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Published work

51 published item(s)

preprint2026arXiv

Physical Adversarial Clothing Evades Visible-Thermal Detectors via Non-Overlapping RGB-T Pattern

Visible-thermal (RGB-T) object detection is a crucial technology for applications such as autonomous driving, where multimodal fusion enhances performance in challenging conditions like low light. However, the security of RGB-T detectors, particularly in the physical world, has been largely overlooked. This paper proposes a novel approach to RGB-T physical attacks using adversarial clothing with a non-overlapping RGB-T pattern (NORP). To simulate full-view (0$^{\circ}$--360$^{\circ}$) RGB-T attacks, we construct 3D RGB-T models for human and adversarial clothing. NORP is a new adversarial pattern design using distinct visible and thermal materials without overlap, avoiding the light reduction in overlapping RGB-T patterns (ORP). To optimize the NORP on adversarial clothing, we propose a spatial discrete-continuous optimization (SDCO) method. We systematically evaluated our method on RGB-T detectors with different fusion architectures, demonstrating high attack success rates both in the digital and physical worlds. Additionally, we introduce a fusion-stage ensemble method that enhances the transferability of adversarial attacks across unseen RGB-T detectors with different fusion architectures.

preprint2025arXiv

Audio Super-Resolution with Latent Bridge Models

Audio super-resolution (SR), i.e., upsampling the low-resolution (LR) waveform to the high-resolution (HR) version, has recently been explored with diffusion and bridge models, while previous methods often suffer from sub-optimal upsampling quality due to their uninformative generation prior. Towards high-quality audio super-resolution, we present a new system with latent bridge models (LBMs), where we compress the audio waveform into a continuous latent space and design an LBM to enable a latent-to-latent generation process that naturally matches the LR-toHR upsampling process, thereby fully exploiting the instructive prior information contained in the LR waveform. To further enhance the training results despite the limited availability of HR samples, we introduce frequency-aware LBMs, where the prior and target frequency are taken as model input, enabling LBMs to explicitly learn an any-to-any upsampling process at the training stage. Furthermore, we design cascaded LBMs and present two prior augmentation strategies, where we make the first attempt to unlock the audio upsampling beyond 48 kHz and empower a seamless cascaded SR process, providing higher flexibility for audio post-production. Comprehensive experimental results evaluated on the VCTK, ESC-50, Song-Describer benchmark datasets and two internal testsets demonstrate that we achieve state-of-the-art objective and perceptual quality for any-to-48kHz SR across speech, audio, and music signals, as well as setting the first record for any-to-192kHz audio SR. Demo at https://AudioLBM.github.io/.

preprint2024arXiv

DGPO: Discovering Multiple Strategies with Diversity-Guided Policy Optimization

Most reinforcement learning algorithms seek a single optimal strategy that solves a given task. However, it can often be valuable to learn a diverse set of solutions, for instance, to make an agent's interaction with users more engaging, or improve the robustness of a policy to an unexpected perturbance. We propose Diversity-Guided Policy Optimization (DGPO), an on-policy algorithm that discovers multiple strategies for solving a given task. Unlike prior work, it achieves this with a shared policy network trained over a single run. Specifically, we design an intrinsic reward based on an information-theoretic diversity objective. Our final objective alternately constraints on the diversity of the strategies and on the extrinsic reward. We solve the constrained optimization problem by casting it as a probabilistic inference task and use policy iteration to maximize the derived lower bound. Experimental results show that our method efficiently discovers diverse strategies in a wide variety of reinforcement learning tasks. Compared to baseline methods, DGPO achieves comparable rewards, while discovering more diverse strategies, and often with better sample efficiency.

preprint2022arXiv

A Roadmap for Big Model

With the rapid development of deep learning, training Big Models (BMs) for multiple downstream tasks becomes a popular paradigm. Researchers have achieved various outcomes in the construction of BMs and the BM application in many fields. At present, there is a lack of research work that sorts out the overall progress of BMs and guides the follow-up research. In this paper, we cover not only the BM technologies themselves but also the prerequisites for BM training and applications with BMs, dividing the BM review into four parts: Resource, Models, Key Technologies and Application. We introduce 16 specific BM-related topics in those four parts, they are Data, Knowledge, Computing System, Parallel Training System, Language Model, Vision Model, Multi-modal Model, Theory&Interpretability, Commonsense Reasoning, Reliability&Security, Governance, Evaluation, Machine Translation, Text Generation, Dialogue and Protein Research. In each topic, we summarize clearly the current studies and propose some future research directions. At the end of this paper, we conclude the further development of BMs in a more general view.

preprint2022arXiv

A Semismooth Newton based Augmented Lagrangian Method for Nonsmooth Optimization on Matrix Manifolds

This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence condition on manifolds, we show that the proposed method converges to a stationary point of the nonsmooth manifold optimization problem. Moreover, we propose a globalized semismooth Newton method to solve the augmented Lagrangian subproblem on manifolds efficiently. The local superlinear convergence of the manifold semismooth Newton method is also established under some suitable conditions. We also prove that the semismoothness on submanifolds can be inherited from that in the ambient manifold. Finally, numerical experiments on compressed modes and (constrained) sparse principal component analysis illustrate the advantages of the proposed method.

preprint2022arXiv

BadDet: Backdoor Attacks on Object Detection

Deep learning models have been deployed in numerous real-world applications such as autonomous driving and surveillance. However, these models are vulnerable in adversarial environments. Backdoor attack is emerging as a severe security threat which injects a backdoor trigger into a small portion of training data such that the trained model behaves normally on benign inputs but gives incorrect predictions when the specific trigger appears. While most research in backdoor attacks focuses on image classification, backdoor attacks on object detection have not been explored but are of equal importance. Object detection has been adopted as an important module in various security-sensitive applications such as autonomous driving. Therefore, backdoor attacks on object detection could pose severe threats to human lives and properties. We propose four kinds of backdoor attacks for object detection task: 1) Object Generation Attack: a trigger can falsely generate an object of the target class; 2) Regional Misclassification Attack: a trigger can change the prediction of a surrounding object to the target class; 3) Global Misclassification Attack: a single trigger can change the predictions of all objects in an image to the target class; and 4) Object Disappearance Attack: a trigger can make the detector fail to detect the object of the target class. We develop appropriate metrics to evaluate the four backdoor attacks on object detection. We perform experiments using two typical object detection models -- Faster-RCNN and YOLOv3 on different datasets. More crucially, we demonstrate that even fine-tuning on another benign dataset cannot remove the backdoor hidden in the object detection model. To defend against these backdoor attacks, we propose Detector Cleanse, an entropy-based run-time detection framework to identify poisoned testing samples for any deployed object detector.

