Multi-sensor fusion systems (MSFs) play a vital role as the perception module in modern autonomous vehicles (AVs). Therefore, ensuring their robustness against common and realistic adversarial semantic transformations, such as rotation and shifting in the physical world, is crucial for the safety of AVs. While empirical evidence suggests that MSFs exhibit improved robustness compared to single-modal models, they are still vulnerable to adversarial semantic transformations. In addition, although many empirical defenses have been proposed, several works show that these defenses can be further attacked by new adaptive attacks. So far, there is no certified defense proposed for MSFs. In this work, we propose the first robustness certification framework COMMIT to certify the robustness of multi-sensor fusion systems against semantic attacks. In particular, we propose a practical anisotropic noise mechanism that leverages randomized smoothing on multi-modal data and performs a grid-based splitting method to characterize complex semantic transformations. We also propose efficient algorithms to compute the certification in terms of object detection accuracy and IoU for large-scale MSF models. Empirically, we evaluate the efficacy of COMMIT in different settings and provide a comprehensive benchmark of certified robustness for different MSF models using the CARLA simulation platform. We show that the certification for MSF models is at most 48.39% higher than that of single-modal models, which validates the advantages of MSF models. We believe our certification framework and benchmark will contribute an important step towards certifiably robust AVs in practice.

Certified robustness is a critical measure for assessing the reliability of machine learning systems. Traditionally, the computational burden associated with certifying the robustness of machine learning models has posed a substantial challenge, particularly with the continuous expansion of model sizes. In this paper, we introduce an innovative approach to expedite the verification process for L2-norm certified robustness through sparse transfer learning. Our approach is both efficient and effective. It leverages verification results obtained from pre-training tasks and applies sparse updates to these results. To enhance performance, we incorporate dynamic sparse mask selection and introduce a novel stability-based regularizer called DiffStab. Empirical results demonstrate that our method accelerates the verification process for downstream tasks by as much as 70-80%, with only slight reductions in certified accuracy compared to dense parameter updates. We further validate that this performance improvement is even more pronounced in the few-shot transfer learning scenario.

Deep learning-based visual perception models lack robustness when faced with camera motion perturbations in practice. The current certification process for assessing robustness is costly and time-consuming due to the extensive number of image projections required for Monte Carlo sampling in the 3D camera motion space. To address these challenges, we present a novel, efficient, and practical framework for certifying the robustness of 3D-2D projective transformations against camera motion perturbations. Our approach leverages a smoothing distribution over the 2D-pixel space instead of in the 3D physical space, eliminating the need for costly camera motion sampling and significantly enhancing the efficiency of robustness certifications. With the pixel-wise smoothed classifier, we are able to fully upper bound the projection errors using a technique of uniform partitioning in camera motion space. Additionally, we extend our certification framework to a more general scenario where only a single-frame point cloud is required in the projection oracle. Through extensive experimentation, we validate the trade-off between effectiveness and efficiency enabled by our proposed method. Remarkably, our approach achieves approximately 80% certified accuracy while utilizing only 30% of the projected image frames.

Conformal prediction has shown spurring performance in constructing statistically rigorous prediction sets for arbitrary black-box machine learning models, assuming the data is exchangeable. However, even small adversarial perturbations during the inference can violate the exchangeability assumption, challenge the coverage guarantees, and result in a subsequent decline in empirical coverage. In this work, we propose a certifiably robust learning-reasoning conformal prediction framework (COLEP) via probabilistic circuits, which comprise a data-driven learning component that trains statistical models to learn different semantic concepts, and a reasoning component that encodes knowledge and characterizes the relationships among the trained models for logic reasoning. To achieve exact and efficient reasoning, we employ probabilistic circuits (PCs) within the reasoning component. Theoretically, we provide end-to-end certification of prediction coverage for COLEP in the presence of $\ell_2$ bounded adversarial perturbations. We also provide certified coverage considering the finite size of the calibration set. Furthermore, we prove that COLEP achieves higher prediction coverage and accuracy over a single model as long as the utilities of knowledge models are non-trivial. Empirically, we show the validity and tightness of our certified coverage, demonstrating the robust conformal prediction of COLEP on various datasets, including GTSRB, CIFAR10, and AwA2. We show that COLEP achieves up to 12% improvement in certified coverage on GTSRB, 9% on CIFAR-10, and 14% on AwA2.

