corpora have driven progress in automatic text generation. While this results in models capable of generating coherent texts, it also prompts models to internalize social biases present in the training corpus. This paper aims to quantify and reduce a particular type of bias exhibited by language models: bias in the sentiment of generated text. Given a conditioning context (e.g., a writing prompt) and a language model, we analyze if (and how) the sentiment of the generated text is affected by changes in values of sensitive attributes (e.g., country names, occupations, genders) in the conditioning context using a form of counterfactual evaluation. We quantify sentiment bias by adopting individual and group fairness metrics from the fair machine learning literature, and demonstrate that large-scale models trained on two different corpora (news articles, and Wikipedia) exhibit considerable levels of bias. We then propose embedding and sentiment prediction-derived regularization on the language model's latent representations. The regularizations improve fairness metrics while retaining comparable levels of perplexity and semantic similarity.

Huan Zhang, Minhao Cheng, Cho-Jui Hsieh

We propose an algorithm to enhance certified robustness of a deep model ensemble by optimally weighting each base model. Unlike previous works on using ensembles to empirically improve robustness, our algorithm is based on optimizing a guaranteed robustness certificate of neural networks. Our proposed ensemble framework with certified robustness, RobBoost, formulates the optimal model selection and weighting task as an optimization problem on a lower bound of classification margin, which can be efficiently solved using coordinate descent. Experiments show that our algorithm can form a more robust ensemble than naively averaging all available models using robustly trained MNIST or CIFAR base models. Additionally, our ensemble typically has better accuracy on clean (unperturbed) data. RobBoost allows us to further improve certified robustness and clean accuracy by creating an ensemble of already certified models.

Hongge Chen, Huan Zhang, Si Si et al.

We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches find the minimal adversarial perturbation by a mixed integer linear programming (MILP) problem, which takes exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles, the verification problem can be cast as a max-clique problem on a multi-partite graph with bounded boxicity. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we develop an efficient multi-level verification algorithm that can give tight lower bounds on the robustness of decision tree ensembles, while allowing iterative improvement and any-time termination. OnRF/GBDT models trained on 10 datasets, our algorithm is hundreds of times faster than the previous approach that requires solving MILPs, and is able to give tight robustness verification bounds on large GBDTs with hundreds of deep trees.

Hongge Chen, Huan Zhang, Duane Boning et al.

Although adversarial examples and model robustness have been extensively studied in the context of linear models and neural networks, research on this issue in tree-based models and how to make tree-based models robust against adversarial examples is still limited. In this paper, we show that tree based models are also vulnerable to adversarial examples and develop a novel algorithm to learn robust trees. At its core, our method aims to optimize the performance under the worst-case perturbation of input features, which leads to a max-min saddle point problem. Incorporating this saddle point objective into the decision tree building procedure is non-trivial due to the discrete nature of trees --- a naive approach to finding the best split according to this saddle point objective will take exponential time. To make our approach practical and scalable, we propose efficient tree building algorithms by approximating the inner minimizer in this saddle point problem, and present efficient implementations for classical information gain based trees as well as state-of-the-art tree boosting models such as XGBoost. Experimental results on real world datasets demonstrate that the proposed algorithms can substantially improve the robustness of tree-based models against adversarial examples.

Huan Zhang, Hongge Chen, Zhao Song et al.

The adversarial training procedure proposed by Madry et al. (2018) is one of the most effective methods to defend against adversarial examples in deep neural networks (DNNs). In our paper, we shed some lights on the practicality and the hardness of adversarial training by showing that the effectiveness (robustness on test set) of adversarial training has a strong correlation with the distance between a test point and the manifold of training data embedded by the network. Test examples that are relatively far away from this manifold are more likely to be vulnerable to adversarial attacks. Consequentially, an adversarial training based defense is susceptible to a new class of attacks, the "blind-spot attack", where the input images reside in "blind-spots" (low density regions) of the empirical distribution of training data but is still on the ground-truth data manifold. For MNIST, we found that these blind-spots can be easily found by simply scaling and shifting image pixel values. Most importantly, for large datasets with high dimensional and complex data manifold (CIFAR, ImageNet, etc), the existence of blind-spots in adversarial training makes defending on any valid test examples difficult due to the curse of dimensionality and the scarcity of training data. Additionally, we find that blind-spots also exist on provable defenses including (Wong & Kolter, 2018) and (Sinha et al., 2018) because these trainable robustness certificates can only be practically optimized on a limited set of training data.