preprint2022arXiv

Boosting Transferability of Targeted Adversarial Examples via Hierarchical Generative Networks

Transfer-based adversarial attacks can evaluate model robustness in the black-box setting. Several methods have demonstrated impressive untargeted transferability, however, it is still challenging to efficiently produce targeted transferability. To this end, we develop a simple yet effective framework to craft targeted transfer-based adversarial examples, applying a hierarchical generative network. In particular, we contribute to amortized designs that well adapt to multi-class targeted attacks. Extensive experiments on ImageNet show that our method improves the success rates of targeted black-box attacks by a significant margin over the existing methods -- it reaches an average success rate of 29.1\% against six diverse models based only on one substitute white-box model, which significantly outperforms the state-of-the-art gradient-based attack methods. Moreover, the proposed method is also more efficient beyond an order of magnitude than gradient-based methods.

preprint2022arXiv

Controllable Evaluation and Generation of Physical Adversarial Patch on Face Recognition

Recent studies have revealed the vulnerability of face recognition models against physical adversarial patches, which raises security concerns about the deployed face recognition systems. However, it is still challenging to ensure the reproducibility for most attack algorithms under complex physical conditions, which leads to the lack of a systematic evaluation of the existing methods. It is therefore imperative to develop a framework that can enable a comprehensive evaluation of the vulnerability of face recognition in the physical world. To this end, we propose to simulate the complex transformations of faces in the physical world via 3D-face modeling, which serves as a digital counterpart of physical faces. The generic framework allows us to control different face variations and physical conditions to conduct reproducible evaluations comprehensively. With this digital simulator, we further propose a Face3DAdv method considering the 3D face transformations and realistic physical variations. Extensive experiments validate that Face3DAdv can significantly improve the effectiveness of diverse physically realizable adversarial patches in both simulated and physical environments, against various white-box and black-box face recognition models.

preprint2022arXiv

CoSCL: Cooperation of Small Continual Learners is Stronger than a Big One

Continual learning requires incremental compatibility with a sequence of tasks. However, the design of model architecture remains an open question: In general, learning all tasks with a shared set of parameters suffers from severe interference between tasks; while learning each task with a dedicated parameter subspace is limited by scalability. In this work, we theoretically analyze the generalization errors for learning plasticity and memory stability in continual learning, which can be uniformly upper-bounded by (1) discrepancy between task distributions, (2) flatness of loss landscape and (3) cover of parameter space. Then, inspired by the robust biological learning system that processes sequential experiences with multiple parallel compartments, we propose Cooperation of Small Continual Learners (CoSCL) as a general strategy for continual learning. Specifically, we present an architecture with a fixed number of narrower sub-networks to learn all incremental tasks in parallel, which can naturally reduce the two errors through improving the three components of the upper bound. To strengthen this advantage, we encourage to cooperate these sub-networks by penalizing the difference of predictions made by their feature representations. With a fixed parameter budget, CoSCL can improve a variety of representative continual learning approaches by a large margin (e.g., up to 10.64% on CIFAR-100-SC, 9.33% on CIFAR-100-RS, 11.45% on CUB-200-2011 and 6.72% on Tiny-ImageNet) and achieve the new state-of-the-art performance.

preprint2022arXiv

DAB-DETR: Dynamic Anchor Boxes are Better Queries for DETR

We present in this paper a novel query formulation using dynamic anchor boxes for DETR (DEtection TRansformer) and offer a deeper understanding of the role of queries in DETR. This new formulation directly uses box coordinates as queries in Transformer decoders and dynamically updates them layer-by-layer. Using box coordinates not only helps using explicit positional priors to improve the query-to-feature similarity and eliminate the slow training convergence issue in DETR, but also allows us to modulate the positional attention map using the box width and height information. Such a design makes it clear that queries in DETR can be implemented as performing soft ROI pooling layer-by-layer in a cascade manner. As a result, it leads to the best performance on MS-COCO benchmark among the DETR-like detection models under the same setting, e.g., AP 45.7\% using ResNet50-DC5 as backbone trained in 50 epochs. We also conducted extensive experiments to confirm our analysis and verify the effectiveness of our methods. Code is available at \url{https://github.com/SlongLiu/DAB-DETR}.

preprint2022arXiv

DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection

We present DINO (\textbf{D}ETR with \textbf{I}mproved de\textbf{N}oising anch\textbf{O}r boxes), a state-of-the-art end-to-end object detector. % in this paper. DINO improves over previous DETR-like models in performance and efficiency by using a contrastive way for denoising training, a mixed query selection method for anchor initialization, and a look forward twice scheme for box prediction. DINO achieves $49.4$AP in $12$ epochs and $51.3$AP in $24$ epochs on COCO with a ResNet-50 backbone and multi-scale features, yielding a significant improvement of $\textbf{+6.0}$\textbf{AP} and $\textbf{+2.7}$\textbf{AP}, respectively, compared to DN-DETR, the previous best DETR-like model. DINO scales well in both model size and data size. Without bells and whistles, after pre-training on the Objects365 dataset with a SwinL backbone, DINO obtains the best results on both COCO \texttt{val2017} ($\textbf{63.2}$\textbf{AP}) and \texttt{test-dev} (\textbf{$\textbf{63.3}$AP}). Compared to other models on the leaderboard, DINO significantly reduces its model size and pre-training data size while achieving better results. Our code will be available at \url{https://github.com/IDEACVR/DINO}.

