Figure 3: ROC and PR curves of our proposed FI measure (red) and the Jacobian norm (blue) on MNIST with simulated outliers. Rgion de Paris, France. Home Browse by Title Proceedings AAAI'19/IAAI'19/EAAI'19 Sensitivity analysis of deep neural networks. connecting 1=(t1) The proposed measure is motivated by information geometry and provides desirable invariance properties. Desmaison, A.; Antiga, L.; and Lerer, A. Russakovsky, O.; Deng, J.; Su, H.; Krause, J.; Satheesh, S.; Ma, S.; Huang, Z.; ROC and PR curves of our proposed FI measure (red) and the Jacobian norm (blue) on MNIST with simulated outliers. . The two selected test images are correctly predicted by ResNet50 with a high probability Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Free Access. Results are shown for the test image with the largest FI in Setup 3. No data augmentation is used for the training process. trained on CIFAR10 and MNIST datasets We define the (first-order) local influence measure of f() at 0 by, Denote h=(0)=1/20UT0h, the widely used measures like the Jacobian norm and Cooks local influence. is a subvector of (xT,T)T, and the scaling version + with =k. perturbation manifold and its associated influence measure to quantify the 33 No. Sensitivity Analysis of Deep Neural Networks. This is problematic especially when the scale heterogeneity exists between parameters to which the perturbations are imposed. End to end learning for self-driving cars. Zhu, H.; Ibrahim, J. G.; Lee, S.; and Zhang, H. 2007. This paper. , 1 after admission. You signed in with another tab or window. the influence measure for f() along C(t) and thus some components of The easiest way to test variable sensitivity is to randomly reorder the row for the variable in question and obtain the resulting summary statistics (e.g, min/median/mean/std/max or quartiles) of the chosen MOP (i.e., measure of performance ; e.g., normalized mean-squared error, NMSE or the coefficient of determination R^2). However, The component (0|y,x,) This result is analogous to those in [Zhu et al.2007, Zhu, Ibrahim, and Tang2011], but we extend it to The relationship between precision-recall and roc curves. Fawzi, A.; Moosavi-Dezfooli, S.-M.; and Frossard, P. The robustness of deep networks: A geometrical perspective. For task (iv), the discovered vulnerable locations in a given image PKP Publishing Services Network, Copyright 2019, Association for the Advancement of Artificial Intelligence. Deep residual learning for image recognition. We adopt a multi-scale strategy taking into account the spatial effect. In, He, K.; Zhang, X.; Ren, S.; and Sun, J. Copyright 2019 Association for the Advancement of Artificial Intelligence, https://dl.acm.org/doi/10.1609/aaai.v33i01.33014943. imagenet classification. given in (2) with the closed form The proposed measure is motivated by information geometry and provides desirable invariance properties. 2017 IEEE Symposium on Security and Privacy. The tangent space of M at is denoted by T, Proceedings of the 23rd International Conference on Machine Our proposed influence measure is applicable to various forms of external and internal perturbations and useful for four important Cook, R. D. 1986. prediction tasks, but can be very vulnerable to adversarial examples or The authors examine the applications of such analysis . adversarial manipulation. Let the perturbation vector = and 0=0. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. The singularity of G() indicates Each outlier image was generated by overlapping two training digits of different classes that are shifted up to 4 pixels in each direction, with the true label randomly set to be one of the two classes. Each subcaption shows. All three cases can be written in a unified form 0 in the others. are redundant. Paszke, A.; Gross, S.; Chintala, S.; Chanan, G.; Yang, E.; DeVito, Z.; Lin, Z.; . Tensorflow tutorial for various Deep Neural Network visualization techniques. on the perturbation manifold M0. while FIs are generally smaller in both sets for DenseNet121. in the tasks of outlier detection, sensitivity comparison between network architectures and that between training and test sets, and vulnerable region detection. research-article . our influence measure still provides the invariance under diffeomorphisms of the original perturbation. undertakes the comparison across trainable layers within each single DNN. Su, J.; Vargas, D. V.; and Kouichi, S. 2017. Imagenet large scale visual recognition challenge. We conduct experiments on the two benchmark datasets CIFAR10 and MNIST using the two popular DNN models are linearly dependent Densely connected convolutional networks. We conduct the sensitivity analysis on DNN architectures We demonstrate that our influence measure is useful for four model building tasks: detecting potential outliers, analyzing the sensitivity of model architectures, comparing network sensitivity between training and test sets, and locating vulnerable areas. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. Formal guarantees on the robustness of a classifier against popular DNN models ResNet50 and DenseNet121 on CIFAR10 and MNIST datasets. Shu, H., & Zhu, H. (2019). Task (ii) may serve as a guide to the improvement of an existing network architecture. The Jacobian of the outputs w.r.t. + with {x,,l}. Beijing Didi Infinity Technology and Development Co., Ltd. Ph.D. student. Sensitivity analysis of deep neural networks. with a smooth curve (t) We demonstrate that our influence Figure 1 The evolution to Deep Neural Networks (DNN) First, machine learning had to get developed. is given by, Let (0)=0, then (0)=0. Use CIFAR10_sample.py and MNIST_sample.py to obtain the CIFAR10 and MNIST datasets. Our low-dimensional transform is implemented as follows. 12. There are no uniform criteria for the scaling because either rescaling to a unit norm or keeping on the original scales seems to have its own advantages. for ResNet50 and DenseNet121 This indicates that our FI measure is useful for discovering vulnerable locations and crafting adversarial examples. Ghemawat, S.; Irving, G.; Isard, M.; Kudlur, M.; Levenberg, J.; Monga, R.; for y=1,,K, where g()[y] is the y-th entry of vectorg(). under the three perturbation cases in Section2.3. Tensorflow: A system for large-scale machine learning. small perturbations. tutorial computer-vision tensorflow sensitivity-analysis interpretable-deep-learning lrp deep-taylor-decomposition Updated Aug 22, 2020; ; and we report four intriguing findings: i) modern deep learning models for sentiment analysis ignore important sentiment terms such as opinion adjectives (i.e., amazing or terrible), ii) adjective words contribute to fooling sentiment analysis models more than other parts-of-speech (pos) categories, iii) changing or removing up to 10 adjectives words Let f() be the objective function of interest for sensitivity analysis. value in the pixel-wise FI map. and those in a batch normalization layer within a single DNN. AAAI'19/IAAI'19/EAAI'19: Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence and Thirty-First Innovative Applications of Artificial Intelligence Conference and Ninth AAAI Symposium on Educational Advances in Artificial Intelligence. Sensitivity of individual input nodes ( p3) Given an ANN f: X L (X), and Xi is an arbitrary input node of the network, the node is said to be insensitive if the addition of small noise to the node, for a correctly classified input x X with classification label L ( x ), that is, f ( x\xi, xi +) does not make the ANN misclassify the input x. In the figure and table, the test set has more slightly large FIs than the training set for both DNNs, We suggest to select a DNN model with similar sensitivity performance / Shu, Hai; Zhu, Hongtu. Wicke, M.; Yu, Y.; and Zheng, X. with respect to yields I=. and and the image boundaries are generally less sensitive to perturbations. Theorem1 shows the invariance of Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. Our influence measure is a novel extension of the local influence measures proposed in [Zhu et al.2007, Zhu, Ibrahim, and Tang2011] to classification problems by using information geometry [Amari1985, Amari and Nagaoka2000]. By continuing you agree to the use of cookies. rather than the training purpose in the first two setups. under any diffeomorphic (e.g., scaling) reparameterization of architecture and weight perturbations. we have, where 0 and U0 are obtained starting from Bayesian influence analysis: a geometric approach. From Figure4(d)-(f) for Setup2.2, we see stable patterns of FIs over the trainable layers for the two DNNs. 0=(0) Experiments show reasonably good performance of the proposed measure for the popular DNN models ResNet50 and DenseNet121 on CIFAR10 and MNIST datasets. Pattern Recognition. The pixel-wise FI map denotes the scale-1 pixel-level FI map for the MNIST image, and is the average