{"title": "Towards Understanding the Importance of Shortcut Connections in Residual Networks", "book": "Advances in Neural Information Processing Systems", "page_first": 7892, "page_last": 7902, "abstract": "Residual Network (ResNet) is undoubtedly a milestone in deep learning. \nResNet is equipped with shortcut connections between layers, and exhibits efficient training using simple first order algorithms. Despite of the great empirical success, the reason behind is far from being well understood. In this paper, we study a two-layer non-overlapping convolutional ResNet. Training such a network requires solving a non-convex optimization problem with a spurious local optimum. We show, however, that gradient descent combined with proper normalization, avoids being trapped by the spurious local optimum, and converges to a global optimum in polynomial time, when the weight of the first layer is initialized at 0, and that of the second layer is initialized arbitrarily in a ball. Numerical experiments are provided to support our theory.", "full_text": "Towards Understanding the Importance of Shortcut\n\nConnections in Residual Networks\n\nTianyi Liu\u2217\nGeorgia Tech\n\nMinshuo Chen\u2217\nGeorgia Tech\n\nMo Zhou\n\nDuke University\n\nSimon S. Du\n\nInstitute for Advanced Study\n\nEnlu Zhou\nGeorgia Tech\n\nTuo Zhao\nGeorgia Tech\n\nAbstract\n\nResidual Network (ResNet) is undoubtedly a milestone in deep learning. ResNet is\nequipped with shortcut connections between layers, and exhibits ef\ufb01cient training\nusing simple \ufb01rst order algorithms. Despite of the great empirical success, the\nreason behind is far from being well understood. In this paper, we study a two-layer\nnon-overlapping convolutional ResNet. Training such a network requires solving\na non-convex optimization problem with a spurious local optimum. We show,\nhowever, that gradient descent combined with proper normalization, avoids being\ntrapped by the spurious local optimum, and converges to a global optimum in\npolynomial time, when the weight of the \ufb01rst layer is initialized at 0, and that of the\nsecond layer is initialized arbitrarily in a ball. Numerical experiments are provided\nto support our theory.\n\nIntroduction\n\n1\nNeural Networks have revolutionized a variety of real world applications in the past few years, such\nas computer vision (Krizhevsky et al., 2012; Goodfellow et al., 2014; Long et al., 2015), natural\nlanguage processing (Graves et al., 2013; Bahdanau et al., 2014; Young et al., 2018), etc. Among\ndifferent types of networks, Residual Network (ResNet, He et al. (2016a)) is undoubted a milestone.\nResNet is equipped with shortcut connections, which skip layers in the forward step of an input.\nSimilar idea also appears in the Highway Networks (Srivastava et al., 2015), and further inspires\ndensely connected convolutional networks (Huang et al., 2017).\nResNet owes its great success to a surprisingly ef\ufb01cient training compared to the widely used\nfeedforward Convolutional Neural Networks (CNN, Krizhevsky et al. (2012)). Feedforward CNNs\nare seldomly used with more than 30 layers in the existing literature. There are experimental results\nsuggest that very deep feedforward CNNs are signi\ufb01cantly slow to train, and yield worse performance\nthan their shallow counterparts (He et al., 2016a). However, simple \ufb01rst order algorithms such as\nstochastic gradient descent and its variants are able to train ResNet with hundreds of layers, and\nachieve better performance than the state-of-the-art. For example, ResNet-152 (He et al., 2016a),\nconsisting of 152 layers, achieves a 19.38% top-1 error on ImageNet. He et al. (2016b) also\ndemonstrated a more aggressive ResNet-1001 on the CIFAR-10 data set with 1000 layers. It achieves\na 4.92% error \u2014 better than shallower ResNets such as ResNet-110.\nDespite the great success and popularity of ResNet, the reason why it can be ef\ufb01ciently trained\nis still largely unknown. One line of research empirically studies ResNet and provides intriguing\nobservations. Veit et al. (2016), for example, suggest that ResNet can be viewed as a collection\nof weakly dependent smaller networks of varying sizes. More interestingly, they reveal that these\n\n\u2217Equal contribution.\n\n33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada.\n\n\fsmaller networks alleviate the vanishing gradient problem. Balduzzi et al. (2017) further elaborate\non the vanishing gradient problem. They show that the gradient in ResNet only decays sublinearly\nin contrast to the exponential decay in feedforward neural networks. Recently, Li et al. (2018)\nvisualize the landscape of neural networks, and show that the shortcut connection yields a smoother\noptimization landscape. In spite of these empirical evidences, rigorous theoretical justi\ufb01cations are\nseriously lacking.\nAnother line of research theoretically investigates ResNet with simple network architectures. Hardt\nand Ma (2016) show that linear ResNet has no spurious local optima (local optima that yield larger\nobjective values than the global optima). Later, Li and Yuan (2017) study using Stochastic Gradient\nDescent (SGD) to train a two-layer ResNet with only one unknown layer. They show that the\noptimization landscape has no spurious local optima and saddle points. They also characterize the\nlocal convergence of SGD around the global optimum. These results, however, are often considered\nto be overoptimistic, due to the oversimpli\ufb01ed assumptions.\nTo better understand ResNet, we study a two-layer non-overlapping convolutional neural network,\nwhose optimization landscape contains a spurious local optimum. Such a network was \ufb01rst studied in\nDu et al. (2017). Speci\ufb01cally, we consider\n\ng(v, a, Z) = a(cid:62)\u03c3(cid:0)Z(cid:62)v(cid:1) ,\n\n(1)\nwhere Z \u2208 Rp\u00d7k is an input, a \u2208 Rk, v \u2208 Rp are the output weight and the convolutional weight,\nrespectively, and \u03c3 is the element-wise ReLU activation. Since the ReLU activation is positive\nhomogeneous, the weights a and v can arbitrarily scale with each other. Thus, we impose the\nassumption (cid:107)v(cid:107)2 = 1 to make the neural network identi\ufb01able. We further decompose v = 1/\u221ap + w\nwith 1 being a vector of 1\u2019s in Rp, and rewrite (1) as\n(2)\nHere 1/\u221ap represents the average pooling shortcut connection, which allows a direct interaction\nbetween the input Z and the output weight a.