preprint2022arXiv

Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models

Diffusion probabilistic models (DPMs) are a class of powerful deep generative models (DGMs). Despite their success, the iterative generation process over the full timesteps is much less efficient than other DGMs such as GANs. Thus, the generation performance on a subset of timesteps is crucial, which is greatly influenced by the covariance design in DPMs. In this work, we consider diagonal and full covariances to improve the expressive power of DPMs. We derive the optimal result for such covariances, and then correct it when the mean of DPMs is imperfect. Both the optimal and the corrected ones can be decomposed into terms of conditional expectations over functions of noise. Building upon it, we propose to estimate the optimal covariance and its correction given imperfect mean by learning these conditional expectations. Our method can be applied to DPMs with both discrete and continuous timesteps. We consider the diagonal covariance in our implementation for computational efficiency. For an efficient practical implementation, we adopt a parameter sharing scheme and a two-stage training process. Empirically, our method outperforms a wide variety of covariance design on likelihood results, and improves the sample quality especially on a small number of timesteps.

preprint2022arXiv

Exploring Memorization in Adversarial Training

Deep learning models have a propensity for fitting the entire training set even with random labels, which requires memorization of every training sample. In this paper, we explore the memorization effect in adversarial training (AT) for promoting a deeper understanding of model capacity, convergence, generalization, and especially robust overfitting of the adversarially trained models. We first demonstrate that deep networks have sufficient capacity to memorize adversarial examples of training data with completely random labels, but not all AT algorithms can converge under the extreme circumstance. Our study of AT with random labels motivates further analyses on the convergence and generalization of AT. We find that some AT approaches suffer from a gradient instability issue and most recently suggested complexity measures cannot explain robust generalization by considering models trained on random labels. Furthermore, we identify a significant drawback of memorization in AT that it could result in robust overfitting. We then propose a new mitigation algorithm motivated by detailed memorization analyses. Extensive experiments on various datasets validate the effectiveness of the proposed method.

preprint2022arXiv

Fast Lossless Neural Compression with Integer-Only Discrete Flows

By applying entropy codecs with learned data distributions, neural compressors have significantly outperformed traditional codecs in terms of compression ratio. However, the high inference latency of neural networks hinders the deployment of neural compressors in practical applications. In this work, we propose Integer-only Discrete Flows (IODF), an efficient neural compressor with integer-only arithmetic. Our work is built upon integer discrete flows, which consists of invertible transformations between discrete random variables. We propose efficient invertible transformations with integer-only arithmetic based on 8-bit quantization. Our invertible transformation is equipped with learnable binary gates to remove redundant filters during inference. We deploy IODF with TensorRT on GPUs, achieving 10x inference speedup compared to the fastest existing neural compressors, while retaining the high compression rates on ImageNet32 and ImageNet64.

preprint2022arXiv

GSmooth: Certified Robustness against Semantic Transformations via Generalized Randomized Smoothing

Certified defenses such as randomized smoothing have shown promise towards building reliable machine learning systems against $\ell_p$-norm bounded attacks. However, existing methods are insufficient or unable to provably defend against semantic transformations, especially those without closed-form expressions (such as defocus blur and pixelate), which are more common in practice and often unrestricted. To fill up this gap, we propose generalized randomized smoothing (GSmooth), a unified theoretical framework for certifying robustness against general semantic transformations via a novel dimension augmentation strategy. Under the GSmooth framework, we present a scalable algorithm that uses a surrogate image-to-image network to approximate the complex transformation. The surrogate model provides a powerful tool for studying the properties of semantic transformations and certifying robustness. Experimental results on several datasets demonstrate the effectiveness of our approach for robustness certification against multiple kinds of semantic transformations and corruptions, which is not achievable by the alternative baselines.

preprint2022arXiv

Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching

Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can be used to define an ODE ("score-based diffusion ODE") for exact likelihood evaluation. However, the relationship between the likelihood of the ODE and the score matching objective is unclear. In this work, we prove that matching the first-order score is not sufficient to maximize the likelihood of the ODE, by showing a gap between the maximum likelihood and score matching objectives. To fill up this gap, we show that the negative likelihood of the ODE can be bounded by controlling the first, second, and third-order score matching errors; and we further present a novel high-order denoising score matching method to enable maximum likelihood training of score-based diffusion ODEs. Our algorithm guarantees that the higher-order matching error is bounded by the training error and the lower-order errors. We empirically observe that by high-order score matching, score-based diffusion ODEs achieve better likelihood on both synthetic data and CIFAR-10, while retaining the high generation quality.

preprint2022arXiv

Memory Replay with Data Compression for Continual Learning

Continual learning needs to overcome catastrophic forgetting of the past. Memory replay of representative old training samples has been shown as an effective solution, and achieves the state-of-the-art (SOTA) performance. However, existing work is mainly built on a small memory buffer containing a few original data, which cannot fully characterize the old data distribution. In this work, we propose memory replay with data compression (MRDC) to reduce the storage cost of old training samples and thus increase their amount that can be stored in the memory buffer. Observing that the trade-off between the quality and quantity of compressed data is highly nontrivial for the efficacy of memory replay, we propose a novel method based on determinantal point processes (DPPs) to efficiently determine an appropriate compression quality for currently-arrived training samples. In this way, using a naive data compression algorithm with a properly selected quality can largely boost recent strong baselines by saving more compressed data in a limited storage space. We extensively validate this across several benchmarks of class-incremental learning and in a realistic scenario of object detection for autonomous driving.

preprint2022arXiv

OoD-Bench: Quantifying and Understanding Two Dimensions of Out-of-Distribution Generalization