Huan Zhang, Tsui-Wei Weng, Pin-Yu Chen et al.

Finding minimum distortion of adversarial examples and thus certifying robustness in neural network classifiers for given data points is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum adversarial distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations. However, a generic robustness certification for general activation functions still remains largely unexplored. To address this issue, in this paper we introduce CROWN, a general framework to certify robustness of neural networks with general activation functions for given input data points. The novelty in our algorithm consists of bounding a given activation function with linear and quadratic functions, hence allowing it to tackle general activation functions including but not limited to four popular choices: ReLU, tanh, sigmoid and arctan. In addition, we facilitate the search for a tighter certified lower bound by adaptively selecting appropriate surrogates for each neuron activation. Experimental results show that CROWN on ReLU networks can notably improve the certified lower bounds compared to the current state-of-the-art algorithm Fast-Lin, while having comparable computational efficiency. Furthermore, CROWN also demonstrates its effectiveness and flexibility on networks with general activation functions, including tanh, sigmoid and arctan.

Tsui-Wei Weng, Huan Zhang, Pin-Yu Chen et al.

CLEVER (Cross-Lipschitz Extreme Value for nEtwork Robustness) is an Extreme Value Theory (EVT) based robustness score for large-scale deep neural networks (DNNs). In this paper, we propose two extensions on this robustness score. First, we provide a new formal robustness guarantee for classifier functions that are twice differentiable. We apply extreme value theory on the new formal robustness guarantee and the estimated robustness is called second-order CLEVER score. Second, we discuss how to handle gradient masking, a common defensive technique, using CLEVER with Backward Pass Differentiable Approximation (BPDA). With BPDA applied, CLEVER can evaluate the intrinsic robustness of neural networks of a broader class -- networks with non-differentiable input transformations. We demonstrate the effectiveness of CLEVER with BPDA in experiments on a 121-layer Densenet model trained on the ImageNet dataset.

Kaidi Xu, Sijia Liu, Pu Zhao et al.

When generating adversarial examples to attack deep neural networks (DNNs), Lp norm of the added perturbation is usually used to measure the similarity between original image and adversarial example. However, such adversarial attacks perturbing the raw input spaces may fail to capture structural information hidden in the input. This work develops a more general attack model, i.e., the structured attack (StrAttack), which explores group sparsity in adversarial perturbations by sliding a mask through images aiming for extracting key spatial structures. An ADMM (alternating direction method of multipliers)-based framework is proposed that can split the original problem into a sequence of analytically solvable subproblems and can be generalized to implement other attacking methods. Strong group sparsity is achieved in adversarial perturbations even with the same level of Lp norm distortion as the state-of-the-art attacks. We demonstrate the effectiveness of StrAttack by extensive experimental results onMNIST, CIFAR-10, and ImageNet. We also show that StrAttack provides better interpretability (i.e., better correspondence with discriminative image regions)through adversarial saliency map (Papernot et al., 2016b) and class activation map(Zhou et al., 2016).

Tsui-Wei Weng, Huan Zhang, Hongge Chen et al.

Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a certified lower bound of the minimum distortion is possible. Current available methods of computing such a bound are either time-consuming or delivering low quality bounds that are too loose to be useful. In this paper, we exploit the special structure of ReLU networks and provide two computationally efficient algorithms Fast-Lin and Fast-Lip that are able to certify non-trivial lower bounds of minimum distortions, by bounding the ReLU units with appropriate linear functions Fast-Lin, or by bounding the local Lipschitz constant Fast-Lip. Experiments show that (1) our proposed methods deliver bounds close to (the gap is 2-3X) exact minimum distortion found by Reluplex in small MNIST networks while our algorithms are more than 10,000 times faster; (2) our methods deliver similar quality of bounds (the gap is within 35% and usually around 10%; sometimes our bounds are even better) for larger networks compared to the methods based on solving linear programming problems but our algorithms are 33-14,000 times faster; (3) our method is capable of solving large MNIST and CIFAR networks up to 7 layers with more than 10,000 neurons within tens of seconds on a single CPU core. In addition, we show that, in fact, there is no polynomial time algorithm that can approximately find the minimum $\ell_1$ adversarial distortion of a ReLU network with a $0.99\ln n$ approximation ratio unless $\mathsf{NP}$=$\mathsf{P}$, where $n$ is the number of neurons in the network.

Minhao Cheng, Jinfeng Yi, Pin-Yu Chen et al.

Crafting adversarial examples has become an important technique to evaluate the robustness of deep neural networks (DNNs). However, most existing works focus on attacking the image classification problem since its input space is continuous and output space is finite. In this paper, we study the much more challenging problem of crafting adversarial examples for sequence-to-sequence (seq2seq) models, whose inputs are discrete text strings and outputs have an almost infinite number of possibilities. To address the challenges caused by the discrete input space, we propose a projected gradient method combined with group lasso and gradient regularization. To handle the almost infinite output space, we design some novel loss functions to conduct non-overlapping attack and targeted keyword attack. We apply our algorithm to machine translation and text summarization tasks, and verify the effectiveness of the proposed algorithm: by changing less than 3 words, we can make seq2seq model to produce desired outputs with high success rates. On the other hand, we recognize that, compared with the well-evaluated CNN-based classifiers, seq2seq models are intrinsically more robust to adversarial attacks.

Tsui-Wei Weng, Huan Zhang, Pin-Yu Chen et al.

The robustness of neural networks to adversarial examples has received great attention due to security implications. Despite various attack approaches to crafting visually imperceptible adversarial examples, little has been developed towards a comprehensive measure of robustness. In this paper, we provide a theoretical justification for converting robustness analysis into a local Lipschitz constant estimation problem, and propose to use the Extreme Value Theory for efficient evaluation. Our analysis yields a novel robustness metric called CLEVER, which is short for Cross Lipschitz Extreme Value for nEtwork Robustness. The proposed CLEVER score is attack-agnostic and computationally feasible for large neural networks. Experimental results on various networks, including ResNet, Inception-v3 and MobileNet, show that (i) CLEVER is aligned with the robustness indication measured by the $\ell_2$ and $\ell_\infty$ norms of adversarial examples from powerful attacks, and (ii) defended networks using defensive distillation or bounded ReLU indeed achieve better CLEVER scores. To the best of our knowledge, CLEVER is the first attack-independent robustness metric that can be applied to any neural network classifier.

Xuanqing Liu, Minhao Cheng, Huan Zhang et al.

Recent studies have revealed the vulnerability of deep neural networks: A small adversarial perturbation that is imperceptible to human can easily make a well-trained deep neural network misclassify. This makes it unsafe to apply neural networks in security-critical applications. In this paper, we propose a new defense algorithm called Random Self-Ensemble (RSE) by combining two important concepts: {\bf randomness} and {\bf ensemble}. To protect a targeted model, RSE adds random noise layers to the neural network to prevent the strong gradient-based attacks, and ensembles the prediction over random noises to stabilize the performance. We show that our algorithm is equivalent to ensemble an infinite number of noisy models $f_ε$ without any additional memory overhead, and the proposed training procedure based on noisy stochastic gradient descent can ensure the ensemble model has a good predictive capability. Our algorithm significantly outperforms previous defense techniques on real data sets. For instance, on CIFAR-10 with VGG network (which has 92\% accuracy without any attack), under the strong C\&W attack within a certain distortion tolerance, the accuracy of unprotected model drops to less than 10\%, the best previous defense technique has $48\%$ accuracy, while our method still has $86\%$ prediction accuracy under the same level of attack. Finally, our method is simple and easy to integrate into any neural network.