Randomized Smoothing (RS) is currently a scalable certified defense method providing robustness certification against adversarial examples. Although significant progress has been achieved in providing defenses against $\ell_p$ adversaries, the interaction between the smoothing distribution and the robustness certification still remains vague. In this work, we comprehensively study the effect of two families of distributions, named Exponential Standard Gaussian (ESG) and Exponential General Gaussian (EGG) distributions, on Randomized Smoothing and Double Sampling Randomized Smoothing (DSRS). We derive an analytic formula for ESG’s certified radius, which converges to the origin formula of RS as the dimension $d$ increases. Additionally, we prove that EGG can provide tighter constant factors than DSRS in providing $\Omega(\sqrt{d})$ lower bounds of $\ell_2$ certified radius, and thus further addresses the curse of dimensionality in RS. Our experiments on real-world datasets confirm our theoretical analysis of the ESG distributions, that they provide almost the same certification under different exponents $\eta$ for both RS and DSRS. In addition, EGG brings a significant improvement to the DSRS certification, but the mechanism can be different when the classifier properties are different. Compared to the primitive DSRS, the increase in certified accuracy provided by EGG is prominent, up to 6.4% on ImageNet.

Large Language Models for code (code LLMs) have witnessed tremendous progress in recent years. With the rapid development of code LLMs, many popular evaluation benchmarks, such as HumanEval, DS-1000, and MBPP, have emerged to measure the performance of code LLMs with a particular focus on code generation tasks. However, they are insufficient to cover the full range of expected capabilities of code LLMs, which span beyond code generation to answering diverse coding-related questions. To fill this gap, we propose InfiBench, the first large-scale freeform question-answering (QA) benchmark for code to our knowledge, comprising 234 carefully selected high-quality Stack Overflow questions that span across 15 programming languages. InfiBench uses four types of model-free automatic metrics to evaluate response correctness where domain experts carefully concretize the criterion for each question. We conduct a systematic evaluation for over 100 latest code LLMs on InfiBench, leading to a series of novel and insightful findings. Our detailed analyses showcase potential directions for further advancement of code LLMs. InfiBench is fully open source at https://infi-coder.github.io/infibench and continuously expanding to foster more scientific and systematic practices for code LLM evaluation.

With the widespread deployment of deep neural networks (DNNs), ensuring the reliability of DNN-based systems is of great importance. Serious reliability issues such as system failures can be caused by numerical defects, one of the most frequent defects in DNNs. To assure high reliability against numerical defects, in this paper, we propose the RANUM approach including novel techniques for three reliability assurance tasks: detection of potential numerical defects, confirmation of potential-defect feasibility, and suggestion of defect fixes. To the best of our knowledge, RANUM is the first approach that confirms potential-defect feasibility with failure-exhibiting tests and suggests fixes automatically. Extensive experiments on the benchmarks of 63 real-world DNN architectures show that RANUM outperforms state-of-the-art approaches across the three reliability assurance tasks. In addition, when the RANUM-generated fixes are compared with developers' fixes on open-source projects, in 37 out of 40 cases, RANUM-generated fixes are equivalent to or even better than human fixes.

Great advances in deep neural networks (DNNs) have led to state-of-the-art performance on a wide range of tasks. However, recent studies have shown that DNNs are vulnerable to adversarial attacks, which have brought great concerns when deploying these models to safety-critical applications such as autonomous driving. Different defense approaches have been proposed against adversarial attacks, including: a) empirical defenses, which can usually be adaptively attacked again without providing robustness certification; and b) certifiably robust approaches, which consist of robustness verification providing the lower bound of robust accuracy against any attacks under certain conditions and corresponding robust training approaches. In this paper, we systematize certifiably robust approaches and related practical and theoretical implications and findings. We also provide the first comprehensive benchmark on existing robustness verification and training approaches on different datasets. In particular, we 1) provide a taxonomy for the robustness verification and training approaches, as well as summarize the methodologies for representative algorithms, 2) reveal the characteristics, strengths, limitations, and fundamental connections among these approaches, 3) discuss current research progresses, theoretical barriers, main challenges, and future directions for certifiably robust approaches for DNNs, and 4) provide an open-sourced unified platform to evaluate 20+ representative certifiably robust approaches.