Deep learning has achieved tremendous success with independent and identically distributed (i.i.d.) data. However, the performance of neural networks often degenerates drastically when encountering out-of-distribution (OoD) data, i.e., when training and test data are sampled from different distributions. While a plethora of algorithms have been proposed for OoD generalization, our understanding of the data used to train and evaluate these algorithms remains stagnant. In this work, we first identify and measure two distinct kinds of distribution shifts that are ubiquitous in various datasets. Next, through extensive experiments, we compare OoD generalization algorithms across two groups of benchmarks, each dominated by one of the distribution shifts, revealing their strengths on one shift as well as limitations on the other shift. Overall, we position existing datasets and algorithms from different research areas seemingly unconnected into the same coherent picture. It may serve as a foothold that can be resorted to by future OoD generalization research. Our code is available at https://github.com/ynysjtu/ood_bench.

preprint2022arXiv

Policy Learning for Robust Markov Decision Process with a Mismatched Generative Model

In high-stake scenarios like medical treatment and auto-piloting, it's risky or even infeasible to collect online experimental data to train the agent. Simulation-based training can alleviate this issue, but may suffer from its inherent mismatches from the simulator and real environment. It is therefore imperative to utilize the simulator to learn a robust policy for the real-world deployment. In this work, we consider policy learning for Robust Markov Decision Processes (RMDP), where the agent tries to seek a robust policy with respect to unexpected perturbations on the environments. Specifically, we focus on the setting where the training environment can be characterized as a generative model and a constrained perturbation can be added to the model during testing. Our goal is to identify a near-optimal robust policy for the perturbed testing environment, which introduces additional technical difficulties as we need to simultaneously estimate the training environment uncertainty from samples and find the worst-case perturbation for testing. To solve this issue, we propose a generic method which formalizes the perturbation as an opponent to obtain a two-player zero-sum game, and further show that the Nash Equilibrium corresponds to the robust policy. We prove that, with a polynomial number of samples from the generative model, our algorithm can find a near-optimal robust policy with a high probability. Our method is able to deal with general perturbations under some mild assumptions and can also be extended to more complex problems like robust partial observable Markov decision process, thanks to the game-theoretical formulation.

preprint2022arXiv

Query-Efficient Black-box Adversarial Attacks Guided by a Transfer-based Prior

Adversarial attacks have been extensively studied in recent years since they can identify the vulnerability of deep learning models before deployed. In this paper, we consider the black-box adversarial setting, where the adversary needs to craft adversarial examples without access to the gradients of a target model. Previous methods attempted to approximate the true gradient either by using the transfer gradient of a surrogate white-box model or based on the feedback of model queries. However, the existing methods inevitably suffer from low attack success rates or poor query efficiency since it is difficult to estimate the gradient in a high-dimensional input space with limited information. To address these problems and improve black-box attacks, we propose two prior-guided random gradient-free (PRGF) algorithms based on biased sampling and gradient averaging, respectively. Our methods can take the advantage of a transfer-based prior given by the gradient of a surrogate model and the query information simultaneously. Through theoretical analyses, the transfer-based prior is appropriately integrated with model queries by an optimal coefficient in each method. Extensive experiments demonstrate that, in comparison with the alternative state-of-the-arts, both of our methods require much fewer queries to attack black-box models with higher success rates.

preprint2022arXiv

Regret Analysis for Hierarchical Experts Bandit Problem

We study an extension of standard bandit problem in which there are R layers of experts. Multi-layered experts make selections layer by layer and only the experts in the last layer can play arms. The goal of the learning policy is to minimize the total regret in this hierarchical experts setting. We first analyze the case that total regret grows linearly with the number of layers. Then we focus on the case that all experts are playing Upper Confidence Bound (UCB) strategy and give several sub-linear upper bounds for different circumstances. Finally, we design some experiments to help the regret analysis for the general case of hierarchical UCB structure and show the practical significance of our theoretical results. This article gives many insights about reasonable hierarchical decision structure.

preprint2022arXiv

Robust Learning of Deep Time Series Anomaly Detection Models with Contaminated Training Data

Time series anomaly detection (TSAD) is an important data mining task with numerous applications in the IoT era. In recent years, a large number of deep neural network-based methods have been proposed, demonstrating significantly better performance than conventional methods on addressing challenging TSAD problems in a variety of areas. Nevertheless, these deep TSAD methods typically rely on a clean training dataset that is not polluted by anomalies to learn the "normal profile" of the underlying dynamics. This requirement is nontrivial since a clean dataset can hardly be provided in practice. Moreover, without the awareness of their robustness, blindly applying deep TSAD methods with potentially contaminated training data can possibly incur significant performance degradation in the detection phase. In this work, to tackle this important challenge, we firstly investigate the robustness of commonly used deep TSAD methods with contaminated training data which provides a guideline for applying these methods when the provided training data are not guaranteed to be anomaly-free. Furthermore, we propose a model-agnostic method which can effectively improve the robustness of learning mainstream deep TSAD models with potentially contaminated data. Experiment results show that our method can consistently prevent or mitigate performance degradation of mainstream deep TSAD models on widely used benchmark datasets.

preprint2022arXiv

Robustness and Accuracy Could Be Reconcilable by (Proper) Definition

The trade-off between robustness and accuracy has been widely studied in the adversarial literature. Although still controversial, the prevailing view is that this trade-off is inherent, either empirically or theoretically. Thus, we dig for the origin of this trade-off in adversarial training and find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance -- an overcorrection towards smoothness. Given this, we advocate employing local equivariance to describe the ideal behavior of a robust model, leading to a self-consistent robust error named SCORE. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty via robust optimization. By simply substituting KL divergence with variants of distance metrics, SCORE can be efficiently minimized. Empirically, our models achieve top-rank performance on RobustBench under AutoAttack. Besides, SCORE provides instructive insights for explaining the overfitting phenomenon and semantic input gradients observed on robust models. Code is available at https://github.com/P2333/SCORE.