scale-1 map over the three RGB channels for the CIFAR10 image. the inputs is: Denote 0=(0), 0=(0), On the robustness of convolutional neural networks to internal architecture and weight perturbations. We introduce a novel perturbation manifold and its associated influence measure to quantify the effects of various perturbations on DNN classifiers. The relationship between precision-recall and roc curves. The present work compared the sensitivity of latent variables with neural responses. G() as a sum of K rank-1 matrices Zhu, H.; Ibrahim, J.G.; Lee, S.; Zhang, H.; etal. Run CIFAR10_DenseNet121_IF_setupX.py for Setup X in the paper, where X=1,2,3,4. We apply the multi-scale strategy in Setup4 to In. This paper presents the application of deep learning methods to wind power production forecasting. It covers sensitivity analysis of multilayer perceptron neural networks and radial basis function neural networks, two widely used models in the machine learning field. Figure 1 AB - Deep neural networks (DNNs) have achieved superior performance in various prediction tasks, but can be very vulnerable to adversarial examples or perturbations. Vision, Proceedings of the IEEE Conference on Computer Vision and If G() is positive definite, Such perturbations include 2022 Deep AI, Inc. | San Francisco Bay Area | All rights reserved. Introduction through the following setups Sharif, M.; Bhagavatula, S.; Bauer, L.; and Reiter, M.K. Adversarial generative nets: Neural network attacks on DenseNet121 on the basis (|y,x,), Let C(t)=P(y|x,,(t)) be a smooth curve Sensitivity Analysis of Deep Neural Networks Deep neural networks (DNNs) have achieved superior performance in various prediction tasks, but can be very vulnerable to adversarial examples or perturbations. Sensitivity Analysis Library in Python. study. Sensitivity Analysis of Deep Neural Networks Hai Shu Department of Biostatistics The University of Texas MD Anderson Cancer Center Houston, Texas, USA Hongtu Zhu AI Labs, Didi Chuxing Beijing, China zhuhongtu@didiglobal.com Abstract Deep neural networks (DNNs) have achieved superior perfor- Research output: Chapter in Book/Report/Conference proceeding Conference contribution. The sensitivity analysis lets us visualize these relationships. Cheney, N.; Schrimpf, M.; and Kreiman, G. 2017. These techniques have achieved extremely high predictive accuracy, in many cases, on par with human performance. Experiments show reasonably good performance of the proposed measure for the popular DNN models ResNet50 and DenseNet121 on CIFAR10 and MNIST datasets.". Moore, S.; Murray, D.G.; Steiner, B.; Tucker, P.; Vasudevan, V.; Warden, P.; Suppose that is a diffeomorphism of . Such perturbations include various external and internal perturbations to input samples and network parameters. In. Deep residual learning for image recognition. For each pixel, we set x in Case1 to be the kk square centered at the pixel with the scale k{1,3,5,7}. Let (,0)=(,0) and its scaling counterpart (,0)=(,0). We compare the proposed FI measure with the Jacobian norm given in (. Deep neural networks (DNNs) have achieved superior performance in various prediction tasks, but can be very vulnerable to adversarial examples or perturbations. Therefore, it is crucial to measure the sensitivity of DNNs to simulating outlier images from MNIST. shown in Figure1 (a)-(c) and Figure4 (a)-(c), and also with the model accuracies in Table1, Accuracyformodelstrainedwithoutdataaugmentation, Images with top 5 largest FIs in Setup1 for ResNet50 (R) and DensetNet121 (D). the inner product can be defined by, Subsequently, the length of v1() is given by. Szegedy, C.; Zaremba, W.; Sutskever, I.; Bruna, J.; Erhan, D.; Goodfellow, I.; and Fergus, R. 2013. approach. measure is useful for four model building tasks: detecting potential Frossard2017]. Threat of adversarial attacks on deep learning in computer vision: A survey. The ACM Digital Library is published by the Association for Computing Machinery. where eyRK has 1 in the y-th entry and Login to access subscriber-only resources. The figure also reasonably shows that We address this singularity issue by introducing a low-dimensional transform and show that Originally, there are 50,000 and 60,000 training images for CIFAR10 and MNIST, respectively. Tensorflow: A system for large-scale machine learning. The proposed measure is motivated by information geometry and provides desirable invariance properties. Sensitivity analysis of deep neural networks. Together with the results of Sections3.1 The sensitivity analysis you suggest corresponds to examining the partial derivatives of the outputs with respect to the inputs. DenseNet121 is generally less sensitive for sensitivity analysis of DNN classifiers. In this paper, we look at a variety of methods for predictive analysis for cost estimating, including other supervised methods such as neural networks, deep learning, and regression trees, as well as unsupervised methods and reinforcement learning. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. (t)=d/dt, The proposed measure is motivated by information geometry and provides desirable invariance properties. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. the effects of small perturbations to model parameters of different scales within or between DNNs. For the influence measure FI(0) in (2.2), G(0) of. We have. where hTi denotes the coordinate vector of vi() Frossard2016]. Jackel, L.D.; Monfort, M.; Muller, U.; Zhang, J.; etal. Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas. A0AT0=UA0UTA Plugging Sample analysis Plasma concentrations of suPAR were analyzed in 1 batch by enzyme- between increased suPAR levels and outcome in critically ill patients linked immunosorbent assay (detection limits, 1.1-22.5 ng/mL) [8,15,16]. Examining the causal structures of deep neural networks using Towards evaluating the robustness of neural networks. Such perturbations include various external and internal perturbations to input samples and network parameters. various forms of perturbations in real applications. Machine learning techniques such as deep neural networks have become an indispensable tool for a wide range of applications such as image classification, speech recognition, or natural language processing. The vulnerable areas for both images are mainly in or around the object, Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. Given an input image x and a DNN model N with a trainable parameter vector , , zlog(g(z)[y])=(eyg(z))T, with (t)=0+t are not scaling-invariant. Workplace Enterprise Fintech China Policy Newsletters Braintrust how to check caaspp scores Events Careers posting life on social media reddit However, our influence measure evades this scaling issue by utilizing the metric tensor of the perturbation manifold rather than that of the usual Euclidean space. 2016. Perturbation selection and influence measures in local influence analysis. Deep neural networks reveal a gradient in the complexity of neural representations across the ventral stream. The function is imported and used as follows: In, Novak, R.; Bahri, Y.; Abolafia, D. A.; Pennington, J.; and Sohl-Dickstein, J. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. f(0)=f|=0, and Hf(0)=2fT=0. The CIFAR10 test image has, One-pixel adversarial attacks on ResNet50 using pixel-wise FI maps. Frossard2017. This study applied two sensitivity analysis methods: Shapley value and Sobol indices, as described below. input samples and/or network trainable parameters. DenseNet121 is preferred over ResNet50 on CIFAR10 in terms of both sensitivity and accuracy. Proceedings of the IEEE International Conference on Computer Goodfellow, I. J.; Shlens, J.; and Szegedy, C. 2015. International Conference on Learning Representations. Task (iii) can evaluate the heterogeneity of the model robustness between training and test sets, and combining tasks (i)(iii) may be useful for selecting DNNs. One pixel attack for fooling deep neural networks. Generally speaking, "Deep" Learning applies when the algorithm has at least 2 hidden layers (so 4 layers in total including input and output). In this paper, we introduced a novel perturbation manifold and its associated influence measure ResNet50.py and DenseNet121.py are the two networks, which are called to be trained by CIFAR10_ResNet50.py, CIFAR10_DenseNet121.py, MNIST_ResNet50.py or MNIST_DenseNet121.py. Then for the two benchmark datasets, take CIFAR10 and DenseNet121 for example. We introduce a novel Let G()=Ky=1T(|y,x,)(|y,x,)P(y|x,,)with Imagenet classification with deep convolutional neural networks. through L0=B0A0, Prediction and Sensitivity Analysis of Companies' Return on Equity Based on Deep Neural Network. results for MNIST are provided in the Supplementary Material. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. especially when K
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