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Deep neural network (DNN) models have achieved phenomenal success for applications in many domains, ranging from academic research in science and engineering to industry and business. The modeling power of DNN is believed to have come from the complexity and over-parameterization of the model, which on the other hand has been criticized for the lack of interpretation. Although certainly not true for every application, in some applications, especially in economics, social science, healthcare industry, and administrative decision making, scientists or practitioners are resistant to use predictions made by a black-box system for multiple reasons. One reason is that a major purpose of a study can be to make discoveries based upon the prediction function, e.g., to reveal the relationships between measurements. Another reason can be that the training dataset is not large enough to make researchers feel completely sure about a purely data-driven result. Being able to examine and interpret the prediction function will enable researchers to connect the result with existing knowledge or gain insights about new directions to explore. Although classic statistical models are much more explainable, their accuracy often falls considerably below DNN. In this paper, we propose an approach to fill the gap between relatively simple explainable models and DNN such that we can more flexibly tune the trade-off between interpretability and accuracy. Our main idea is a mixture of discriminative models that is trained with the guidance from a DNN. Although mixtures of discriminative models have been studied before, our way of generating the mixture is quite different.
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This paper proposes a dual-supervised uncertainty inference (DS-UI) framework for improving Bayesian estimation-based uncertainty inference (UI) in deep neural network (DNN)-based image recognition. In the DS-UI, we combine the classifier of a DNN, i.e., the last fully-connected (FC) layer, with a mixture of Gaussian mixture models (MoGMM) to obtain an MoGMM-FC layer. Unlike existing UI methods for DNNs, which only calculate the means or modes of the DNN outputs distributions, the proposed MoGMM-FC layer acts as a probabilistic interpreter for the features that are inputs of the classifier to directly calculate the probability density of them for the DS-UI. In addition, we propose a dual-supervised stochastic gradient-based variational Bayes (DS-SGVB) algorithm for the MoGMM-FC layer optimization. Unlike conventional SGVB and optimization algorithms in other UI methods, the DS-SGVB not only models the samples in the specific class for each Gaussian mixture model (GMM) in the MoGMM, but also considers the negative samples from other classes for the GMM to reduce the intra-class distances and enlarge the inter-class margins simultaneously for enhancing the learning ability of the MoGMM-FC layer in the DS-UI. Experimental results show the DS-UI outperforms the state-of-the-art UI methods in misclassification detection. We further evaluate the DS-UI in open-set out-of-domain/-distribution detection and find statistically significant improvements. Visualizations of the feature spaces demonstrate the superiority of the DS-UI.
This paper presents a general framework for norm-based capacity control for $L_{p,q}$ weight normalized deep neural networks. We establish the upper bound on the Rademacher complexities of this family. With an $L_{p,q}$ normalization where $qle p^*$, and $1/p+1/p^{*}=1$, we discuss properties of a width-independent capacity control, which only depends on depth by a square root term. We further analyze the approximation properties of $L_{p,q}$ weight normalized deep neural networks. In particular, for an $L_{1,infty}$ weight normalized network, the approximation error can be controlled by the $L_1$ norm of the output layer, and the corresponding generalization error only depends on the architecture by the square root of the depth.
This paper studies learning node representations with GNNs for unsupervised scenarios. We make a theoretical understanding and empirical demonstration about the non-steady performance of GNNs over different graph datasets, when the supervision signals are not appropriately defined. The performance of GNNs depends on both the node feature smoothness and the graph locality. To smooth the discrepancy of node proximity measured by graph topology and node feature, we proposed KS2L - a novel graph underline{K}nowledge distillation regularized underline{S}elf-underline{S}upervised underline{L}earning framework, with two complementary regularization modules, for intra-and cross-model graph knowledge distillation. We demonstrate the competitive performance of KS2L on a variety of benchmarks. Even with a single GCN layer, KS2L has consistently competitive or even better performance on various benchmark datasets.
The vulnerability of deep neural networks (DNNs) to adversarial attack, which is an attack that can mislead state-of-the-art classifiers into making an incorrect classification with high confidence by deliberately perturbing the original inputs, raises concerns about the robustness of DNNs to such attacks. Adversarial training, which is the main heuristic method for improving adversarial robustness and the first line of defense against adversarial attacks, requires many sample-by-sample calculations to increase training size and is usually insufficiently strong for an entire network. This paper provides a new perspective on the issue of adversarial robustness, one that shifts the focus from the network as a whole to the critical part of the region close to the decision boundary corresponding to a given class. From this perspective, we propose a method to generate a single but image-agnostic adversarial perturbation that carries the semantic information implying the directions to the fragile parts on the decision boundary and causes inputs to be misclassified as a specified target. We call the adversarial training based on such perturbations region adversarial training (RAT), which resembles classical adversarial training but is distinguished in that it reinforces the semantic information missing in the relevant regions. Experimental results on the MNIST and CIFAR-10 datasets show that this approach greatly improves adversarial robustness even using a very small dataset from the training data; moreover, it can defend against FGSM adversarial attacks that have a completely different pattern from the model seen during retraining.
The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced in [20], where it was proven that in the infinite width limit the NTK converges to an explicit limiting kernel and it stays constant during training. The NTK was also implicit in some other recent papers [6,13,14]. In the overparametrization regime, a fully-trained deep neural network is indeed equivalent to the kernel regression predictor using the limiting NTK. And the gradient descent achieves zero training loss for a deep overparameterized neural network. However, it was observed in [5] that there is a performance gap between the kernel regression using the limiting NTK and the deep neural networks. This performance gap is likely to originate from the change of the NTK along training due to the finite width effect. The change of the NTK along the training is central to describe the generalization features of deep neural networks. In the current paper, we study the dynamic of the NTK for finite width deep fully-connected neural networks. We derive an infinite hierarchy of ordinary differential equations, the neural tangent hierarchy (NTH) which captures the gradient descent dynamic of the deep neural network. Moreover, under certain conditions on the neural network width and the data set dimension, we prove that the truncated hierarchy of NTH approximates the dynamic of the NTK up to arbitrary precision. This description makes it possible to directly study the change of the NTK for deep neural networks, and sheds light on the observation that deep neural networks outperform kernel regressions using the corresponding limiting NTK.
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