preprint2022arXiv

Thompson Sampling for (Combinatorial) Pure Exploration

Existing methods of combinatorial pure exploration mainly focus on the UCB approach. To make the algorithm efficient, they usually use the sum of upper confidence bounds within arm set $S$ to represent the upper confidence bound of $S$, which can be much larger than the tight upper confidence bound of $S$ and leads to a much higher complexity than necessary, since the empirical means of different arms in $S$ are independent. To deal with this challenge, we explore the idea of Thompson Sampling (TS) that uses independent random samples instead of the upper confidence bounds, and design the first TS-based algorithm TS-Explore for (combinatorial) pure exploration. In TS-Explore, the sum of independent random samples within arm set $S$ will not exceed the tight upper confidence bound of $S$ with high probability. Hence it solves the above challenge, and achieves a lower complexity upper bound than existing efficient UCB-based algorithms in general combinatorial pure exploration. As for pure exploration of classic multi-armed bandit, we show that TS-Explore achieves an asymptotically optimal complexity upper bound.

preprint2022arXiv

Tianshou: a Highly Modularized Deep Reinforcement Learning Library

In this paper, we present Tianshou, a highly modularized Python library for deep reinforcement learning (DRL) that uses PyTorch as its backend. Tianshou intends to be research-friendly by providing a flexible and reliable infrastructure of DRL algorithms. It supports online and offline training with more than 20 classic algorithms through a unified interface. To facilitate related research and prove Tianshou's reliability, we have released Tianshou's benchmark of MuJoCo environments, covering eight classic algorithms with state-of-the-art performance. We open-sourced Tianshou at https://github.com/thu-ml/tianshou/.

preprint2022arXiv

Towards Job-Transition-Tag Graph for a Better Job Title Representation Learning

Works on learning job title representation are mainly based on \textit{Job-Transition Graph}, built from the working history of talents. However, since these records are usually messy, this graph is very sparse, which affects the quality of the learned representation and hinders further analysis. To address this specific issue, we propose to enrich the graph with additional nodes that improve the quality of job title representation. Specifically, we construct \textit{Job-Transition-Tag Graph}, a heterogeneous graph containing two types of nodes, i.e., job titles and tags (i.e., words related to job responsibilities or functionalities). Along this line, we reformulate job title representation learning as the task of learning node embedding on the \textit{Job-Transition-Tag Graph}. Experiments on two datasets show the interest of our approach.

preprint2022arXiv

Two Coupled Rejection Metrics Can Tell Adversarial Examples Apart

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

preprint2021arXiv

Cognitive Visual Inspection Service for LCD Manufacturing Industry

With the rapid growth of display devices, quality inspection via machine vision technology has become increasingly important for flat-panel displays (FPD) industry. This paper discloses a novel visual inspection system for liquid crystal display (LCD), which is currently a dominant type in the FPD industry. The system is based on two cornerstones: robust/high-performance defect recognition model and cognitive visual inspection service architecture. A hybrid application of conventional computer vision technique and the latest deep convolutional neural network (DCNN) leads to an integrated defect detection, classfication and impact evaluation model that can be economically trained with only image-level class annotations to achieve a high inspection accuracy. In addition, the properly trained model is robust to the variation of the image qulity, significantly alleviating the dependency between the model prediction performance and the image aquisition environment. This in turn justifies the decoupling of the defect recognition functions from the front-end device to the back-end serivce, motivating the design and realization of the cognitive visual inspection service architecture. Empirical case study is performed on a large-scale real-world LCD dataset from a manufacturing line with different layers and products, which shows the promising utility of our system, which has been deployed in a real-world LCD manufacturing line from a major player in the world.

preprint2021arXiv

DNN2LR: Automatic Feature Crossing for Credit Scoring

Credit scoring is a major application of machine learning for financial institutions to decide whether to approve or reject a credit loan. For sake of reliability, it is necessary for credit scoring models to be both accurate and globally interpretable. Simple classifiers, e.g., Logistic Regression (LR), are white-box models, but not powerful enough to model complex nonlinear interactions among features. Fortunately, automatic feature crossing is a promising way to find cross features to make simple classifiers to be more accurate without heavy handcrafted feature engineering. However, credit scoring is usually based on different aspects of users, and the data usually contains hundreds of feature fields. This makes existing automatic feature crossing methods not efficient for credit scoring. In this work, we find local piece-wise interpretations in Deep Neural Networks (DNNs) of a specific feature are usually inconsistent in different samples, which is caused by feature interactions in the hidden layers. Accordingly, we can design an automatic feature crossing method to find feature interactions in DNN, and use them as cross features in LR. We give definition of the interpretation inconsistency in DNN, based on which a novel feature crossing method for credit scoring prediction called DNN2LR is proposed. Apparently, the final model, i.e., a LR model empowered with cross features, generated by DNN2LR is a white-box model. Extensive experiments have been conducted on both public and business datasets from real-world credit scoring applications. Experimental shows that, DNN2LR can outperform the DNN model, as well as several feature crossing methods. Moreover, comparing with the state-of-the-art feature crossing methods, i.e., AutoCross, DNN2LR can accelerate the speed for feature crossing by about 10 to 40 times on datasets with large numbers of feature fields.

preprint2021arXiv

Efficient Inference of Flexible Interaction in Spiking-neuron Networks

Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling inhibitory interactions among neurons. Instead, the nonlinear Hawkes process allows for a more flexible influence pattern with excitatory or inhibitory interactions. In this paper, three sets of auxiliary latent variables (Pólya-Gamma variables, latent marked Poisson processes and sparsity variables) are augmented to make functional connection weights in a Gaussian form, which allows for a simple iterative algorithm with analytical updates. As a result, an efficient expectation-maximization (EM) algorithm is derived to obtain the maximum a posteriori (MAP) estimate. We demonstrate the accuracy and efficiency performance of our algorithm on synthetic and real data. For real neural recordings, we show our algorithm can estimate the temporal dynamics of interaction and reveal the interpretable functional connectivity underlying neural spike trains.