Point cloud models with neural network architectures have achieved great success and been widely used in safety-critical applications, such as Lidar-based recognition systems in autonomous vehicles. However, such models are shown vulnerable against adversarial attacks which aim to apply stealthy semantic transformations such as rotation and tapering to mislead model predictions. In this paper, we propose a transformation-specific smoothing framework TPC, which provides tight and scalable robustness guarantees for point cloud models against semantic transformation attacks. We first categorize common 3D transformations into two categories: composable (e.g., rotation) and indirectly composable (e.g., tapering), and we present generic robustness certification strategies for both categories. We then specify unique certification protocols for a range of specific semantic transformations and derive strong robustness guarantees. Extensive experiments on several common 3D transformations show that TPC significantly outperforms the state of the art. For example, our framework boosts the certified accuracy against twisting transformation along z-axis (within $\pm$20{\textdegree}) from 20.3% to 83.8%. Codes and models are available at https://github.com/Qianhewu/Point-Cloud-Smoothing.

Neural networks (NNs) are known to be vulnerable against adversarial perturbations, and thus there is a line of work aiming to provide robustness certification for NNs, such as randomized smoothing, which samples smoothing noises from a certain distribution to certify the robustness for a smoothed classifier. However, as previous work shows, the certified robust radius in randomized smoothing suffers from scaling to large datasets ("curse of dimensionality"). To overcome this hurdle, we propose a Double Sampling Randomized Smoothing (DSRS) framework, which exploits the sampled probability from an additional smoothing distribution to tighten the robustness certification of the previous smoothed classifier. Theoretically, under mild assumptions, we prove that DSRS can certify $\Theta(\sqrt d)$ robust radius under $\ell_2$ norm where $d$ is the input dimension, which implies that DSRS may be able to break the curse of dimensionality of randomized smoothing. We instantiate DSRS for a generalized family of Gaussian smoothing and propose an efficient and sound computing method based on customized dual optimization considering sampling error. Extensive experiments on MNIST, CIFAR-10, and ImageNet verify our theory and show that DSRS certifies larger robust radii than existing baselines consistently under different settings. Code is available at https://github.com/llylly/DSRS.

Certifying the robustness of model performance under bounded data distribution drifts has recently attracted intensive interest under the umbrella of distributional robustness. However, existing techniques either make strong assumptions on the model class and loss functions that can be certified, such as smoothness expressed via Lipschitz continuity of gradients, or require to solve complex optimization problems. As a result, the wider application of these techniques is currently limited by its scalability and flexibility — these techniques often do not scale to large-scale datasets with modern deep neural networks or cannot handle loss functions which may be non-smooth such as the 0-1 loss. In this paper, we focus on the problem of certifying distributional robustness for blackbox models and bounded loss functions, and propose a novel certification framework based on the Hellinger distance. Our certification technique scales to ImageNet-scale datasets, complex models, and a diverse set of loss functions. We then focus on one specific application enabled by such scalability and flexibility, i.e., certifying out-of-domain generalization for large neural networks and loss functions such as accuracy and AUC. We experimentally validate our certification method on a number of datasets, ranging from ImageNet, where we provide the first non-vacuous certified out-of-domain generalization, to smaller classification tasks where we are able to compare with the state-of-the-art and show that our method performs considerably better.

Automatic machine learning, or AutoML, holds the promise of truly democratizing the use of machine learning (ML), by substantially automating the work of data scientists. However, the huge combinatorial search space of candidate pipelines means that current AutoML techniques, generate sub-optimal pipelines, or none at all, especially on large, complex datasets. In this work we propose an AutoML technique SapientML, that can learn from a corpus of existing datasets and their human-written pipelines, and efficiently generate a high-quality pipeline for a predictive task on a new dataset. To combat the search space explosion of AutoML, SapientML employs a novel divide-and-conquer strategy realized as a three-stage program synthesis approach, that reasons on successively smaller search spaces. The first stage uses meta-learning to predict a set of plausible ML components to constitute a pipeline. In the second stage, this is then refined into a small pool of viable concrete pipelines using a pipeline dataflow model derived from the corpus. Dynamically evaluating these few pipelines, in the third stage, provides the best solution. We instantiate SapientML as part of a fully automated tool-chain that creates a cleaned, labeled learning corpus by mining Kaggle, learns from it, and uses the learned models to then synthesize pipelines for new predictive tasks. We have created a training corpus of 1,094 pipelines spanning 170 datasets, and evaluated SapientML on a set of 41 benchmark datasets, including 10 new, large, real-world datasets from Kaggle, and against 3 state-of-the-art AutoML tools and 4 baselines. Our evaluation shows that SapientML produces the best or comparable accuracy on 27 of the benchmarks while the second best tool fails to even produce a pipeline on 9 of the instances. This difference is amplified on the 10 most challenging benchmarks, where SapientML wins on 9 instances with the other tools failing to produce pipelines on 4 or more benchmarks.

