Qinghua Tao

Qinghua Tao, Li Li, Xiaolin Huang et al.

As a powerful modelling method, PieceWise Linear Neural Networks (PWLNNs) have proven successful in various fields, most recently in deep learning. To apply PWLNN methods, both the representation and the learning have long been studied. In 1977, the canonical representation pioneered the works of shallow PWLNNs learned by incremental designs, but the applications to large-scale data were prohibited. In 2010, the Rectified Linear Unit (ReLU) advocated the prevalence of PWLNNs in deep learning. Ever since, PWLNNs have been successfully applied to extensive tasks and achieved advantageous performances. In this Primer, we systematically introduce the methodology of PWLNNs by grouping the works into shallow and deep networks. Firstly, different PWLNN representation models are constructed with elaborated examples. With PWLNNs, the evolution of learning algorithms for data is presented and fundamental theoretical analysis follows up for in-depth understandings. Then, representative applications are introduced together with discussions and outlooks.

Jiani Liu, Qinghua Tao, Ce Zhu et al.

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient representations for such tasks, while preserving structural task-relations. In this paper, a new MTL method is proposed by leveraging low-rank tensor analysis and constructing tensorized Least Squares Support Vector Machines, namely the tLSSVM-MTL, where multilinear modelling and its nonlinear extensions can be flexibly exerted. We employ a high-order tensor for all the weights with each mode relating to an index and factorize it with CP decomposition, assigning a shared factor for all tasks and retaining task-specific latent factors along each index. Then an alternating algorithm is derived for the nonconvex optimization, where each resulting subproblem is solved by a linear system. Experimental results demonstrate promising performances of our tLSSVM-MTL.

Kun Fang, Qinghua Tao, Xiaolin Huang et al.

Existing Out-of-Distribution (OoD) detection methods address to detect OoD samples from In-Distribution (InD) data mainly by exploring differences in features, logits and gradients in Deep Neural Networks (DNNs). We in this work propose a new perspective upon loss landscape and mode ensemble to investigate OoD detection. In the optimization of DNNs, there exist many local optima in the parameter space, or namely modes. Interestingly, we observe that these independent modes, which all reach low-loss regions with InD data (training and test data), yet yield significantly different loss landscapes with OoD data. Such an observation provides a novel view to investigate the OoD detection from the loss landscape, and further suggests significantly fluctuating OoD detection performance across these modes. For instance, FPR values of the RankFeat method can range from 46.58% to 84.70% among 5 modes, showing uncertain detection performance evaluations across independent modes. Motivated by such diversities on OoD loss landscape across modes, we revisit the deep ensemble method for OoD detection through mode ensemble, leading to improved performance and benefiting the OoD detector with reduced variances. Extensive experiments covering varied OoD detectors and network structures illustrate high variances across modes and validate the superiority of mode ensemble in boosting OoD detection. We hope this work could attract attention in the view of independent modes in the loss landscape of OoD data and more reliable evaluations on OoD detectors.

Kun Fang, Qinghua Tao, Kexin Lv et al.

Out-of-Distribution (OoD) detection is vital for the reliability of Deep Neural Networks (DNNs). Existing works have shown the insufficiency of Principal Component Analysis (PCA) straightforwardly applied on the features of DNNs in detecting OoD data from In-Distribution (InD) data. The failure of PCA suggests that the network features residing in OoD and InD are not well separated by simply proceeding in a linear subspace, which instead can be resolved through proper non-linear mappings. In this work, we leverage the framework of Kernel PCA (KPCA) for OoD detection, and seek suitable non-linear kernels that advocate the separability between InD and OoD data in the subspace spanned by the principal components. Besides, explicit feature mappings induced from the devoted task-specific kernels are adopted so that the KPCA reconstruction error for new test samples can be efficiently obtained with large-scale data. Extensive theoretical and empirical results on multiple OoD data sets and network structures verify the superiority of our KPCA detector in efficiency and efficacy with state-of-the-art detection performance.

Kun Fang, Qinghua Tao, Mingzhen He et al.

Out-of-Distribution (OoD) detection is vital for the reliability of deep neural networks, the key of which lies in effectively characterizing the disparities between OoD and In-Distribution (InD) data. In this work, such disparities are exploited through a fresh perspective of non-linear feature subspace. That is, a discriminative non-linear subspace is learned from InD features to capture representative patterns of InD, while informative patterns of OoD features cannot be well captured in such a subspace due to their different distribution. Grounded on this perspective, we exploit the deviations of InD and OoD features in such a non-linear subspace for effective OoD detection. To be specific, we leverage the framework of Kernel Principal Component Analysis (KPCA) to attain the discriminative non-linear subspace and deploy the reconstruction error on such subspace to distinguish InD and OoD data. Two challenges emerge: (i) the learning of an effective non-linear subspace, i.e., the selection of kernel function in KPCA, and (ii) the computation of the kernel matrix with large-scale InD data. For the former, we reveal two vital non-linear patterns that closely relate to the InD-OoD disparity, leading to the establishment of a Cosine-Gaussian kernel for constructing the subspace. For the latter, we introduce two techniques to approximate the Cosine-Gaussian kernel with significantly cheap computations. In particular, our approximation is further tailored by incorporating the InD data confidence, which is demonstrated to promote the learning of discriminative subspaces for OoD data. Our study presents new insights into the non-linear feature subspace for OoD detection and contributes practical explorations on the associated kernel design and efficient computations, yielding a KPCA detection method with distinctively improved efficacy and efficiency.