\nWe investigate the convergence of training ResNet by considering a realizable case. Speci\ufb01cally,\nthe training data is generated from a teacher network with true parameters a\u2217, v\u2217 with (cid:107)v\u2217(cid:107)2 = 1.\nWe aim to recover the teacher neural network using a student network de\ufb01ned in (2) by solving an\noptimization problem:\n\nf (w, a, Z) = a(cid:62)\u03c3(cid:0)Z(cid:62)(1/\u221ap + w)(cid:1) ,\n\n1\n2\n\nEZ [f (w, a, Z) \u2212 g(v\u2217, a\u2217, Z)]2 ,\n\n(3)\n\n((cid:98)w,(cid:98)a) = argmin\n\nw,a\n\nwhere Z is independent Gaussian input. Although largely simpli\ufb01ed, (3) is nonconvex and possesses\na nuisance \u2014 There exists a spurious local optimum (see an explicit characterization in Section 2).\nEarly work, Du et al. (2017), show that when the student network has the same architecture as the\nteacher network, GD with random initialization can be trapped in a spurious local optimum with a\nconstant probability2. A natural question here is\n\nDoes the shortcut connection ease the training?\n\nThis paper suggests a positive answer: When initialized with w = 0 and a arbitrarily in a ball,\nGD with proper normalization converges to a global optimum of (3) in polynomial time, under the\nassumption that (v\u2217)(cid:62)(1/\u221ap) is close to 1. Such an assumption requires that there exists a w\u2217\nof relatively small magnitude, such that v\u2217 = 1/\u221ap + w\u2217. This assumption is supported by both\nempirical and theoretical evidences. Speci\ufb01cally, the experiments in Li et al. (2016) and Yu et al.\n(2018), show that the weight in well-trained deep ResNet has a small magnitude, and the weight for\neach layer has vanishing norm as the depth tends to in\ufb01nity. Hardt and Ma (2016) suggest that, when\nusing linear ResNet to approximate linear transformations, the norm of the weight in each layer scales\nas O(1/D) with D being the depth. Bartlett et al. (2018) further show that deep nonlinear ResNet,\nwith the norm of the weight of order O(log D/D), is suf\ufb01cient to express differentiable functions\nunder certain regularity conditions. These results motivate us to assume w\u2217 is relatively small.\nOur analysis shows that the convergence of GD exhibits 2 stages. Speci\ufb01cally, our initialization\nguarantees w is suf\ufb01ciently away from the spurious local optimum. In the \ufb01rst stage, with proper step\n\n2The probability is bounded between 1/4 and 3/4. Numerical experiments show that this probability can be\n\nas bad as 1/2 with the worst con\ufb01guration of a, v.\n\n2\n\n\fFigure 2: Illustrative examples of the teacher and student networks with k = 3 and p = 4. BN notes\nbatch normalization.\n\nsizes, we show that the shortcut connection helps the algorithm avoid being attracted by the spurious\nlocal optima. Meanwhile, the shortcut connection guides the algorithm to evolve towards a global\noptimum. In the second stage, the algorithm enters the basin of attraction of the global optimum.\nWith properly chosen step sizes, w and a jointly converge to the global optimum.\nOur analysis thus explains why ResNet bene\ufb01ts training, when the weights are simply initialized at\nzero (Li et al., 2016), or using the Fixup initialization in Zhang et al. (2019). We remark that our\nchoice of step sizes is also related to learning rate warmup (Goyal et al., 2017), and other learning\nrate schemes for more ef\ufb01cient training of neural networks (Smith, 2017; Smith and Topin, 2018).\nWe refer readers to Section 5 for a more detailed discussion.\nNotations: Given a vector v = (v1, . . . , vm)(cid:62) \u2208 Rm, we denote the Euclidean norm (cid:107)v(cid:107)2\n2 = v(cid:62)v.\nGiven two vectors u, v \u2208 Rd, we denote the angle between them as \u2220(u, v) = arccos\n, and\n(cid:107)u(cid:107)2(cid:107)v(cid:107)2\nthe inner product as (cid:104)u, v(cid:105) = u(cid:62)v. We denote 1 \u2208 Rd as the vector of all the entries being 1. We\nalso denote B0(r) \u2208 Rd as the Euclidean ball centered at 0 with radius r.\n2 Model and Algorithm\nModel. We consider the realizable setting where the label is\ngenerated from a noiseless teacher network in the following form\n\nu(cid:62)v\n\ng(v\u2217, a\u2217, Z) =(cid:80)k\n\nj=1 a\u2217j \u03c3(cid:0)Z(cid:62)j v\u2217(cid:1) .\n\nHere v\u2217, a\u2217, Zj\u2019s are the true convolutional weight, true output\nweight, and input. \u03c3 denotes the element-wise ReLU activation.\nOur student network is de\ufb01ned in (2). For notational convenience,\nwe expand the second layer and rewrite (2) as\n\n(4)\n\nf (w, a, Z) =(cid:80)k\n\nj=1 aj\u03c3(cid:0)Z(cid:62)j (1/\u221ap + w)(cid:1) ,\n\n(5)\nwhere w \u2208 Rp, aj \u2208 R, and Zj \u2208 Rp for all j = 1, 2, . . . , k. We\nassume the input data Zj\u2019s are identically independently sampled\nfrom N (0, I). Note that the above network is not identi\ufb01able,\nbecause of the positive homogeneity of the ReLU function, that is\n1\u221ap + w and a can scale with each other by any positive constant without changing the output value.\nThus, to achieve identi\ufb01ability, instead of (5), we propose to train the following student network,\n\nFigure 1: The non-overlapping\ntwo layer residual network with\nnormalization layer.\n\n(6)\n\nf (w, a, Z) =(cid:80)k\n\nj=1 aj\u03c3(cid:16)Z(cid:62)j\n\n1/\u221ap+w\n\n(cid:107)1/\u221ap+w(cid:107)2(cid:17) .\n\nAn illustration of (6) is provided in Figure 1. An example of the teacher network (4) and the student\nnetwork (6) is shown in Figure 2.\nWe then recover (v\u2217, a\u2217) of our teacher network by solving a nonconvex optimization problem\n\nw,a L(w, a) =\nmin\n\n1\n2\n\nEZ[g(v\u2217, a\u2217, Z) \u2212 f (w, a, Z)]2.