preprint2021arXiv

Fork or Fail: Cycle-Consistent Training with Many-to-One Mappings

Cycle-consistent training is widely used for jointly learning a forward and inverse mapping between two domains of interest without the cumbersome requirement of collecting matched pairs within each domain. In this regard, the implicit assumption is that there exists (at least approximately) a ground-truth bijection such that a given input from either domain can be accurately reconstructed from successive application of the respective mappings. But in many applications no such bijection can be expected to exist and large reconstruction errors can compromise the success of cycle-consistent training. As one important instance of this limitation, we consider practically-relevant situations where there exists a many-to-one or surjective mapping between domains. To address this regime, we develop a conditional variational autoencoder (CVAE) approach that can be viewed as converting surjective mappings to implicit bijections whereby reconstruction errors in both directions can be minimized, and as a natural byproduct, realistic output diversity can be obtained in the one-to-many direction. As theoretical motivation, we analyze a simplified scenario whereby minima of the proposed CVAE-based energy function align with the recovery of ground-truth surjective mappings. On the empirical side, we consider a synthetic image dataset with known ground-truth, as well as a real-world application involving natural language generation from knowledge graphs and vice versa, a prototypical surjective case. For the latter, our CVAE pipeline can capture such many-to-one mappings during cycle training while promoting textural diversity for graph-to-text tasks. Our code is available at github.com/QipengGuo/CycleGT *A condensed version of this paper has been accepted to AISTATS 2021. This version contains additional content and updates.

preprint2021arXiv

ORDisCo: Effective and Efficient Usage of Incremental Unlabeled Data for Semi-supervised Continual Learning

Continual learning usually assumes the incoming data are fully labeled, which might not be applicable in real applications. In this work, we consider semi-supervised continual learning (SSCL) that incrementally learns from partially labeled data. Observing that existing continual learning methods lack the ability to continually exploit the unlabeled data, we propose deep Online Replay with Discriminator Consistency (ORDisCo) to interdependently learn a classifier with a conditional generative adversarial network (GAN), which continually passes the learned data distribution to the classifier. In particular, ORDisCo replays data sampled from the conditional generator to the classifier in an online manner, exploiting unlabeled data in a time- and storage-efficient way. Further, to explicitly overcome the catastrophic forgetting of unlabeled data, we selectively stabilize parameters of the discriminator that are important for discriminating the pairs of old unlabeled data and their pseudo-labels predicted by the classifier. We extensively evaluate ORDisCo on various semi-supervised learning benchmark datasets for SSCL, and show that ORDisCo achieves significant performance improvement on SVHN, CIFAR10 and Tiny-ImageNet, compared to strong baselines.

preprint2021arXiv

Relaxed Conditional Image Transfer for Semi-supervised Domain Adaptation

Semi-supervised domain adaptation (SSDA), which aims to learn models in a partially labeled target domain with the assistance of the fully labeled source domain, attracts increasing attention in recent years. To explicitly leverage the labeled data in both domains, we naturally introduce a conditional GAN framework to transfer images without changing the semantics in SSDA. However, we identify a label-domination problem in such an approach. In fact, the generator tends to overlook the input source image and only memorizes prototypes of each class, which results in unsatisfactory adaptation performance. To this end, we propose a simple yet effective Relaxed conditional GAN (Relaxed cGAN) framework. Specifically, we feed the image without its label to our generator. In this way, the generator has to infer the semantic information of input data. We formally prove that its equilibrium is desirable and empirically validate its practical convergence and effectiveness in image transfer. Additionally, we propose several techniques to make use of unlabeled data in the target domain, enhancing the model in SSDA settings. We validate our method on the well-adopted datasets: Digits, DomainNet, and Office-Home. We achieve state-of-the-art performance on DomainNet, Office-Home and most digit benchmarks in low-resource and high-resource settings.

preprint2021arXiv

Rethinking Natural Adversarial Examples for Classification Models

Recently, it was found that many real-world examples without intentional modifications can fool machine learning models, and such examples are called "natural adversarial examples". ImageNet-A is a famous dataset of natural adversarial examples. By analyzing this dataset, we hypothesized that large, cluttered and/or unusual background is an important reason why the images in this dataset are difficult to be classified. We validated the hypothesis by reducing the background influence in ImageNet-A examples with object detection techniques. Experiments showed that the object detection models with various classification models as backbones obtained much higher accuracy than their corresponding classification models. A detection model based on the classification model EfficientNet-B7 achieved a top-1 accuracy of 53.95%, surpassing previous state-of-the-art classification models trained on ImageNet, suggesting that accurate localization information can significantly boost the performance of classification models on ImageNet-A. We then manually cropped the objects in images from ImageNet-A and created a new dataset, named ImageNet-A-Plus. A human test on the new dataset showed that the deep learning-based classifiers still performed quite poorly compared with humans. Therefore, the new dataset can be used to study the robustness of classification models to the internal variance of objects without considering the background disturbance.

preprint2020arXiv

A Wasserstein Minimum Velocity Approach to Learning Unnormalized Models

Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family of learning objectives including score matching, by observing a new connection between these objectives and Wasserstein gradient flows. We present applications with promise in learning neural density estimators on manifolds, and training implicit variational and Wasserstein auto-encoders with a manifold-valued prior.

preprint2020arXiv

Analyzing the Noise Robustness of Deep Neural Networks

Adversarial examples, generated by adding small but intentionally imperceptible perturbations to normal examples, can mislead deep neural networks (DNNs) to make incorrect predictions. Although much work has been done on both adversarial attack and defense, a fine-grained understanding of adversarial examples is still lacking. To address this issue, we present a visual analysis method to explain why adversarial examples are misclassified. The key is to compare and analyze the datapaths of both the adversarial and normal examples. A datapath is a group of critical neurons along with their connections. We formulate the datapath extraction as a subset selection problem and solve it by constructing and training a neural network. A multi-level visualization consisting of a network-level visualization of data flows, a layer-level visualization of feature maps, and a neuron-level visualization of learned features, has been designed to help investigate how datapaths of adversarial and normal examples diverge and merge in the prediction process. A quantitative evaluation and a case study were conducted to demonstrate the promise of our method to explain the misclassification of adversarial examples.