Pin-Yu Chen, Yash Sharma, Huan Zhang et al.

Recent studies have highlighted the vulnerability of deep neural networks (DNNs) to adversarial examples - a visually indistinguishable adversarial image can easily be crafted to cause a well-trained model to misclassify. Existing methods for crafting adversarial examples are based on $L_2$ and $L_\infty$ distortion metrics. However, despite the fact that $L_1$ distortion accounts for the total variation and encourages sparsity in the perturbation, little has been developed for crafting $L_1$-based adversarial examples. In this paper, we formulate the process of attacking DNNs via adversarial examples as an elastic-net regularized optimization problem. Our elastic-net attacks to DNNs (EAD) feature $L_1$-oriented adversarial examples and include the state-of-the-art $L_2$ attack as a special case. Experimental results on MNIST, CIFAR10 and ImageNet show that EAD can yield a distinct set of adversarial examples with small $L_1$ distortion and attains similar attack performance to the state-of-the-art methods in different attack scenarios. More importantly, EAD leads to improved attack transferability and complements adversarial training for DNNs, suggesting novel insights on leveraging $L_1$ distortion in adversarial machine learning and security implications of DNNs.

Pin-Yu Chen, Huan Zhang, Yash Sharma et al.

Deep neural networks (DNNs) are one of the most prominent technologies of our time, as they achieve state-of-the-art performance in many machine learning tasks, including but not limited to image classification, text mining, and speech processing. However, recent research on DNNs has indicated ever-increasing concern on the robustness to adversarial examples, especially for security-critical tasks such as traffic sign identification for autonomous driving. Studies have unveiled the vulnerability of a well-trained DNN by demonstrating the ability of generating barely noticeable (to both human and machines) adversarial images that lead to misclassification. Furthermore, researchers have shown that these adversarial images are highly transferable by simply training and attacking a substitute model built upon the target model, known as a black-box attack to DNNs. Similar to the setting of training substitute models, in this paper we propose an effective black-box attack that also only has access to the input (images) and the output (confidence scores) of a targeted DNN. However, different from leveraging attack transferability from substitute models, we propose zeroth order optimization (ZOO) based attacks to directly estimate the gradients of the targeted DNN for generating adversarial examples. We use zeroth order stochastic coordinate descent along with dimension reduction, hierarchical attack and importance sampling techniques to efficiently attack black-box models. By exploiting zeroth order optimization, improved attacks to the targeted DNN can be accomplished, sparing the need for training substitute models and avoiding the loss in attack transferability. Experimental results on MNIST, CIFAR10 and ImageNet show that the proposed ZOO attack is as effective as the state-of-the-art white-box attack and significantly outperforms existing black-box attacks via substitute models.

Huan Zhang, Si Si, Cho-Jui Hsieh

In this paper, we present a novel massively parallel algorithm for accelerating the decision tree building procedure on GPUs (Graphics Processing Units), which is a crucial step in Gradient Boosted Decision Tree (GBDT) and random forests training. Previous GPU based tree building algorithms are based on parallel multi-scan or radix sort to find the exact tree split, and thus suffer from scalability and performance issues. We show that using a histogram based algorithm to approximately find the best split is more efficient and scalable on GPU. By identifying the difference between classical GPU-based image histogram construction and the feature histogram construction in decision tree training, we develop a fast feature histogram building kernel on GPU with carefully designed computational and memory access sequence to reduce atomic update conflict and maximize GPU utilization. Our algorithm can be used as a drop-in replacement for histogram construction in popular tree boosting systems to improve their scalability. As an example, to train GBDT on epsilon dataset, our method using a main-stream GPU is 7-8 times faster than histogram based algorithm on CPU in LightGBM and 25 times faster than the exact-split finding algorithm in XGBoost on a dual-socket 28-core Xeon server, while achieving similar prediction accuracy.