Federated learning provides an effective paradigm to jointly optimize a model benefited from rich distributed data while protecting data privacy. Nonetheless, the heterogeneity nature of distributed data, especially in the non-IID setting, makes it challenging to define and ensure fairness among local agents. For instance, it is intuitively ``unfair" for agents with data of high quality to sacrifice their performance due to other agents with low quality data. Currently popular egalitarian and weighted equity-based fairness measures suffer from the aforementioned pitfall. In this work, we aim to formally represent this problem and address these fairness issues using concepts from co-operative game theory and social choice theory. We model the task of learning a shared predictor in the federated setting as a fair public decision making problem, and then define the notion of core-stable fairness: Given $N$ agents, there is no subset of agents $S$ that can benefit significantly by forming a coalition among themselves based on their utilities $U_N$ and $U_S$ (i.e., $ (|S|/ N) U_S \geq U_N$). Core-stable predictors are robust to low quality local data from some agents, and additionally they satisfy Proportionality (each agent gets at least $1/n$ fraction of the best utility that she can get from any predictor) and Pareto-optimality (there exists no model that can increase the utility of an agent without decreasing the utility of another), two well sought-after fairness and efficiency notions within social choice. We then propose an efficient federated learning protocol CoreFed to optimize a core stable predictor. CoreFed determines a core-stable predictor when the loss functions of the agents are convex. CoreFed also determines approximate core-stable predictors when the loss functions are not convex, like smooth neural networks. We further show the existence of core-stable predictors in more general settings using Kakutani's fixed point theorem. Finally, we empirically validate our analysis on two real-world datasets, and we show that CoreFed achieves higher core-stability fairness than FedAvg while maintaining similar accuracy.

Extensive efforts have been made to understand and improve the fairness of machine learning models based on observational metrics, especially in high-stakes domains such as medical insurance, education, and hiring decisions. However, there is a lack of certified fairness considering the end-to-end performance of an ML model. In this paper, we first formulate the certified fairness of an ML model trained on a given data distribution as an optimization problem based on the model performance loss bound on a fairness constrained distribution, which is within bounded distributional distance with the training distribution. We then propose a general fairness certification framework and instantiate it for both sensitive shifting and general shifting scenarios. In particular, we propose to solve the optimization problem by decomposing the original data distribution into analytical subpopulations and proving the convexity of the subproblems to solve them. We evaluate our certified fairness on six real-world datasets and show that our certification is tight in the sensitive shifting scenario and provides non-trivial certification under general shifting. Our framework is flexible to integrate additional non-skewness constraints and we show that it provides even tighter certification under different real-world scenarios. We also compare our certified fairness bound with adapted existing distributional robustness bounds on Gaussian data and demonstrate that our method is significantly tighter.

Recent studies show that training deep neural networks (DNNs) with Lipschitz constraints are able to enhance adversarial robustness and other model properties such as stability. In this paper, we propose a layer-wise orthogonal training method (LOT) to effectively train 1-Lipschitz convolution layers via parametrizing an orthogonal matrix with an unconstrained matrix. We then efficiently compute the inverse square root of a convolution kernel by transforming the input domain to the Fourier frequency domain. On the other hand, as existing works show that semi-supervised training helps improve empirical robustness, we aim to bridge the gap and prove that semi-supervised learning also improves the certified robustness of Lipschitz-bounded models. We conduct comprehensive evaluations for LOT under different settings. We show that LOT significantly outperforms baselines regarding deterministic l2 certified robustness, and scales to deeper neural networks. Under the supervised scenario, we improve the state-of-the-art certified robustness for all architectures (e.g. from 59.04% to 63.50% on CIFAR-10 and from 32.57% to 34.59% on CIFAR-100 at radius $\rho=36/255$ for 40-layer networks). With semi-supervised learning over unlabelled data, we are able to improve state-of-the-art certified robustness on CIFAR-10 at $\rho=108/255$ from 36.04% to 42.39%. In addition, LOT consistently outperforms baselines on different model architectures with only 1/3 evaluation time.

Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation radius. Given that existing pure data-driven statistical approaches have reached a bottleneck, in this paper, we propose to integrate statistical ML models with knowledge (expressed as logical rules) as a reasoning component using Markov logic networks (MLN), so as to further improve the overall certified robustness. This opens new research questions about certifying the robustness of such a paradigm, especially the reasoning component (e.g., MLN). As the first step towards understanding these questions, we first prove that the computational complexity of certifying the robustness of MLN is #P-hard. Guided by this hardness result, we then derive the first certified robustness bound for MLN by carefully analyzing different model regimes. Finally, we conduct extensive experiments on five datasets including both high-dimensional images and natural language texts, and we show that the certified robustness with knowledge-based logical reasoning indeed significantly outperforms that of the state-of-the-arts.

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 $\alpha,\beta$-CROWN verifier, the VNN-COMP 2022 winner. Code is available at http://PaperCode.cc/GCP-CROWN.

Gradient estimation and vector space projection have been studied as two distinct topics. We aim to bridge the gap between the two by investigating how to efficiently estimate gradient based on a projected low-dimensional space. We first provide lower and upper bounds for gradient estimation under both linear and nonlinear projections, and outline checkable sufficient conditions under which one is better than the other. Moreover, we analyze the query complexity for the projection-based gradient estimation and present a sufficient condition for query-efficient estimators. Built upon our theoretic analysis, we propose a novel query-efficient Nonlinear Gradient Projection-based Boundary Blackbox Attack (NonLinear-BA). We conduct extensive experiments on four image datasets: ImageNet, CelebA, CIFAR-10, and MNIST, and show the superiority of the proposed methods compared with the state-of-the-art baselines. In particular, we show that the projection-based boundary blackbox attacks are able to achieve much smaller magnitude of perturbations with 100% attack success rate based on efficient queries. Both linear and nonlinear projections demonstrate their advantages under different conditions. We also evaluate NonLinear-BA against the commercial online API MEGVII Face++, and demonstrate the high blackbox attack performance both quantitatively and qualitatively. The code is publicly available at https://github.com/AI-secure/NonLinear-BA.

As machine learning (ML) systems become pervasive, safeguarding their security is critical. However, recently it has been demonstrated that motivated adversaries are able to mislead ML systems by perturbing test data using semantic transformations. While there exists a rich body of research providing provable robustness guarantees for ML models against Lp bounded adversarial perturbations, guarantees against semantic perturbations remain largely underexplored. In this paper, we provide TSS-a unified framework for certifying ML robustness against general adversarial semantic transformations. First, depending on the properties of each transformation, we divide common transformations into two categories, namely resolvable (e.g., Gaussian blur) and differentially resolvable (e.g., rotation) transformations. For the former, we propose transformation-specific randomized smoothing strategies and obtain strong robustness certification. The latter category covers transformations that involve interpolation errors, and we propose a novel approach based on stratified sampling to certify the robustness. Our framework TSS leverages these certification strategies and combines with consistency-enhanced training to provide rigorous certification of robustness. We conduct extensive experiments on over ten types of challenging semantic transformations and show that TSS significantly outperforms the state of the art. Moreover, to the best of our knowledge, TSS is the first approach that achieves nontrivial certified robustness on the large-scale ImageNet dataset. For instance, our framework achieves 30.4% certified robust accuracy against rotation attack (within ±30°) on ImageNet. Moreover, to consider a broader range of transformations, we show TSS is also robust against adaptive attacks and unforeseen image corruptions such as CIFAR-10-C and ImageNet-C.