\n\n(7)\n\n3\n\nZ1(null)(null)(null)(null)Z2(null)(null)(null)(null)Z3(null)(null)(null)(null)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(w,a,Z)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AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=1ppAAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=1ppAAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=AAACFXicbVDLSsNAFJ3UV62vqEs3g0VwISURQZdFNy4r2Ac0oUwmk3boZCbOTIQS8hNu/BU3LhRxK7jzb5y0WdjWA8MczrmXe+8JEkaVdpwfq7Kyura+Ud2sbW3v7O7Z+wcdJVKJSRsLJmQvQIowyklbU81IL5EExQEj3WB8U/jdRyIVFfxeTxLix2jIaUQx0kYa2GdeJBHOvECwUE1i82VunmeeepB6Tk3yPB/YdafhTAGXiVuSOijRGtjfXihwGhOuMUNK9V0n0X6GpKaYkbzmpYokCI/RkPQN5Sgmys+mV+XwxCghjIQ0j2s4Vf92ZChWxXKmMkZ6pBa9QvzP66c6uvIzypNUE45ng6KUQS1gEREMqSRYs4khCEtqdoV4hExM2gRZMyG4iycvk855w3Ua7t1FvXldxlEFR+AYnAIXXIImuAUt0AYYPIEX8AberWfr1fqwPmelFavsOQRzsL5+Add0oSA=Z>11/pp+w||1/pp+w||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>21/pp+w||1/pp+w||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>31/pp+w||1/pp+w||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\u2713Z>11/pp+w||1/pp+w||2\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\u2713Z>21/pp+w||1/pp+w||2\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\u2713Z>31/pp+w||1/pp+w||2\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BNAAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2Nre2d4q7pb39g8Oj8vFJ26hUU9aiSijdDYlhgkvWstwK1k00I3EoWCec3Mz9zhPThiv5YKcJC2IykjzilFgntfthhBt3g3LFq3oL4HXi56QCOZqD8ld/qGgaM2mpIMb0fC+xQUa05VSwWamfGpYQOiEj1nNUkpiZIFtcO8MXThniSGlX0uKF+nsiI7Ex0zh0nTGxY7PqzcX/vF5qo+sg4zJJLZN0uShKBbYKz1/HQ64ZtWLqCKGau1sxHRNNqHUBlVwI/urL66Rdq/pe1b+vVeqNPI4inME5XIIPV1CHW2hCCyg8wjO8whtS6AW9o49lawHlM6fwB+jzB7LGjog=AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2Nre2d4q7pb39g8Oj8vFJ26hUU9aiSijdDYlhgkvWstwK1k00I3EoWCec3Mz9zhPThiv5YKcJC2IykjzilFgntfthhBt3g3LFq3oL4HXi56QCOZqD8ld/qGgaM2mpIMb0fC+xQUa05VSwWamfGpYQOiEj1nNUkpiZIFtcO8MXThniSGlX0uKF+nsiI7Ex0zh0nTGxY7PqzcX/vF5qo+sg4zJJLZN0uShKBbYKz1/HQ64ZtWLqCKGau1sxHRNNqHUBlVwI/urL66Rdq/pe1b+vVeqNPI4inME5XIIPV1CHW2hCCyg8wjO8whtS6AW9o49lawHlM6fwB+jzB7LGjog=AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2Nre2d4q7pb39g8Oj8vFJ26hUU9aiSijdDYlhgkvWstwK1k00I3EoWCec3Mz9zhPThiv5YKcJC2IykjzilFgntfthhBt3g3LFq3oL4HXi56QCOZqD8ld/qGgaM2mpIMb0fC+xQUa05VSwWamfGpYQOiEj1nNUkpiZIFtcO8MXThniSGlX0uKF+nsiI7Ex0zh0nTGxY7PqzcX/vF5qo+sg4zJJLZN0uShKBbYKz1/HQ64ZtWLqCKGau1sxHRNNqHUBlVwI/urL66Rdq/pe1b+vVeqNPI4inME5XIIPV1CHW2hCCyg8wjO8whtS6AW9o49lawHlM6fwB+jzB7LGjog=AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2Nre2d4q7pb39g8Oj8vFJ26hUU9aiSijdDYlhgkvWstwK1k00I3EoWCec3Mz9zhPThiv5YKcJC2IykjzilFgntfthhBt3g3LFq3oL4HXi56QCOZqD8ld/qGgaM2mpIMb0fC+xQUa05VSwWamfGpYQOiEj1nNUkpiZIFtcO8MXThniSGlX0uKF+nsiI7Ex0zh0nTGxY7PqzcX/vF5qo+sg4zJJLZN0uShKBbYKz1/HQ64ZtWLqCKGau1sxHRNNqHUBlVwI/urL66Rdq/pe1b+vVeqNPI4inME5XIIPV1CHW2hCCyg8wjO8whtS6AW9o49lawHlM6fwB+jzB7LGjog=BNAAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2Nre2d4q7pb39g8Oj8vFJ26hUU9aiSijdDYlhgkvWstwK1k00I3EoWCec3Mz9zhPThiv5YKcJC2IykjzilFgntfthhBt3g3LFq3oL4HXi56QCOZqD8ld/qGgaM2mpIMb0fC+xQUa05VSwWamfGpYQOiEj1nNUkpiZIFtcO8MXThniSGlX0uKF+nsiI7Ex0zh0nTGxY7PqzcX/vF5qo+sg4zJJLZN0uShKBbYKz1/HQ64ZtWLqCKGau1sxHRNNqHUBlVwI/urL66Rdq/pe1b+vVeqNPI4inME5XIIPV1CHW2hCCyg8wjO8whtS6AW9o49lawHlM6fwB+jzB7LGjog=AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2Nre2d4q7pb39g8Oj8vFJ26hUU9aiSijdDYlhgkvWstwK1k00I3EoWCec3Mz9zhPThiv5YKcJC2IykjzilFgntfthhBt3g3LFq3oL4HXi56QCOZqD8ld/qGgaM2mpIMb0fC+xQUa05VSwWamfGpYQOiEj1nNUkpiZIFtcO8MXThniSGlX0uKF+nsiI7Ex0zh0nTGxY7PqzcX/vF5qo+sg4zJJLZN0uShKBbYKz1/HQ64ZtWLqCKGau1sxHRNNqHUBlVwI/urL66Rdq/pe1b+vVeqNPI4inME5XIIPV1CHW2hCCyg8wjO8whtS6AW9o49lawHlM6fwB+jzB7LGjog=AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2Nre2d4q7pb39g8Oj8vFJ26hUU9aiSijdDYlhgkvWstwK1k00I3EoWCec3Mz9zhPThiv5YKcJC2IykjzilFgntfthhBt3g3LFq3oL4HXi56QCOZqD8ld/qGgaM2mpIMb0fC+xQUa05VSwWamfGpYQOiEj1nNUkpiZIFtcO8MXThniSGlX0uKF+nsiI7Ex0zh0nTGxY7PqzcX/vF5qo+sg4zJJLZN0uShKBbYKz1/HQ64ZtWLqCKGau1sxHRNNqHUBlVwI/urL66Rdq/pe1b+vVeqNPI4inME5XIIPV1CHW2hCCyg8wjO8whtS6AW9o49lawHlM6fwB+jzB7LGjog=AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqez2osdSL56kgv2AdinZNNvGZpMlyQpl6X/w4kERr/4fb/4b03YP2vpg4PHeDDPzwkRwYz3vGxU2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TAol5DPc+CtuXCjitjv/xkmaRW29MMzhnHu55x43ZFQqy/oxCmvrG5tbxe3Szu7e/oF5eNSSQSQwaeKABaLjIkkY5aSpqGKkEwqCfJeRtju+T/X2hAhJA/6opiFxfDTk1KMYKU31zathpecGbCCnvv7iSfJ8cblIoIzwkRq5XvyUnPfNslW1soKrwM5BGeTV6Juz3iDAkU+4wgxJ2bWtUDkxEopiRpJSL5IkRHiMhqSrIUc+kU6cHZbAM80MoBcI/biCGbs4ESNfpkZ1Z2pRLmsp+Z/WjZR358SUh5EiHM8XeRGDKoBpSnBABcGKTTVAWFDtFeIREggrnWVJh2Avn7wKWtdV26raDzflWj2PowhOwCmoABvcghqogwZoAgxewBv4AJ/Gq/FufBnf89aCkc8cgz9lzH4BiiOgtA==AAACGHicbVDLSsNAFJ3UV62vqEs3g0WoIjURQZcFN11WsA9sY5lMJ+3QySTMTAol5DPc+CtuXCjitjv/xkmaRW29MMzhnHu55x43ZFQqy/oxCmvrG5tbxe3Szu7e/oF5eNSSQSQwaeKABaLjIkkY5aSpqGKkEwqCfJeRtju+T/X2hAhJA/6opiFxfDTk1KMYKU31zathpecGbCCnvv7iSfJ8cblIoIzwkRq5XvyUnPfNslW1soKrwM5BGeTV6Juz3iDAkU+4wgxJ2bWtUDkxEopiRpJSL5IkRHiMhqSrIUc+kU6cHZbAM80MoBcI/biCGbs4ESNfpkZ1Z2pRLmsp+Z/WjZR358SUh5EiHM8XeRGDKoBpSnBABcGKTTVAWFDtFeIREggrnWVJh2Avn7wKWtdV26raDzflWj2PowhOwCmoABvcghqogwZoAgxewBv4AJ/Gq/FufBnf89aCkc8cgz9lzH4BiiOgtA==AAACGHicbVDLSsNAFJ3UV62vqEs3g0WoIjURQZcFN11WsA9sY5lMJ+3QySTMTAol5DPc+CtuXCjitjv/xkmaRW29MMzhnHu55x43ZFQqy/oxCmvrG5tbxe3Szu7e/oF5eNSSQSQwaeKABaLjIkkY5aSpqGKkEwqCfJeRtju+T/X2hAhJA/6opiFxfDTk1KMYKU31zathpecGbCCnvv7iSfJ8cblIoIzwkRq5XvyUnPfNslW1soKrwM5BGeTV6Juz3iDAkU+4wgxJ2bWtUDkxEopiRpJSL5IkRHiMhqSrIUc+kU6cHZbAM80MoBcI/biCGbs4ESNfpkZ1Z2pRLmsp+Z/WjZR358SUh5EiHM8XeRGDKoBpSnBABcGKTTVAWFDtFeIREggrnWVJh2Avn7wKWtdV26raDzflWj2PowhOwCmoABvcghqogwZoAgxewBv4AJ/Gq/FufBnf89aCkc8cgz9lzH4BiiOgtA==AAACGHicbVDLSsNAFJ3UV62vqEs3g0WoIjURQZcFN11WsA9sY5lMJ+3QySTMTAol5DPc+CtuXCjitjv/xkmaRW29MMzhnHu55x43ZFQqy/oxCmvrG5tbxe3Szu7e/oF5eNSSQSQwaeKABaLjIkkY5aSpqGKkEwqCfJeRtju+T/X2hAhJA/6opiFxfDTk1KMYKU31zathpecGbCCnvv7iSfJ8cblIoIzwkRq5XvyUnPfNslW1soKrwM5BGeTV6Juz3iDAkU+4wgxJ2bWtUDkxEopiRpJSL5IkRHiMhqSrIUc+kU6cHZbAM80MoBcI/biCGbs4ESNfpkZ1Z2pRLmsp+Z/WjZR358SUh5EiHM8XeRGDKoBpSnBABcGKTTVAWFDtFeIREggrnWVJh2Avn7wKWtdV26raDzflWj2PowhOwCmoABvcghqogwZoAgxewBv4AJ/Gq/FufBnf89aCkc8cgz9lzH4BiiOgtA==a1AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPBS48V7Qe0oUy2m3bpZhN2N0IJ/QlePCji1V/kzX/jps1BWx8MPN6bYWZekAiujet+O6WNza3tnfJuZW//4PCoenzS0XGqKGvTWMSqF6BmgkvWNtwI1ksUwygQrBtM73K/+8SU5rF8NLOE+RGOJQ85RWOlBxx6w2rNrbsLkHXiFaQGBVrD6tdgFNM0YtJQgVr3PTcxfobKcCrYvDJINUuQTnHM+pZKjJj2s8Wpc3JhlREJY2VLGrJQf09kGGk9iwLbGaGZ6FUvF//z+qkJb/2MyyQ1TNLlojAVxMQk/5uMuGLUiJklSBW3txI6QYXU2HQqNgRv9eV10rmqe27du7+uNZpFHGU4g3O4BA9uoAFNaEEbKIzhGV7hzRHOi/PufCxbS04xcwp/4Hz+AOpljY8=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPBS48V7Qe0oUy2m3bpZhN2N0IJ/QlePCji1V/kzX/jps1BWx8MPN6bYWZekAiujet+O6WNza3tnfJuZW//4PCoenzS0XGqKGvTWMSqF6BmgkvWNtwI1ksUwygQrBtM73K/+8SU5rF8NLOE+RGOJQ85RWOlBxx6w2rNrbsLkHXiFaQGBVrD6tdgFNM0YtJQgVr3PTcxfobKcCrYvDJINUuQTnHM+pZKjJj2s8Wpc3JhlREJY2VLGrJQf09kGGk9iwLbGaGZ6FUvF//z+qkJb/2MyyQ1TNLlojAVxMQk/5uMuGLUiJklSBW3txI6QYXU2HQqNgRv9eV10rmqe27du7+uNZpFHGU4g3O4BA9uoAFNaEEbKIzhGV7hzRHOi/PufCxbS04xcwp/4Hz+AOpljY8=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPBS48V7Qe0oUy2m3bpZhN2N0IJ/QlePCji1V/kzX/jps1BWx8MPN6bYWZekAiujet+O6WNza3tnfJuZW//4PCoenzS0XGqKGvTWMSqF6BmgkvWNtwI1ksUwygQrBtM73K/+8SU5rF8NLOE+RGOJQ85RWOlBxx6w2rNrbsLkHXiFaQGBVrD6tdgFNM0YtJQgVr3PTcxfobKcCrYvDJINUuQTnHM+pZKjJj2s8Wpc3JhlREJY2VLGrJQf09kGGk9iwLbGaGZ6FUvF//z+qkJb/2MyyQ1TNLlojAVxMQk/5uMuGLUiJklSBW3txI6QYXU2HQqNgRv9eV10rmqe27du7+uNZpFHGU4g3O4BA9uoAFNaEEbKIzhGV7hzRHOi/PufCxbS04xcwp/4Hz+AOpljY8=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPBS48V7Qe0oUy2m3bpZhN2N0IJ/QlePCji1V/kzX/jps1BWx8MPN6bYWZekAiujet+O6WNza3tnfJuZW//4PCoenzS0XGqKGvTWMSqF6BmgkvWNtwI1ksUwygQrBtM73K/+8SU5rF8NLOE+RGOJQ85RWOlBxx6w2rNrbsLkHXiFaQGBVrD6tdgFNM0YtJQgVr3PTcxfobKcCrYvDJINUuQTnHM+pZKjJj2s8Wpc3JhlREJY2VLGrJQf09kGGk9iwLbGaGZ6FUvF//z+qkJb/2MyyQ1TNLlojAVxMQk/5uMuGLUiJklSBW3txI6QYXU2HQqNgRv9eV10rmqe27du7+uNZpFHGU4g3O4BA9uoAFNaEEbKIzhGV7hzRHOi/PufCxbS04xcwp/4Hz+AOpljY8=a2AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKUI8FLz1WtB/QhrLZTtqlm03Y3Qgl9Cd48aCIV3+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RS2tnd294r7pYPDo+OT8ulZR8epYthmsYhVL6AaBZfYNtwI7CUKaRQI7AbTu4XffUKleSwfzSxBP6JjyUPOqLHSAx3WhuWKW3WXIJvEy0kFcrSG5a/BKGZphNIwQbXue25i/Iwqw5nAeWmQakwom9Ix9i2VNELtZ8tT5+TKKiMSxsqWNGSp/p7IaKT1LApsZ0TNRK97C/E/r5+a8NbPuExSg5KtFoWpICYmi7/JiCtkRswsoUxxeythE6ooMzadkg3BW395k3RqVc+tevc3lUYzj6MIF3AJ1+BBHRrQhBa0gcEYnuEV3hzhvDjvzseqteDkM+fwB87nD+vpjZA=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKUI8FLz1WtB/QhrLZTtqlm03Y3Qgl9Cd48aCIV3+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RS2tnd294r7pYPDo+OT8ulZR8epYthmsYhVL6AaBZfYNtwI7CUKaRQI7AbTu4XffUKleSwfzSxBP6JjyUPOqLHSAx3WhuWKW3WXIJvEy0kFcrSG5a/BKGZphNIwQbXue25i/Iwqw5nAeWmQakwom9Ix9i2VNELtZ8tT5+TKKiMSxsqWNGSp/p7IaKT1LApsZ0TNRK97C/E/r5+a8NbPuExSg5KtFoWpICYmi7/JiCtkRswsoUxxeythE6ooMzadkg3BW395k3RqVc+tevc3lUYzj6MIF3AJ1+BBHRrQhBa0gcEYnuEV3hzhvDjvzseqteDkM+fwB87nD+vpjZA=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKUI8FLz1WtB/QhrLZTtqlm03Y3Qgl9Cd48aCIV3+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RS2tnd294r7pYPDo+OT8ulZR8epYthmsYhVL6AaBZfYNtwI7CUKaRQI7AbTu4XffUKleSwfzSxBP6JjyUPOqLHSAx3WhuWKW3WXIJvEy0kFcrSG5a/BKGZphNIwQbXue25i/Iwqw5nAeWmQakwom9Ix9i2VNELtZ8tT5+TKKiMSxsqWNGSp/p7IaKT1LApsZ0TNRK97C/E/r5+a8NbPuExSg5KtFoWpICYmi7/JiCtkRswsoUxxeythE6ooMzadkg3BW395k3RqVc+tevc3lUYzj6MIF3AJ1+BBHRrQhBa0gcEYnuEV3hzhvDjvzseqteDkM+fwB87nD+vpjZA=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKUI8FLz1WtB/QhrLZTtqlm03Y3Qgl9Cd48aCIV3+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RS2tnd294r7pYPDo+OT8ulZR8epYthmsYhVL6AaBZfYNtwI7CUKaRQI7AbTu4XffUKleSwfzSxBP6JjyUPOqLHSAx3WhuWKW3WXIJvEy0kFcrSG5a/BKGZphNIwQbXue25i/Iwqw5nAeWmQakwom9Ix9i2VNELtZ8tT5+TKKiMSxsqWNGSp/p7IaKT1LApsZ0TNRK97C/E/r5+a8NbPuExSg5KtFoWpICYmi7/JiCtkRswsoUxxeythE6ooMzadkg3BW395k3RqVc+tevc3lUYzj6MIF3AJ1+BBHRrQhBa0gcEYnuEV3hzhvDjvzseqteDkM+fwB87nD+vpjZA=a3AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0m0oMeClx4r2g9oQ9lsJ+3SzSbsboQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJaPZpqgH9GR5CFn1FjpgQ6uB+WKW3UXIOvEy0kFcjQH5a/+MGZphNIwQbXueW5i/Iwqw5nAWamfakwom9AR9iyVNELtZ4tTZ+TCKkMSxsqWNGSh/p7IaKT1NApsZ0TNWK96c/E/r5ea8NbPuExSg5ItF4WpICYm87/JkCtkRkwtoUxxeythY6ooMzadkg3BW315nbSvqp5b9e5rlXojj6MIZ3AOl+DBDdShAU1oAYMRPMMrvDnCeXHenY9la8HJZ07hD5zPH+1tjZE=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0m0oMeClx4r2g9oQ9lsJ+3SzSbsboQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJaPZpqgH9GR5CFn1FjpgQ6uB+WKW3UXIOvEy0kFcjQH5a/+MGZphNIwQbXueW5i/Iwqw5nAWamfakwom9AR9iyVNELtZ4tTZ+TCKkMSxsqWNGSh/p7IaKT1NApsZ0TNWK96c/E/r5ea8NbPuExSg5ItF4WpICYm87/JkCtkRkwtoUxxeythY6ooMzadkg3BW315nbSvqp5b9e5rlXojj6MIZ3AOl+DBDdShAU1oAYMRPMMrvDnCeXHenY9la8HJZ07hD5zPH+1tjZE=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0m0oMeClx4r2g9oQ9lsJ+3SzSbsboQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJaPZpqgH9GR5CFn1FjpgQ6uB+WKW3UXIOvEy0kFcjQH5a/+MGZphNIwQbXueW5i/Iwqw5nAWamfakwom9AR9iyVNELtZ4tTZ+TCKkMSxsqWNGSh/p7IaKT1NApsZ0TNWK96c/E/r5ea8NbPuExSg5ItF4WpICYm87/JkCtkRkwtoUxxeythY6ooMzadkg3BW315nbSvqp5b9e5rlXojj6MIZ3AOl+DBDdShAU1oAYMRPMMrvDnCeXHenY9la8HJZ07hD5zPH+1tjZE=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0m0oMeClx4r2g9oQ9lsJ+3SzSbsboQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJaPZpqgH9GR5CFn1FjpgQ6uB+WKW3UXIOvEy0kFcjQH5a/+MGZphNIwQbXueW5i/Iwqw5nAWamfakwom9AR9iyVNELtZ4tTZ+TCKkMSxsqWNGSh/p7IaKT1NApsZ0TNWK96c/E/r5ea8NbPuExSg5ItF4WpICYm87/JkCtkRkwtoUxxeythY6ooMzadkg3BW315nbSvqp5b9e5rlXojj6MIZ3AOl+DBDdShAU1oAYMRPMMrvDnCeXHenY9la8HJZ07hD5zPH+1tjZE=(a).TeacherNetworkAAAB/XicbVDLSsNAFJ34rPUVHzs3g0Wom5B0o8uCG1dSpS9oQ5lMb9qhk0yYmSg1FH/FjQtF3Pof7vwbp20W2nrgwuGce7n3niDhTGnX/bZWVtfWNzYLW8Xtnd29ffvgsKlEKik0qOBCtgOigLMYGpppDu1EAokCDq1gdDX1W/cgFRNxXY8T8CMyiFnIKNFG6tnHZXLu4DoQOgSJb0A/CDnq2SXXcWfAy8TLSQnlqPXsr25f0DSCWFNOlOp4bqL9jEjNKIdJsZsqSAgdkQF0DI1JBMrPZtdP8JlR+jgU0lSs8Uz9PZGRSKlxFJjOiOihWvSm4n9eJ9XhpZ+xOEk1xHS+KEw51gJPo8B9JoFqPjaEUMnMrZgOiSRUm8CKJgRv8eVl0qw4nut4t5VS9S6Po4BO0CkqIw9doCq6RjXUQBQ9omf0it6sJ+vFerc+5q0rVj5zhP7A+vwB6B6URw==AAAB/XicbVDLSsNAFJ34rPUVHzs3g0Wom5B0o8uCG1dSpS9oQ5lMb9qhk0yYmSg1FH/FjQtF3Pof7vwbp20W2nrgwuGce7n3niDhTGnX/bZWVtfWNzYLW8Xtnd29ffvgsKlEKik0qOBCtgOigLMYGpppDu1EAokCDq1gdDX1W/cgFRNxXY8T8CMyiFnIKNFG6tnHZXLu4DoQOgSJb0A/CDnq2SXXcWfAy8TLSQnlqPXsr25f0DSCWFNOlOp4bqL9jEjNKIdJsZsqSAgdkQF0DI1JBMrPZtdP8JlR+jgU0lSs8Uz9PZGRSKlxFJjOiOihWvSm4n9eJ9XhpZ+xOEk1xHS+KEw51gJPo8B9JoFqPjaEUMnMrZgOiSRUm8CKJgRv8eVl0qw4nut4t5VS9S6Po4BO0CkqIw9doCq6RjXUQBQ9omf0it6sJ+vFerc+5q0rVj5zhP7A+vwB6B6URw==AAAB/XicbVDLSsNAFJ34rPUVHzs3g0Wom5B0o8uCG1dSpS9oQ5lMb9qhk0yYmSg1FH/FjQtF3Pof7vwbp20W2nrgwuGce7n3niDhTGnX/bZWVtfWNzYLW8Xtnd29ffvgsKlEKik0qOBCtgOigLMYGpppDu1EAokCDq1gdDX1W/cgFRNxXY8T8CMyiFnIKNFG6tnHZXLu4DoQOgSJb0A/CDnq2SXXcWfAy8TLSQnlqPXsr25f0DSCWFNOlOp4bqL9jEjNKIdJsZsqSAgdkQF0DI1JBMrPZtdP8JlR+jgU0lSs8Uz9PZGRSKlxFJjOiOihWvSm4n9eJ9XhpZ+xOEk1xHS+KEw51gJPo8B9JoFqPjaEUMnMrZgOiSRUm8CKJgRv8eVl0qw4nut4t5VS9S6Po4BO0CkqIw9doCq6RjXUQBQ9omf0it6sJ+vFerc+5q0rVj5zhP7A+vwB6B6URw==AAAB/XicbVDLSsNAFJ34rPUVHzs3g0Wom5B0o8uCG1dSpS9oQ5lMb9qhk0yYmSg1FH/FjQtF3Pof7vwbp20W2nrgwuGce7n3niDhTGnX/bZWVtfWNzYLW8Xtnd29ffvgsKlEKik0qOBCtgOigLMYGpppDu1EAokCDq1gdDX1W/cgFRNxXY8T8CMyiFnIKNFG6tnHZXLu4DoQOgSJb0A/CDnq2SXXcWfAy8TLSQnlqPXsr25f0DSCWFNOlOp4bqL9jEjNKIdJsZsqSAgdkQF0DI1JBMrPZtdP8JlR+jgU0lSs8Uz9PZGRSKlxFJjOiOihWvSm4n9eJ9XhpZ+xOEk1xHS+KEw51gJPo8B9JoFqPjaEUMnMrZgOiSRUm8CKJgRv8eVl0qw4nut4t5VS9S6Po4BO0CkqIw9doCq6RjXUQBQ9omf0it6sJ+vFerc+5q0rVj5zhP7A+vwB6B6URw==(b).StudentNetworkAAAB/XicbVC7TsMwFL3hWcorPDYWiwqpLFXSBcZKLEyoPPqQ2qhyHKe16sSR7YBKVPErLAwgxMp/sPE3uG0GaDmSpaNz7rWPj59wprTjfFtLyyura+uFjeLm1vbOrr2331QilYQ2iOBCtn2sKGcxbWimOW0nkuLI57TlDy8mfuueSsVEfKdHCfUi3I9ZyAjWRurZh2X/tIJudRrQWKMrqh+EHPbsklNxpkCLxM1JCXLUe/ZXNxAkjcwdhGOlOq6TaC/DUjPC6bjYTRVNMBniPu0YGuOIKi+bph+jE6MEKBTSHJNhqv7eyHCk1CjyzWSE9UDNexPxP6+T6vDcy1icpJrGZPZQmHKkBZpUgQImKdF8ZAgmkpmsiAywxESbwoqmBHf+y4ukWa24TsW9rpZqN3kdBTiCYyiDC2dQg0uoQwMIPMIzvMKb9WS9WO/Wx2x0ycp3DuAPrM8fLOKUcw==AAAB/XicbVC7TsMwFL3hWcorPDYWiwqpLFXSBcZKLEyoPPqQ2qhyHKe16sSR7YBKVPErLAwgxMp/sPE3uG0GaDmSpaNz7rWPj59wprTjfFtLyyura+uFjeLm1vbOrr2331QilYQ2iOBCtn2sKGcxbWimOW0nkuLI57TlDy8mfuueSsVEfKdHCfUi3I9ZyAjWRurZh2X/tIJudRrQWKMrqh+EHPbsklNxpkCLxM1JCXLUe/ZXNxAkjcwdhGOlOq6TaC/DUjPC6bjYTRVNMBniPu0YGuOIKi+bph+jE6MEKBTSHJNhqv7eyHCk1CjyzWSE9UDNexPxP6+T6vDcy1icpJrGZPZQmHKkBZpUgQImKdF8ZAgmkpmsiAywxESbwoqmBHf+y4ukWa24TsW9rpZqN3kdBTiCYy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ZXVtfaO4Wdra3tndc/cPmlqmitAGkVyqdog15UzQhmGG03aiKI5DTlvh6Hrqtx6o0kyKezNOaDfGA8EiRrCxUs89DQgVhqosCCN0aSvxgKK6lHbeIAjQ3VAqQ1Iz6bllr+LNgJaJn5My5Kj33K+gL0ka2+mEY607vpeYboaVYYTTSSlINU0wGdl9HUsFjqnuZrODJujEKn0USWWfMGim/u7IcKz1OA5tZYzNUC96U/E/r5Oa6KKbMZGkhgoyXxSlHBmJpumgPlOUGD62BBPF7F8RGWKFiY1Il2wI/uLJy6RZrfhexb+tlmtXeRxFOIJjOAMfzqEGN1CHBhB4hGd4hTfnyXlx3p2PeWnByXsO4Q+czx8BNJ0vv\u21e41AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=v\u21e42AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==v\u21e43AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=v\u21e44AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=v\u21e41AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=v\u21e42AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==v\u21e43AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=v\u21e44AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5JIQY8FLz1WMG2hjWWznbRLN5uwuymU0t/gxYMiXv1B3vw3btsctPXBwOO9GWbmhang2rjut7OxubW9s1vYK+4fHB4dl05OmzrJFEOfJSJR7ZBqFFyib7gR2E4V0jgU2ApH93O/NUaleSIfzSTFIKYDySPOqLGSP+5Vn657pbJbcRcg68TLSRlyNHqlr24/YVmM0jBBte54bmqCKVWGM4GzYjfTmFI2ogPsWCppjDqYLo6dkUur9EmUKFvSkIX6e2JKY60ncWg7Y2qGetWbi/95ncxEd8GUyzQzKNlyUZQJYhIy/5z0uUJmxMQSyhS3txI2pIoyY/Mp2hC81ZfXSfOm4rkV76FartXzOApwDhdwBR7cQg3q0AAfGHB4hld4c6Tz4rw7H8vWDSefOYM/cD5/AClvjkM=v\u21e41AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBZBPJREBD0WvPRYwbSFNpbNdtou3WzC7qZQQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZFyaCa+O6305hY3Nre6e4W9rbPzg8Kh+fNHWcKoY+i0Ws2iHVKLhE33AjsJ0opFEosBWO7+d+a4JK81g+mmmCQUSHkg84o8ZK/qTnPV31yhW36i5A1omXkwrkaPTKX91+zNIIpWGCat3x3MQEGVWGM4GzUjfVmFA2pkPsWCpphDrIFsfOyIVV+mQQK1vSkIX6eyKjkdbTKLSdETUjverNxf+8TmoGd0HGZZIalGy5aJAKYmIy/5z0uUJmxNQSyhS3txI2oooyY/Mp2RC81ZfXSfO66rlV7+GmUqvncRThDM7hEjy4hRrUoQE+MODwDK/w5kjnxXl3PpatBSefOYU/cD5/ACTdjkA=v\u21e42AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5IUQY8FLz1WsB/QxrLZbtqlm03YnRRK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzgkQKg6777Wxsbm3v7Bb2ivsHh0fHpZPTlolTzXiTxTLWnYAaLoXiTRQoeSfRnEaB5O1gfD/32xOujYjVI04T7kd0qEQoGEUrNSf96tN1v1R2K+4CZJ14OSlDjka/9NUbxCyNuEImqTFdz03Qz6hGwSSfFXup4QllYzrkXUsVjbjxs8WxM3JplQEJY21LIVmovycyGhkzjQLbGVEcmVVvLv7ndVMM7/xMqCRFrthyUZhKgjGZf04GQnOGcmoJZVrYWwkbUU0Z2nyKNgRv9eV10qpWPLfiPdyUa/U8jgKcwwVcgQe3UIM6NKAJDAQ8wyu8Ocp5cd6dj2XrhpPPnMEfOJ8/JmOOQQ==v\u21e43AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr9EiUKFvSkLn6e2JCY63HcWg7Y2oGetmbif957cxEd8GEyzQzKNliUZQJYhIy+5z0uEJmxNgSyhS3txI2oIoyY/Mp2hC85ZdXSeOq4rkV7+GmXK3lcRTgFM7gAjy4hSrUoA4+MODwDK/w5kjnxXl3Phata04+cwJ/4Hz+ACfpjkI=AAAB7HicbVBNS8NAEJ34WetX1aOXxSKIh5KooMeClx4rmLbQxrLZTtqlm03Y3RRK6W/w4kERr/4gb/4bt20O2vpg4PHeDDPzwlRwbVz321lb39jc2i7sFHf39g8OS0fHDZ1kiqHPEpGoVkg1Ci7RN9wIbKUKaRwKbIbD+5nfHKHSPJGPZpxiENO+5BFn1FjJH3Wvny67pbJbcecgq8TLSRly1Lulr04vYVmM0jBBtW57bmqCCVWGM4HTYifTmFI2pH1sWyppjDqYzI+dknOr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NormLayerReLUwAAAB6HicbVDLTgJBEOzFF+IL9ehlIjHxRHbRRI9ELx4hkUcCGzI79MLI7OxmZlZDCF/gxYPGePWTvPk3DrAHBSvppFLVne6uIBFcG9f9dnJr6xubW/ntws7u3v5B8fCoqeNUMWywWMSqHVCNgktsGG4EthOFNAoEtoLR7cxvPaLSPJb3ZpygH9GB5CFn1Fip/tQrltyyOwdZJV5GSpCh1it+dfsxSyOUhgmqdcdzE+NPqDKcCZwWuqnGhLIRHWDHUkkj1P5kfuiUnFmlT8JY2ZKGzNXfExMaaT2OAtsZUTPUy95M/M/rpCa89idcJqlByRaLwlQQE5PZ16TPFTIjxpZQpri9lbAhVZQZm03BhuAtv7xKmpWyd1Gu1C9L1ZssjjycwCmcgwdXUIU7qEEDGCA8wyu8OQ/Oi/PufCxac042cwx/4Hz+AOYDjP8=aAAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJu2XK27VnYOsEi8nFcjR6Je/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/ND52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasJrP+MySQ1KtlgUpoKYmMy+JgOukBkxsYQyxe2thI2ooszYbEo2BG/55VXSrlW9i2qteVmp3+RxFOEETuEcPLiCOtxBA1rAAOEZXuHNeXRenHfnY9FacPKZY/gD5/MHxKuM6Q==yAAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOl5qRfrrhVdw6ySrycVCBHo1/+6g1ilkYoDRNU667nJsbPqDKcCZyWeqnGhLIxHWLXUkkj1H42P3RKzqwyIGGsbElD5urviYxGWk+iwHZG1Iz0sjcT//O6qQmv/YzLJDUo2WJRmApiYjL7mgy4QmbExBLKFLe3EjaiijJjsynZELzll1dJu1b1Lqq15mWlfpPHUYQTOIVz8OAK6nAHDWgBA4RneIU359F5cd6dj0VrwclnjuEPnM8f6QuNAQ==\fRecall that we assume (cid:107)v\u2217(cid:107)2 = 1. One can easily verify that (7) has global optima and spurious local\noptima. The characterization is analogous to Du et al. (2017), although the objective is different.