Qinghua Tao, Xiangming Xi, Jun Xu et al.

For the linear inverse problem with sparsity constraints, the $l_0$ regularized problem is NP-hard, and existing approaches either utilize greedy algorithms to find almost-optimal solutions or to approximate the $l_0$ regularization with its convex counterparts. In this paper, we propose a novel and concise regularization, namely the sparse group $k$-max regularization, which can not only simultaneously enhance the group-wise and in-group sparsity, but also casts no additional restraints on the magnitude of variables in each group, which is especially important for variables at different scales, so that it approximate the $l_0$ norm more closely. We also establish an iterative soft thresholding algorithm with local optimality conditions and complexity analysis provided. Through numerical experiments on both synthetic and real-world datasets, we verify the effectiveness and flexibility of the proposed method.

Tao Li, Lei Tan, Qinghua Tao et al.

Deep neural networks (DNNs) usually contain massive parameters, but there is redundancy such that it is guessed that the DNNs could be trained in low-dimensional subspaces. In this paper, we propose a Dynamic Linear Dimensionality Reduction (DLDR) based on low-dimensional properties of the training trajectory. The reduction is efficient, which is supported by comprehensive experiments: optimization in 40 dimensional spaces can achieve comparable performance as regular training over thousands or even millions of parameters. Since there are only a few optimization variables, we develop a quasi-Newton-based algorithm and also obtain robustness against label noises, which are two follow-up experiments to show the advantages of finding low-dimensional subspaces.

Kun Fang, Qinghua Tao, Yingwen Wu et al.

Deep Neural Networks (DNNs) are vulnerable to invisible perturbations on the images generated by adversarial attacks, which raises researches on the adversarial robustness of DNNs. A series of methods represented by the adversarial training and its variants have proven as one of the most effective techniques in enhancing the DNN robustness. Generally, adversarial training focuses on enriching the training data by involving perturbed data. Such data augmentation effect of the involved perturbed data in adversarial training does not contribute to the robustness of DNN itself and usually suffers from clean accuracy drop. Towards the robustness of DNN itself, we in this paper propose a novel defense that aims at augmenting the model in order to learn features that are adaptive to diverse inputs, including adversarial examples. More specifically, to augment the model, multiple paths are embedded into the network, and an orthogonality constraint is imposed on these paths to guarantee the diversity among them. A margin-maximization loss is then designed to further boost such DIversity via Orthogonality (DIO). In this way, the proposed DIO augments the model and enhances the robustness of DNN itself as the learned features can be corrected by these mutually-orthogonal paths. Extensive empirical results on various data sets, structures and attacks verify the stronger adversarial robustness of the proposed DIO utilizing model augmentation. Besides, DIO can also be flexibly combined with different data augmentation techniques (e.g., TRADES and DDPM), further promoting robustness gains.

Yusen Huo, Qinghua Tao, Jianming Hu

Traffic signal control has long been considered as a critical topic in intelligent transportation systems. Most existing learning methods mainly focus on isolated intersections and suffer from inefficient training. This paper aims at the cooperative control for large scale multi-intersection traffic signal, in which a novel end-to-end learning based model is established and the efficient training method is proposed correspondingly. In the proposed model, the input traffic status in multi-intersections is represented by a tensor, which not only significantly reduces dimensionality than using a single matrix but also avoids information loss. For the output, a multidimensional boolean vector is employed for the control policy to indicate whether the signal state changes or not, which simplifies the representation and abides the practical phase changing rules. In the proposed model, a multi-task learning structure is used to get the cooperative policy by learning. Instead of only using the reinforcement learning to train the model, we employ imitation learning to integrate a rule based model with neural networks to do the pre-training, which provides a reliable and satisfactory stage solution and greatly accelerates the convergence. Afterwards, the reinforcement learning method is adopted to continue the fine training, where proximal policy optimization algorithm is incorporated to solve the policy collapse problem in multi-dimensional output situation. In numerical experiments, the advantages of the proposed model are demonstrated with comparison to the related state-of-the-art methods.

Jun Xu, Qinghua Tao, Zhen Li et al.

In this paper, the efficient hinging hyperplanes (EHH) neural network is proposed based on the model of hinging hyperplanes (HH). The EHH neural network is a distributed representation, the training of which involves solving several convex optimization problems and is fast. It is proved that for every EHH neural network, there is an equivalent adaptive hinging hyperplanes (AHH) tree, which was also proposed based on the model of HH and find good applications in system identification. The construction of the EHH neural network includes 2 stages. First the initial structure of the EHH neural network is randomly determined and the Lasso regression is used to choose the appropriate network. To alleviate the impact of randomness, secondly, the stacking strategy is employed to formulate a more general network structure. Different from other neural networks, the EHH neural network has interpretability ability, which can be easily obtained through its ANOVA decomposition (or interaction matrix). The interpretability can then be used as a suggestion for input variable selection. The EHH neural network is applied in nonlinear system identification, the simulation results show that the regression vector selected is reasonable and the identification speed is fast, while at the same time, the simulation accuracy is satisfactory.