Boundary based blackbox attack has been recognized as practical and effective, given that an attacker only needs to access the final model prediction. However, the query efficiency of it is in general high especially for high dimensional image data. In this paper, we show that such efficiency highly depends on the scale at which the attack is applied, and attacking at the optimal scale significantly improves the efficiency. In particular, we propose a theoretical framework to analyze and show three key characteristics to improve the query efficiency. We prove that there exists an optimal scale for projective gradient estimation. Our framework also explains the satisfactory performance achieved by existing boundary black-box attacks. Based on our theoretical framework, we propose Progressive-Scale enabled projective Boundary Attack (PSBA) to improve the query efficiency via progressive scaling techniques. In particular, we employ Progressive-GAN to optimize the scale of projections, which we call PSBA-PGAN. We evaluate our approach on both spatial and frequency scales. Extensive experiments on MNIST, CIFAR-10, CelebA, and ImageNet against different models including a real-world face recognition API show that PSBA-PGAN significantly outperforms existing baseline attacks in terms of query efficiency and attack success rate. We also observe relatively stable optimal scales for different models and datasets. The code is publicly available at https://github.com/AI-secure/PSBA.

Adversarial Transferability is an intriguing property - adversarial perturbation crafted against one model is also effective against another model, while these models are from different model families or training processes. To better protect ML systems against adversarial attacks, several questions are raised: what are the sufficient conditions for adversarial transferability, and how to bound it? Is there a way to reduce the adversarial transferability in order to improve the robustness of an ensemble ML model? To answer these questions, in this work we first theoretically analyze and outline sufficient conditions for adversarial transferability between models; then propose a practical algorithm to reduce the transferability between base models within an ensemble to improve its robustness. Our theoretical analysis shows that only promoting the orthogonality between gradients of base models is not enough to ensure low transferability; in the meantime, the model smoothness is an important factor to control the transferability. We also provide the lower and upper bounds of adversarial transferability under certain conditions. Inspired by our theoretical analysis, we propose an effective Transferability Reduced Smooth (TRS) ensemble training strategy to train a robust ensemble with low transferability by enforcing both gradient orthogonality and model smoothness between base models. We conduct extensive experiments on TRS and compare with 6 state-of-the-art ensemble baselines against 8 whitebox attacks on different datasets, demonstrating that the proposed TRS outperforms all baselines significantly.

For large industrial applications, system test cases are still often described in natural language (NL), and their number can reach thousands. Test automation is to automatically execute the test cases. Achieving test automation typically requires substantial manual effort for creating executable test scripts from these NL test cases. In particular, given that each NL test case consists of a sequence of NL test steps, testers first implement a test API method for each test step and then write a test script for invoking these test API methods sequentially for test automation. Across different test cases, multiple test steps can share semantic similarities, supposedly mapped to the same API method. However, due to numerous test steps in various NL forms under manual inspection, testers may not realize those semantically similar test steps and thus waste effort to implement duplicate test API methods for them. To address this issue, in this paper, we propose a new approach based on natural language processing to cluster similar NL test steps together such that the test steps in each cluster can be mapped to the same test API method. Our approach includes domain-specific word embedding training along with measurement based on Relaxed Word Mover’sDistance to analyze the similarity of test steps. Our approach also includes a technique to combine hierarchical agglomerative clustering and K-means clustering post-refinement to derive high-quality and manually-adjustable clustering results. The evaluation results of our approach on a large industrial mobile app, WeChat, show that our approach can cluster the test steps with high accuracy, substantially reducing the number of clusters and thus reducing the downstream manual effort. In particular, compared with the baseline approach, our approach achieves 79.8% improvement on cluster quality, reducing 65.9% number of clusters, i.e., the number of test API methods to be implemented.

Machine learning techniques, especially deep neural networks (DNNs), have been widely adopted in various applications. However, DNNs are recently found to be vulnerable against adversarial examples, i.e., maliciously perturbed inputs that can mislead the models to make arbitrary prediction errors. Empirical defenses have been studied, but many of them can be adaptively attacked again. Provable defenses provide provable error bound of DNNs, while such bound so far is far from satisfaction. To address this issue, in this paper, we present our approach named Robustra for effectively improving the provable error bound of DNNs. We leverage the adversarial space of a reference model as the feasible region to solve the min-max game between the attackers and defenders. We solve its dual problem by linearly approximating the attackers' best strategy and utilizing the monotonicity of the slack variables introduced by the reference model. The evaluation results show that our approach can provide significantly better provable adversarial error bounds on MNIST and CIFAR10 datasets, compared to the state-of-the-art results. In particular, bounded by L^infty, with epsilon = 0.1, on MNIST we reduce the error bound from 2.74% to 2.09%; with epsilon = 0.3, we reduce the error bound from 24.19% to 16.91%.