\nProposition 1. For any constant \u03b1 > 0, (w, a) is a global optimum of (7), if 1/\u221ap + w = \u03b1v\u2217 and\na = a\u2217; (w, a) is a spurious local optimum of (7), if 1/\u221ap + w = \u2212\u03b1v\u2217 and a = (11(cid:62) + (\u03c0 \u2212\n1)I)\u22121(11(cid:62) \u2212 I)a\u2217.\nThe proof is adapted from Du et al. (2017), and the details are provided in Appendix B.1.\nNow we formalize the assumption on v\u2217 in Section 1, which is supported by the theoretical and\nempirical evidence in Li et al. (2016); Yu et al. (2018); Hardt and Ma (2016); Bartlett et al. (2018).\nAssumption 1 (Shortcut Prior). There exists a w\u2217 with (cid:107)w\u2217(cid:107)2 \u2264 1, such that v\u2217 = w\u2217 + 1/\u221ap.\nAssumption 1 implies (1/\u221ap)(cid:62)v\u2217 \u2265 1/2. We remark that our analysis actually applies to any w\u2217\nsatisfying (cid:107)w\u2217(cid:107)2 \u2264 c for any positive constant c \u2208 (0,\u221a2). Here we consider (cid:107)w\u2217(cid:107)2 \u2264 1 to ease the\npresentation. Throughout the rest of the paper, we assume this assumption holds true.\n\nGD with Normalization. We solve the optimization problem (7) by gradient descent. Speci\ufb01cally,\nat the (t + 1)-th iteration, we compute\n\nwt+1 =\n\n(cid:101)wt+1 = wt \u2212 \u03b7w\u2207wL(wt, at),\n1/\u221ap + (cid:101)wt+1\n(cid:107)1/\u221ap + (cid:101)wt+1(cid:107)2 \u2212\n\nat+1 = at \u2212 \u03b7a\u2207aL(wt, at).\n\n1\n\u221ap\n\n,\n\n(8)\n\nNote that we normalize 1/\u221ap + w in (8), which essentially guarantees Var(cid:0)Z(cid:62)j (1/\u221ap + wt+1)(cid:1) =\n1. As Zj is sampled from N (0, I), we further have E(cid:0)Z(cid:62)j (1/\u221ap + wt+1)(cid:1) = 0. The normalization\nstep in (8) can be viewed as a population version of the widely used batch normalization trick to\naccelerate the training of neural networks (Ioffe and Szegedy, 2015). Moreover, (7) has one unique\noptimal solution under such a normalization. Speci\ufb01cally, (w\u2217, a\u2217) is the unique global optimum,\nand ( \u00afw, \u00afa) is the only spurious local optimum along the solution path, where \u00afw = \u2212(1/\u221ap) \u2212 v\u2217\nand \u00afa = (11(cid:62) + (\u03c0 \u2212 1)I)\u22121(11(cid:62) \u2212 I)a\u2217.\nWe initialize our algorithm at (w0, a0) satisfy-\ning: w0 = 0 and a0 \u2208 B0(|1(cid:62)a\u2217|/\u221ak). We set\na0 with a magnitude of O(1/\u221ak) to match com-\nmon initialization techniques (Glorot and Ben-\ngio, 2010; LeCun et al., 2012; He et al., 2015).\nWe highlight that our algorithm starts with an\narbitrary initialization on a, which is different\nfrom random initialization. The step sizes \u03b7a\nand \u03b7w will be speci\ufb01ed later in our analysis.\n3 Convergence Analysis\nWe characterize the algorithmic behavior of the\ngradient descent algorithm. Our analysis shows\nthat under Assumption 1, the convergence of\nGD exhibits two stages. In the \ufb01rst stage, the\nalgorithm avoids being trapped by the spurious\nlocal optimum. Given the algorithm is suf\ufb01-\nciently away from the spurious local optima, the\nalgorithm enters the basin of attraction of the\nglobal optimum and \ufb01nally converge to it.\nTo present our main result, we begin with some notations. Denote\n\u03c6t = \u2220(1/\u221ap + wt, 1/\u221ap + w\u2217)\n\nFigure 3: The left panel shows random initializa-\ntion on feedforward CNN can be trapped in the\nspurious local optimum with probability at least\n1/4 (Du et al., 2017). The right panel demonstrates:\n1). Under the shortcut prior, our initialization of\n(w, a) avoids starting near the spurious local opti-\nmum; 2). Convergence of GD exhibits two stages\n(I. improvement of a and avoid being attracted by\n( \u00afw, \u00afa) II. joint convergence).\n\nas the angle between 1/\u221ap + wt and the ground truth at the t-th iteration. Throughout the rest of\n), and\n\nthe paper, we assume (cid:107)a\u2217(cid:107)2 is a constant. The notation (cid:101)O(\u00b7) hides poly((cid:107)a\u2217(cid:107)2), poly(\npolylog((cid:107)a\u2217(cid:107)2) factors. Then we state the convergence of GD in the following theorem.\n\n(cid:107)a\u2217(cid:107)2\n\n1\n\n4\n\n(v\u21e4,a\u21e4)AAAB/3icbVBLSwMxGMzWV62vVcGLl2ARapGyK4Iei148VrAPaLclm822odlkSbKFsvbgX/HiQRGv/g1v/hvTdg/aOhAyzHwfmYwfM6q043xbuZXVtfWN/GZha3tnd8/eP2gokUhM6lgwIVs+UoRRTuqaakZasSQo8hlp+sPbqd8cEamo4A96HBMvQn1OQ4qRNlLPPur4ggVqHJkrLY265XPULZ9NenbRqTgzwGXiZqQIMtR69lcnEDiJCNeYIaXarhNrL0VSU8zIpNBJFIkRHqI+aRvKUUSUl87yT+CpUQIYCmkO13Cm/t5IUaSmEc1khPRALXpT8T+vnejw2kspjxNNOJ4/FCYMagGnZcCASoI1GxuCsKQmK8QDJBHWprKCKcFd/PIyaVxUXKfi3l8WqzdZHXlwDE5ACbjgClTBHaiBOsDgETyDV/BmPVkv1rv1MR/NWdnOIfgD6/MHEpKVdg==AAAB/3icbVBLSwMxGMzWV62vVcGLl2ARapGyK4Iei148VrAPaLclm822odlkSbKFsvbgX/HiQRGv/g1v/hvTdg/aOhAyzHwfmYwfM6q043xbuZXVtfWN/GZha3tnd8/eP2gokUhM6lgwIVs+UoRRTuqaakZasSQo8hlp+sPbqd8cEamo4A96HBMvQn1OQ4qRNlLPPur4ggVqHJkrLY265XPULZ9NenbRqTgzwGXiZqQIMtR69lcnEDiJCNeYIaXarhNrL0VSU8zIpNBJFIkRHqI+aRvKUUSUl87yT+CpUQIYCmkO13Cm/t5IUaSmEc1khPRALXpT8T+vnejw2kspjxNNOJ4/FCYMagGnZcCASoI1GxuCsKQmK8QDJBHWprKCKcFd/PIyaVxUXKfi3l8WqzdZHXlwDE5ACbjgClTBHaiBOsDgETyDV/BmPVkv1rv1MR/NWdnOIfgD6/MHEpKVdg==AAAB/3icbVBLSwMxGMzWV62vVcGLl2ARapGyK4Iei148VrAPaLclm822odlkSbKFsvbgX/HiQRGv/g1v/hvTdg/aOhAyzHwfmYwfM6q043xbuZXVtfWN/GZha3tnd8/eP2gokUhM6lgwIVs+UoRRTuqaakZasSQo8hlp+sPbqd8cEamo4A96HBMvQn1OQ4qRNlLPPur4ggVqHJkrLY265XPULZ9NenbRqTgzwGXiZqQIMtR69lcnEDiJCNeYIaXarhNrL0VSU8zIpNBJFIkRHqI+aRvKUUSUl87yT+CpUQIYCmkO13Cm/t5IUaSmEc1khPRALXpT8T+vnejw2kspjxNNOJ4/FCYMagGnZcCASoI1GxuCsKQmK8QDJBHWprKCKcFd/PIyaVxUXKfi3l8WqzdZHXlwDE5ACbjgClTBHaiBOsDgETyDV/BmPVkv1rv1MR/NWdnOIfgD6/MHEpKVdg==AAAB/3icbVBLSwMxGMzWV62vVcGLl2ARapGyK4Iei148VrAPaLclm822odlkSbKFsvbgX/HiQRGv/g1v/hvTdg/aOhAyzHwfmYwfM6q043xbuZXVtfWN/GZha3tnd8/eP2gokUhM6lgwIVs+UoRRTuqaakZasSQo8hlp+sPbqd8cEamo4A96HBMvQn1OQ4qRNlLPPur4ggVqHJkrLY265XPULZ9NenbRqTgzwGXiZqQIMtR69lcnEDiJCNeYIaXarhNrL0VSU8zIpNBJFIkRHqI+aRvKUUSUl87yT+CpUQIYCmkO13Cm/t5IUaSmEc1khPRALXpT8T+vnejw2kspjxNNOJ4/FCYMagGnZcCASoI1GxuCsKQmK8QDJBHWprKCKcFd/PIyaVxUXKfi3l8WqzdZHXlwDE5ACbjgClTBHaiBOsDgETyDV/BmPVkv1rv1MR/NWdnOIfgD6/MHEpKVdg==(\u00afv,\u00afa)AAACB3icbVDLSsNAFJ3UV62vqEtBBotQQUoigi6LblxWsA9oQplMJu3QSSbMTAolZOfGX3HjQhG3/oI7/8ZJmoW2Hhju4Zx7mXuPFzMqlWV9G5WV1bX1jepmbWt7Z3fP3D/oSp4ITDqYMy76HpKE0Yh0FFWM9GNBUOgx0vMmt7nfmxIhKY8e1CwmbohGEQ0oRkpLQ/PY8Tjz5SzUJW04HhLpNDsvKsrOsqFZt5pWAbhM7JLUQYn20PxyfI6TkEQKMyTlwLZi5aZIKIoZyWpOIkmM8ASNyEDTCIVEumlxRwZPteLDgAv9IgUL9fdEikKZr6o7Q6TGctHLxf+8QaKCazelUZwoEuH5R0HCoOIwDwX6VBCs2EwThAXVu0I8RgJhpaOr6RDsxZOXSfeiaVtN+/6y3rop46iCI3ACGsAGV6AF7kAbdAAGj+AZvII348l4Md6Nj3lrxShnDsEfGJ8/pDiZyA==AAACB3icbVDLSsNAFJ3UV62vqEtBBotQQUoigi6LblxWsA9oQplMJu3QSSbMTAolZOfGX3HjQhG3/oI7/8ZJmoW2Hhju4Zx7mXuPFzMqlWV9G5WV1bX1jepmbWt7Z3fP3D/oSp4ITDqYMy76HpKE0Yh0FFWM9GNBUOgx0vMmt7nfmxIhKY8e1CwmbohGEQ0oRkpLQ/PY8Tjz5SzUJW04HhLpNDsvKsrOsqFZt5pWAbhM7JLUQYn20PxyfI6TkEQKMyTlwLZi5aZIKIoZyWpOIkmM8ASNyEDTCIVEumlxRwZPteLDgAv9IgUL9fdEikKZr6o7Q6TGctHLxf+8QaKCazelUZwoEuH5R0HCoOIwDwX6VBCs2EwThAXVu0I8RgJhpaOr6RDsxZOXSfeiaVtN+/6y3rop46iCI3ACGsAGV6AF7kAbdAAGj+AZvII348l4Md6Nj3lrxShnDsEfGJ8/pDiZyA==AAACB3icbVDLSsNAFJ3UV62vqEtBBotQQUoigi6LblxWsA9oQplMJu3QSSbMTAolZOfGX3HjQhG3/oI7/8ZJmoW2Hhju4Zx7mXuPFzMqlWV9G5WV1bX1jepmbWt7Z3fP3D/oSp4ITDqYMy76HpKE0Yh0FFWM9GNBUOgx0vMmt7nfmxIhKY8e1CwmbohGEQ0oRkpLQ/PY8Tjz5SzUJW04HhLpNDsvKsrOsqFZt5pWAbhM7JLUQYn20PxyfI6TkEQKMyTlwLZi5aZIKIoZyWpOIkmM8ASNyEDTCIVEumlxRwZPteLDgAv9IgUL9fdEikKZr6o7Q6TGctHLxf+8QaKCazelUZwoEuH5R0HCoOIwDwX6VBCs2EwThAXVu0I8RgJhpaOr6RDsxZOXSfeiaVtN+/6y3rop46iCI3ACGsAGV6AF7kAbdAAGj+AZvII348l4Md6Nj3lrxShnDsEfGJ8/pDiZyA==AAACB3icbVDLSsNAFJ3UV62vqEtBBotQQUoigi6LblxWsA9oQplMJu3QSSbMTAolZOfGX3HjQhG3/oI7/8ZJmoW2Hhju4Zx7mXuPFzMqlWV9G5WV1bX1jepmbWt7Z3fP3D/oSp4ITDqYMy76HpKE0Yh0FFWM9GNBUOgx0vMmt7nfmxIhKY8e1CwmbohGEQ0oRkpLQ/PY8Tjz5SzUJW04HhLpNDsvKsrOsqFZt5pWAbhM7JLUQYn20PxyfI6TkEQKMyTlwLZi5aZIKIoZyWpOIkmM8ASNyEDTCIVEumlxRwZPteLDgAv9IgUL9fdEikKZr6o7Q6TGctHLxf+8QaKCazelUZwoEuH5R0HCoOIwDwX6VBCs2EwThAXVu0I8RgJhpaOr6RDsxZOXSfeiaVtN+/6y3rop46iCI3ACGsAGV6AF7kAbdAAGj+AZvII348l4Md6Nj3lrxShnDsEfGJ8/pDiZyA==a>a\u21e4AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw==AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw==AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw==AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw===\\(v,v\u21e4)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AAAB/XicbVBNS8NAEJ34WWvV6NWDi0WoIiXxohdB8OKxgv2AJpbNZtMu3WzC7qZQQo9e/CtePCji3/Dmv3HT9qCtD5Z5vDfDzrwg5Uxpx/m2VlbX1jc2S1vl7crO7p69X2mpJJOENknCE9kJsKKcCdrUTHPaSSXFccBpOxjeFn57RKViiXjQ45T6Me4LFjGCtZF69pEXJDxU49iU3EsH7NrDos9pbXQ+ejw7nfTsqlN3pkDLxJ2TKszR6NlfXpiQLKZCE46V6rpOqv0cS80Ip5OylymaYjLEfdo1VOCYKj+fHjJBJ0YJUZRI84RGU/X3RI5jVexqOmOsB2rRK8T/vG6moys/ZyLNNBVk9lGUcaQTVKSCQiYp0XxsCCaSmV0RGWCJiTbZlU0I7uLJy6R1UXedunvvQAkO4Rhq4MIl3MAdNKAJBJ7gBd7g3Xq2Xq2PWVwr1jy3A/gD6/MH5hqYJw==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AAAB/XicbVBNS8NAEJ34WWvV6NWDi0WoIiXxohdB8OKxgv2AJpbNZtMu3WzC7qZQQo9e/CtePCji3/Dmv3HT9qCtD5Z5vDfDzrwg5Uxpx/m2VlbX1jc2S1vl7crO7p69X2mpJJOENknCE9kJsKKcCdrUTHPaSSXFccBpOxjeFn57RKViiXjQ45T6Me4LFjGCtZF69pEXJDxU49iU3EsH7NrDos9pbXQ+ejw7nfTsqlN3pkDLxJ2TKszR6NlfXpiQLKZCE46V6rpOqv0cS80Ip5OylymaYjLEfdo1VOCYKj+fHjJBJ0YJUZRI84RGU/X3RI5jVexqOmOsB2rRK8T/vG6moys/ZyLNNBVk9lGUcaQTVKSCQiYp0XxsCCaSmV0RGWCJiTbZlU0I7uLJy6R1UXedunvvQAkO4Rhq4MIl3MAdNKAJBJ7gBd7g3Xq2Xq2PWVwr1jy3A/gD6/MH5hqYJw==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AAAB+XicbVBNT8JAEN3iF+JX1aOXjcTEE2m56JHoxSMmFkigIdtlCxu2u83uFCUN/8SLB43x6j/x5r9xgR4UfMkkL+/NZGZelApuwPO+ndLG5tb2Tnm3srd/cHjkHp+0jMo0ZQFVQulORAwTXLIAOAjWSTUjSSRYOxrfzv32hGnDlXyAacrChAwljzklYKW+6/aAPUEU54EcS/UoZ3236tW8BfA68QtSRQWafferN1A0S5gEKogxXd9LIcyJBk4Fm1V6mWEpoWMyZF1LJUmYCfPF5TN8YZUBjpW2JQEv1N8TOUmMmSaR7UwIjMyqNxf/87oZxNdhzmWaAZN0uSjOBAaF5zHgAdeMgphaQqjm9lZMR0QTCjasig3BX315nbTqNd+r+ff1auOmiKOMztA5ukQ+ukINdIeaKEAUTdAzekVvTu68OO/Ox7K15BQzp+gPnM8fWVyUGg==AAAB+XicbVBNT8JAEN3iF+JX1aOXjcTEE2m56JHoxSMmFkigIdtlCxu2u83uFCUN/8SLB43x6j/x5r9xgR4UfMkkL+/NZGZelApuwPO+ndLG5tb2Tnm3srd/cHjkHp+0jMo0ZQFVQulORAwTXLIAOAjWSTUjSSRYOxrfzv32hGnDlXyAacrChAwljzklYKW+6/aAPUEU54EcS/UoZ3236tW8BfA68QtSRQWafferN1A0S5gEKogxXd9LIcyJBk4Fm1V6mWEpoWMyZF1LJUmYCfPF5TN8YZUBjpW2JQEv1N8TOUmMmSaR7UwIjMyqNxf/87oZxNdhzmWaAZN0uSjOBAaF5zHgAdeMgphaQqjm9lZMR0QTCjasig3BX315nbTqNd+r+ff1auOmiKOMztA5ukQ+ukINdIeaKEAUTdAzekVvTu68OO/Ox7K15BQzp+gPnM8fWVyUGg==AAAB+XicbVBNT8JAEN3iF+JX1aOXjcTEE2m56JHoxSMmFkigIdtlCxu2u83uFCUN/8SLB43x6j/x5r9xgR4UfMkkL+/NZGZelApuwPO+ndLG5tb2Tnm3srd/cHjkHp+0jMo0ZQFVQulORAwTXLIAOAjWSTUjSSRYOxrfzv32hGnDlXyAacrChAwljzklYKW+6/aAPUEU54EcS/UoZ3236tW8BfA68QtSRQWafferN1A0S5gEKogxXd9LIcyJBk4Fm1V6mWEpoWMyZF1LJUmYCfPF5TN8YZUBjpW2JQEv1N8TOUmMmSaR7UwIjMyqNxf/87oZxNdhzmWaAZN0uSjOBAaF5zHgAdeMgphaQqjm9lZMR0QTCjasig3BX315nbTqNd+r+ff1auOmiKOMztA5ukQ+ukINdIeaKEAUTdAzekVvTu68OO/Ox7K15BQzp+gPnM8fWVyUGg==UnknownAAAB+XicbVBNT8JAEN3iF+JX1aOXjcTEE2m56JHoxSMmFkigIdtlCxu2u83uFCUN/8SLB43x6j/x5r9xgR4UfMkkL+/NZGZelApuwPO+ndLG5tb2Tnm3srd/cHjkHp+0jMo0ZQFVQulORAwTXLIAOAjWSTUjSSRYOxrfzv32hGnDlXyAacrChAwljzklYKW+6/aAPUEU54EcS/UoZ3236tW8BfA68QtSRQWafferN1A0S5gEKogxXd9LIcyJBk4Fm1V6mWEpoWMyZF1LJUmYCfPF5TN8YZUBjpW2JQEv1N8TOUmMmSaR7UwIjMyqNxf/87oZxNdhzmWaAZN0uSjOBAaF5zHgAdeMgphaQqjm9lZMR0QTCjasig3BX315nbTqNd+r+ff1auOmiKOMztA5ukQ+ukINdIeaKEAUTdAzekVvTu68OO/Ox7K15BQzp+gPnM8fWVyUGg==AAAB+XicbVBNT8JAEN3iF+JX1aOXjcTEE2m56JHoxSMmFkigIdtlCxu2u83uFCUN/8SLB43x6j/x5r9xgR4UfMkkL+/NZGZelApuwPO+ndLG5tb2Tnm3srd/cHjkHp+0jMo0ZQFVQulORAwTXLIAOAjWSTUjSSRYOxrfzv32hGnDlXyAacrChAwljzklYKW+6/aAPUEU54EcS/UoZ3236tW8BfA68QtSRQWafferN1A0S5gEKogxXd9LIcyJBk4Fm1V6mWEpoWMyZF1LJUmYCfPF5TN8YZUBjpW2JQEv1N8TOUmMmSaR7UwIjMyqNxf/87oZxNdhzmWaAZN0uSjOBAaF5zHgAdeMgphaQqjm9lZMR0QTCjasig3BX315nbTqNd+r+ff1auOmiKOMztA5ukQ+ukINdIeaKEAUTdAzekVvTu68OO/Ox7K15BQzp+gPnM8fWVyUGg==AAAB+XicbVBNT8JAEN3iF+JX1aOXjcTEE2m56JHoxSMmFkigIdtlCxu2u83uFCUN/8SLB43x6j/x5r9xgR4UfMkkL+/NZGZelApuwPO+ndLG5tb2Tnm3srd/cHjkHp+0jMo0ZQFVQulORAwTXLIAOAjWSTUjSSRYOxrfzv32hGnDlXyAacrChAwljzklYKW+6/aAPUEU54EcS/UoZ3236tW8BfA68QtSRQWafferN1A0S5gEKogxXd9LIcyJBk4Fm1V6mWEpoWMyZF1LJUmYCfPF5TN8YZUBjpW2JQEv1N8TOUmMmSaR7UwIjMyqNxf/87oZxNdhzmWaAZN0uSjOBAaF5zHgAdeMgphaQqjm9lZMR0QTCjasig3BX315nbTqNd+r+ff1auOmiKOMztA5ukQ+ukINdIeaKEAUTdAzekVvTu68OO/Ox7K15BQzp+gPnM8fWVyUGg==AAAB+XicbVBNT8JAEN3iF+JX1aOXjcTEE2m56JHoxSMmFkigIdtlCxu2u83uFCUN/8SLB43x6j/x5r9xgR4UfMkkL+/NZGZelApuwPO+ndLG5tb2Tnm3srd/cHjkHp+0jMo0ZQFVQulORAwTXLIAOAjWSTUjSSRYOxrfzv32hGnDlXyAacrChAwljzklYKW+6/aAPUEU54EcS/UoZ3236tW8BfA68QtSRQWafferN1A0S5gEKogxXd9LIcyJBk4Fm1V6mWEpoWMyZF1LJUmYCfPF5TN8YZUBjpW2JQEv1N8TOUmMmSaR7UwIjMyqNxf/87oZxNdhzmWaAZN0uSjOBAaF5zHgAdeMgphaQqjm9lZMR0QTCjasig3BX315