preprint2020arXiv

Design and Interpretation of Universal Adversarial Patches in Face Detection

We consider universal adversarial patches for faces -- small visual elements whose addition to a face image reliably destroys the performance of face detectors. Unlike previous work that mostly focused on the algorithmic design of adversarial examples in terms of improving the success rate as an attacker, in this work we show an interpretation of such patches that can prevent the state-of-the-art face detectors from detecting the real faces. We investigate a phenomenon: patches designed to suppress real face detection appear face-like. This phenomenon holds generally across different initialization, locations, scales of patches, backbones, and state-of-the-art face detection frameworks. We propose new optimization-based approaches to automatic design of universal adversarial patches for varying goals of the attack, including scenarios in which true positives are suppressed without introducing false positives. Our proposed algorithms perform well on real-world datasets, deceiving state-of-the-art face detectors in terms of multiple precision/recall metrics and transferability.

preprint2020arXiv

Dynamic Window-level Granger Causality of Multi-channel Time Series

Granger causality method analyzes the time series causalities without building a complex causality graph. However, the traditional Granger causality method assumes that the causalities lie between time series channels and remain constant, which cannot model the real-world time series data with dynamic causalities along the time series channels. In this paper, we present the dynamic window-level Granger causality method (DWGC) for multi-channel time series data. We build the causality model on the window-level by doing the F-test with the forecasting errors on the sliding windows. We propose the causality indexing trick in our DWGC method to reweight the original time series data. Essentially, the causality indexing is to decrease the auto-correlation and increase the cross-correlation causal effects, which improves the DWGC method. Theoretical analysis and experimental results on two synthetic and one real-world datasets show that the improved DWGC method with causality indexing better detects the window-level causalities.

preprint2020arXiv

Improving Black-box Adversarial Attacks with a Transfer-based Prior

We consider the black-box adversarial setting, where the adversary has to generate adversarial perturbations without access to the target models to compute gradients. Previous methods tried to approximate the gradient either by using a transfer gradient of a surrogate white-box model, or based on the query feedback. However, these methods often suffer from low attack success rates or poor query efficiency since it is non-trivial to estimate the gradient in a high-dimensional space with limited information. To address these problems, we propose a prior-guided random gradient-free (P-RGF) method to improve black-box adversarial attacks, which takes the advantage of a transfer-based prior and the query information simultaneously. The transfer-based prior given by the gradient of a surrogate model is appropriately integrated into our algorithm by an optimal coefficient derived by a theoretical analysis. Extensive experiments demonstrate that our method requires much fewer queries to attack black-box models with higher success rates compared with the alternative state-of-the-art methods.

preprint2020arXiv

Learning Implicit Generative Models by Teaching Explicit Ones

Implicit generative models are difficult to train as no explicit density functions are defined. Generative adversarial nets (GANs) present a minimax framework to train such models, which however can suffer from mode collapse due to the nature of the JS-divergence. This paper presents a learning by teaching (LBT) approach to learning implicit models, which intrinsically avoids the mode collapse problem by optimizing a KL-divergence rather than the JS-divergence in GANs. In LBT, an auxiliary density estimator is introduced to fit the implicit model's distribution while the implicit model teaches the density estimator to match the data distribution. LBT is formulated as a bilevel optimization problem, whose optimal generator matches the true data distribution. LBT can be naturally integrated with GANs to derive a hybrid LBT-GAN that enjoys complimentary benefits. Finally, we present a stochastic gradient ascent algorithm with unrolling to solve the challenging learning problems. Experimental results demonstrate the effectiveness of our method.

preprint2020arXiv

Mixup Inference: Better Exploiting Mixup to Defend Adversarial Attacks

It has been widely recognized that adversarial examples can be easily crafted to fool deep networks, which mainly root from the locally non-linear behavior nearby input examples. Applying mixup in training provides an effective mechanism to improve generalization performance and model robustness against adversarial perturbations, which introduces the globally linear behavior in-between training examples. However, in previous work, the mixup-trained models only passively defend adversarial attacks in inference by directly classifying the inputs, where the induced global linearity is not well exploited. Namely, since the locality of the adversarial perturbations, it would be more efficient to actively break the locality via the globality of the model predictions. Inspired by simple geometric intuition, we develop an inference principle, named mixup inference (MI), for mixup-trained models. MI mixups the input with other random clean samples, which can shrink and transfer the equivalent perturbation if the input is adversarial. Our experiments on CIFAR-10 and CIFAR-100 demonstrate that MI can further improve the adversarial robustness for the models trained by mixup and its variants.

preprint2020arXiv

Nonparametric Score Estimators

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable densities. Kernel estimators based on Stein's methods or score matching have shown promise, however their theoretical properties and relationships have not been fully-understood. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. It allows us to analyse existing estimators and construct new ones with desirable properties by choosing different hypothesis spaces and regularizers. A unified convergence analysis is provided for such estimators. Finally, we propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.

preprint2020arXiv

Rethinking Softmax Cross-Entropy Loss for Adversarial Robustness

Previous work shows that adversarially robust generalization requires larger sample complexity, and the same dataset, e.g., CIFAR-10, which enables good standard accuracy may not suffice to train robust models. Since collecting new training data could be costly, we focus on better utilizing the given data by inducing the regions with high sample density in the feature space, which could lead to locally sufficient samples for robust learning. We first formally show that the softmax cross-entropy (SCE) loss and its variants convey inappropriate supervisory signals, which encourage the learned feature points to spread over the space sparsely in training. This inspires us to propose the Max-Mahalanobis center (MMC) loss to explicitly induce dense feature regions in order to benefit robustness. Namely, the MMC loss encourages the model to concentrate on learning ordered and compact representations, which gather around the preset optimal centers for different classes. We empirically demonstrate that applying the MMC loss can significantly improve robustness even under strong adaptive attacks, while keeping state-of-the-art accuracy on clean inputs with little extra computation compared to the SCE loss.

preprint2020arXiv

SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models

Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. If parameterized by an encoder-decoder architecture, the parameters of the encoder can be optimized to minimize its variance of this estimator. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost. This estimator also allows use of latent variable models for tasks where unbiased estimators, rather than marginal likelihood lower bounds, are preferred, such as minimizing reverse KL divergences and estimating score functions.

preprint2020arXiv

Superconducting proximity effect in a transparent van der Waals superconductor-metal junction

We report on Andreev reflections at clean NbSe2-bilayer graphene junctions. The high transparency of the junction, which manifests as a large conductance enhancement of up to 1.8, enables us to see clear evidence of a proximity-induced superconducting gap in bilayer graphene and two Andreev reflections through a vertical NbSe2-graphene and a lateral graphene-graphene junction respectively. Quantum transport simulations capture the complexity of the experimental data and illuminate the impact of various microscopic parameters on the transmission of the junction. Our work establishes the practice and understanding of an all-van-der-Waals, high-performance superconducting junction. The realization of a highly transparent proximized graphene-graphene junction opens up possibilities to engineer emergent quantum phenomena.

preprint2020arXiv

To Relieve Your Headache of Training an MRF, Take AdVIL

We propose a black-box algorithm called {\it Adversarial Variational Inference and Learning} (AdVIL) to perform inference and learning on a general Markov random field (MRF). AdVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function of an MRF, respectively. The two variational distributions provide an estimate of the negative log-likelihood of the MRF as a minimax optimization problem, which is solved by stochastic gradient descent. AdVIL is proven convergent under certain conditions. On one hand, compared with contrastive divergence, AdVIL requires a minimal assumption about the model structure and can deal with a broader family of MRFs. On the other hand, compared with existing black-box methods, AdVIL provides a tighter estimate of the log partition function and achieves much better empirical results.

preprint2020arXiv

Triple Generative Adversarial Networks

We propose a unified game-theoretical framework to perform classification and conditional image generation given limited supervision. It is formulated as a three-player minimax game consisting of a generator, a classifier and a discriminator, and therefore is referred to as Triple Generative Adversarial Network (Triple-GAN). The generator and the classifier characterize the conditional distributions between images and labels to perform conditional generation and classification, respectively. The discriminator solely focuses on identifying fake image-label pairs. Under a nonparametric assumption, we prove the unique equilibrium of the game is that the distributions characterized by the generator and the classifier converge to the data distribution. As a byproduct of the three-player mechanism, Triple-GAN is flexible to incorporate different semi-supervised classifiers and GAN architectures. We evaluate Triple-GAN in two challenging settings, namely, semi-supervised learning and the extreme low data regime. In both settings, Triple-GAN can achieve excellent classification results and generate meaningful samples in a specific class simultaneously. In particular, using a commonly adopted 13-layer CNN classifier, Triple-GAN outperforms extensive semi-supervised learning methods substantially on more than 10 benchmarks no matter data augmentation is applied or not.

preprint2020arXiv

Triple Memory Networks: a Brain-Inspired Method for Continual Learning

Continual acquisition of novel experience without interfering previously learned knowledge, i.e. continual learning, is critical for artificial neural networks, but limited by catastrophic forgetting. A neural network adjusts its parameters when learning a new task, but then fails to conduct the old tasks well. By contrast, the brain has a powerful ability to continually learn new experience without catastrophic interference. The underlying neural mechanisms possibly attribute to the interplay of hippocampus-dependent memory system and neocortex-dependent memory system, mediated by prefrontal cortex. Specifically, the two memory systems develop specialized mechanisms to consolidate information as more specific forms and more generalized forms, respectively, and complement the two forms of information in the interplay. Inspired by such brain strategy, we propose a novel approach named triple memory networks (TMNs) for continual learning. TMNs model the interplay of hippocampus, prefrontal cortex and sensory cortex (a neocortex region) as a triple-network architecture of generative adversarial networks (GAN). The input information is encoded as specific representation of the data distributions in a generator, or generalized knowledge of solving tasks in a discriminator and a classifier, with implementing appropriate brain-inspired algorithms to alleviate catastrophic forgetting in each module. Particularly, the generator replays generated data of the learned tasks to the discriminator and the classifier, both of which are implemented with a weight consolidation regularizer to complement the lost information in generation process. TMNs achieve new state-of-the-art performance on a variety of class-incremental learning benchmarks on MNIST, SVHN, CIFAR-10 and ImageNet-50, comparing with strong baseline methods.

preprint2020arXiv

Understanding and Stabilizing GANs' Training Dynamics with Control Theory

Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the function space and provide simple yet effective methods to stabilize GANs' training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, where CLC is implemented as a squared $L2$ regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.

preprint2020arXiv

VFlow: More Expressive Generative Flows with Variational Data Augmentation

Generative flows are promising tractable models for density modeling that define probabilistic distributions with invertible transformations. However, tractability imposes architectural constraints on generative flows, making them less expressive than other types of generative models. In this work, we study a previously overlooked constraint that all the intermediate representations must have the same dimensionality with the original data due to invertibility, limiting the width of the network. We tackle this constraint by augmenting the data with some extra dimensions and jointly learning a generative flow for augmented data as well as the distribution of augmented dimensions under a variational inference framework. Our approach, VFlow, is a generalization of generative flows and therefore always performs better. Combining with existing generative flows, VFlow achieves a new state-of-the-art 2.98 bits per dimension on the CIFAR-10 dataset and is more compact than previous models to reach similar modeling quality.

preprint2019arXiv

Ferromagnetic van der Waals compound MnSb$_{1.8}$Bi$_{0.2}$Te$_4$

The intersection of topology and magnetism represents a new playground to discover novel quantum phenomena and device concepts. In this work, we show that a van der Waals compound MnSb$_{1.8}$Bi$_{0.2}$Te$_4$ exhibits a ferromagnetic ground state with a Curie temperature of 26 K, in contrast to the antiferromagnetic order previously found for other members of the Mn(Sb, Bi)$_2$Te$_4$ family. We employ magneto-transport, bulk magnetization and neutron scattering studies to illustrate the magnetic and electrical properties of MnSb$_{1.8}$Bi$_{0.2}$Te$_4$ and report on the observation of an unusual anomalous Hall effect. Our results are an important step in the synthesis and understanding of ferromagnetic topological insulators.