nbTqNd+r+ff1auOmiKOMztA5ukQ+ukINdIeaKEAUTdAzekVvTu68OO/Ox7K15BQzp+gPnM8fWVyUGg==ConvergeAAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLjBVdGItEH1IbVY7rtFYdO7JvUKuov8LCAEKs/Agbf4PTZoCWI1k6Oudc+/qEieAGPO/b2dre2d3bLx2UD4+OT07ds0rHqFRT1qZKKN0LiWGCS9YGDoL1Es1IHArWDafN3O8+MW24ko8wT1gQk7HkEacErDR0KwNgMwijrKmkzY3Zojx0q17NWwJvEr8gVVSgNXS/BiNF05hJoIIY0/e9BIKMaOBU2AsHqWEJoVMyZn1LJYmZCbLl7gt8ZZURjpS2RwJeqr8nMhIbM49Dm4wJTMy6l4v/ef0Uotsg4zJJgUm6eihKBQaF8yLwiGtGQcwtIVRzuyumE6IJBVtXXoK//uVN0qnXfK/mP9SrjbuijhK6QJfoGvnoBjXQPWqhNqJohp7RK3pzFs6L8+58rKJbTjFzjv7A+fwBLrqUgQ==AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLjBVdGItEH1IbVY7rtFYdO7JvUKuov8LCAEKs/Agbf4PTZoCWI1k6Oudc+/qEieAGPO/b2dre2d3bLx2UD4+OT07ds0rHqFRT1qZKKN0LiWGCS9YGDoL1Es1IHArWDafN3O8+MW24ko8wT1gQk7HkEacErDR0KwNgMwijrKmkzY3Zojx0q17NWwJvEr8gVVSgNXS/BiNF05hJoIIY0/e9BIKMaOBU2AsHqWEJoVMyZn1LJYmZCbLl7gt8ZZURjpS2RwJeqr8nMhIbM49Dm4wJTMy6l4v/ef0Uotsg4zJJgUm6eihKBQaF8yLwiGtGQcwtIVRzuyumE6IJBVtXXoK//uVN0qnXfK/mP9SrjbuijhK6QJfoGvnoBjXQPWqhNqJohp7RK3pzFs6L8+58rKJbTjFzjv7A+fwBLrqUgQ==AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLjBVdGItEH1IbVY7rtFYdO7JvUKuov8LCAEKs/Agbf4PTZoCWI1k6Oudc+/qEieAGPO/b2dre2d3bLx2UD4+OT07ds0rHqFRT1qZKKN0LiWGCS9YGDoL1Es1IHArWDafN3O8+MW24ko8wT1gQk7HkEacErDR0KwNgMwijrKmkzY3Zojx0q17NWwJvEr8gVVSgNXS/BiNF05hJoIIY0/e9BIKMaOBU2AsHqWEJoVMyZn1LJYmZCbLl7gt8ZZURjpS2RwJeqr8nMhIbM49Dm4wJTMy6l4v/ef0Uotsg4zJJgUm6eihKBQaF8yLwiGtGQcwtIVRzuyumE6IJBVtXXoK//uVN0qnXfK/mP9SrjbuijhK6QJfoGvnoBjXQPWqhNqJohp7RK3pzFs6L8+58rKJbTjFzjv7A+fwBLrqUgQ==AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLjBVdGItEH1IbVY7rtFYdO7JvUKuov8LCAEKs/Agbf4PTZoCWI1k6Oudc+/qEieAGPO/b2dre2d3bLx2UD4+OT07ds0rHqFRT1qZKKN0LiWGCS9YGDoL1Es1IHArWDafN3O8+MW24ko8wT1gQk7HkEacErDR0KwNgMwijrKmkzY3Zojx0q17NWwJvEr8gVVSgNXS/BiNF05hJoIIY0/e9BIKMaOBU2AsHqWEJoVMyZn1LJYmZCbLl7gt8ZZURjpS2RwJeqr8nMhIbM49Dm4wJTMy6l4v/ef0Uotsg4zJJgUm6eihKBQaF8yLwiGtGQcwtIVRzuyumE6IJBVtXXoK//uVN0qnXfK/mP9SrjbuijhK6QJfoGvnoBjXQPWqhNqJohp7RK3pzFs6L8+58rKJbTjFzjv7A+fwBLrqUgQ==TrappedAAAB+nicbVC7TsNAEDyHVwgvB0oaiwiJKrLTQBlBQxmkvKTEis7ndXLK+aG7NRCZfAoNBQjR8iV0/A3nxAUkjLTSaGZXuzteIrhC2/42ShubW9s75d3K3v7B4ZFZPe6qOJUMOiwWsex7VIHgEXSQo4B+IoGGnoCeN73J/d49SMXjqI2zBNyQjiMecEZRSyOzOkR4RC/I2pImCfjzysis2XV7AWudOAWpkQKtkfk19GOWhhAhE1SpgWMn6GZUImcC5pVhqiChbErHMNA0oiEoN1ucPrfOteJbQSx1RWgt1N8TGQ2VmoWe7gwpTtSql4v/eYMUgys341GSIkRsuShIhYWxledg+VwCQzHThDLJ9a0Wm1BJGeq08hCc1ZfXSbdRd+y6c9eoNa+LOMrklJyRC+KQS9Ikt6RFOoSRB/JMXsmb8WS8GO/Gx7K1ZBQzJ+QPjM8fY5KUDg==AAAB+nicbVC7TsNAEDyHVwgvB0oaiwiJKrLTQBlBQxmkvKTEis7ndXLK+aG7NRCZfAoNBQjR8iV0/A3nxAUkjLTSaGZXuzteIrhC2/42ShubW9s75d3K3v7B4ZFZPe6qOJUMOiwWsex7VIHgEXSQo4B+IoGGnoCeN73J/d49SMXjqI2zBNyQjiMecEZRSyOzOkR4RC/I2pImCfjzysis2XV7AWudOAWpkQKtkfk19GOWhhAhE1SpgWMn6GZUImcC5pVhqiChbErHMNA0oiEoN1ucPrfOteJbQSx1RWgt1N8TGQ2VmoWe7gwpTtSql4v/eYMUgys341GSIkRsuShIhYWxledg+VwCQzHThDLJ9a0Wm1BJGeq08hCc1ZfXSbdRd+y6c9eoNa+LOMrklJyRC+KQS9Ikt6RFOoSRB/JMXsmb8WS8GO/Gx7K1ZBQzJ+QPjM8fY5KUDg==AAAB+nicbVC7TsNAEDyHVwgvB0oaiwiJKrLTQBlBQxmkvKTEis7ndXLK+aG7NRCZfAoNBQjR8iV0/A3nxAUkjLTSaGZXuzteIrhC2/42ShubW9s75d3K3v7B4ZFZPe6qOJUMOiwWsex7VIHgEXSQo4B+IoGGnoCeN73J/d49SMXjqI2zBNyQjiMecEZRSyOzOkR4RC/I2pImCfjzysis2XV7AWudOAWpkQKtkfk19GOWhhAhE1SpgWMn6GZUImcC5pVhqiChbErHMNA0oiEoN1ucPrfOteJbQSx1RWgt1N8TGQ2VmoWe7gwpTtSql4v/eYMUgys341GSIkRsuShIhYWxledg+VwCQzHThDLJ9a0Wm1BJGeq08hCc1ZfXSbdRd+y6c9eoNa+LOMrklJyRC+KQS9Ikt6RFOoSRB/JMXsmb8WS8GO/Gx7K1ZBQzJ+QPjM8fY5KUDg==AAAB+nicbVC7TsNAEDyHVwgvB0oaiwiJKrLTQBlBQxmkvKTEis7ndXLK+aG7NRCZfAoNBQjR8iV0/A3nxAUkjLTSaGZXuzteIrhC2/42ShubW9s75d3K3v7B4ZFZPe6qOJUMOiwWsex7VIHgEXSQo4B+IoGGnoCeN73J/d49SMXjqI2zBNyQjiMecEZRSyOzOkR4RC/I2pImCfjzysis2XV7AWudOAWpkQKtkfk19GOWhhAhE1SpgWMn6GZUImcC5pVhqiChbErHMNA0oiEoN1ucPrfOteJbQSx1RWgt1N8TGQ2VmoWe7gwpTtSql4v/eYMUgys341GSIkRsuShIhYWxledg+VwCQzHThDLJ9a0Wm1BJGeq08hCc1ZfXSbdRd+y6c9eoNa+LOMrklJyRC+KQS9Ikt6RFOoSRB/JMXsmb8WS8GO/Gx7K1ZBQzJ+QPjM8fY5KUDg==a>a\u21e4AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw==AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw==AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw==AAACAnicbVDLSsNAFJ34rPEVdSVuBosgLkoigi6LblxWsA9o0jKZTNqhk5kwMxFKKG78FTcuFHHrV7jzb5y0WWjrgWEO59zLvfeEKaNKu+63tbS8srq2XtmwN7e2d3advf2WEpnEpIkFE7ITIkUY5aSpqWakk0qCkpCRdji6Kfz2A5GKCn6vxykJEjTgNKYYaSP1nUM/FCxS48R8Oer5WqQQ9c4mtt13qm7NnQIuEq8kVVCi0Xe+/EjgLCFcY4aU6npuqoMcSU0xIxPbzxRJER6hAekaylFCVJBPT5jAE6NEMBbSPK7hVP3dkaNEFVuaygTpoZr3CvE/r5vp+CrIKU8zTTieDYozBrWARR4wopJgzcaGICyp2RXiIZIIa5NaEYI3f/IiaZ3XPLfm3V1U69dlHBVwBI7BKfDAJaiDW9AATYDBI3gGr+DNerJerHfrY1a6ZJU9B+APrM8fYE+Wuw==CNNAAACB3icbVDLSsNAFJ34rPVVdelmsAiuSlIXuix001WpYB/QhDKZTNqhk0mYuRFL6Af4A271D9yJWz/DH/A7nLRZaOuBC4dz7ovjJ4JrsO0va2Nza3tnt7RX3j84PDqunJz2dJwqyro0FrEa+EQzwSXrAgfBBoliJPIF6/vTZu73H5jSPJb3MEuYF5Gx5CGnBIzkusAewQ+zZrs9H1Wqds1eAK8TpyBVVKAzqny7QUzTiEmggmg9dOwEvIwo4FSwedlNNUsInZIxGxoqScS0ly1+nuNLowQ4jJUpCXih/p7ISKT1LPJNZ0Rgole9XPzXC3S+cOU6hLdexmWSApN0eTxMBYYY56HggCtGQcwMIVRx8z+mE6IIBRNd2QTjrMawTnr1mnNdq9/Vq41WEVEJnaMLdIUcdIMaqIU6qIsoStAzekGv1pP1Zr1bH8vWDauYOUN/YH3+AKj6mjc=ResNetAAACDHicbVDLSsNAFJ34rPXRqEs3wSK4Kkld6LLgpiupYh/QhjKZ3LRDJw9mbsQS+gv+gFv9A3fi1n/wB/wOJ20W2nrgwuGc++J4ieAKbfvLWFvf2NzaLu2Ud/f2Dyrm4VFHxalk0GaxiGXPowoEj6CNHAX0Egk09AR0vcl17ncfQCoeR/c4TcAN6SjiAWcUtTQ0KwOER/SC7A7UDeBsaFbtmj2HtUqcglRJgdbQ/B74MUtDiJAJqlTfsRN0MyqRMwGz8iBVkFA2oSPoaxrREJSbzR+fWWda8a0glroitObq74mMhkpNQ093hhTHatnLxX89X+ULl65jcOVmPEpShIgtjgepsDC28mQsn0tgKKaaUCa5/t9iYyopQ51fWQfjLMewSjr1mnNRq9/Wq41mEVGJnJBTck4cckkapElapE0YSckzeSGvxpPxZrwbH4vWNaOYOSZ/YHz+APB6m/g==\\(1pp+w,v\u21e4)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AAAB+XicbVA9T8MwEHX4LOUrwMhiUSExVUkXGCtYYCuCfkhtVTnupbXqOJF9qaii/hMWBhBi5Z+w8W9w2wzQ8qSTnt67s+9ekEhh0PO+nbX1jc2t7cJOcXdv/+DQPTpumDjVHOo8lrFuBcyAFArqKFBCK9HAokBCMxjdzPzmGLQRsXrESQLdiA2UCAVnaKWe63YQnjAIswdkA6B3055b8sreHHSV+DkpkRy1nvvV6cc8jUAhl8yYtu8l2M2YRsElTIud1EDC+Mg+37ZUsQhMN5tvPqXnVunTMNa2FNK5+nsiY5ExkyiwnRHDoVn2ZuJ/XjvF8KqbCZWkCIovPgpTSTGmsxhoX2jgKCeWMK6F3ZXyIdOMow2raEPwl09eJY1K2ffK/n2lVL3O4yiQU3JGLohPLkmV3JIaqRNOxuSZvJI3J3NenHfnY9G65uQzJ+QPnM8feViThw==AAAB+XicbVA9T8MwEHX4LOUrwMhiUSExVUkXGCtYYCuCfkhtVTnupbXqOJF9qaii/hMWBhBi5Z+w8W9w2wzQ8qSTnt67s+9ekEhh0PO+nbX1jc2t7cJOcXdv/+DQPTpumDjVHOo8lrFuBcyAFArqKFBCK9HAokBCMxjdzPzmGLQRsXrESQLdiA2UCAVnaKWe63YQnjAIswdkA6B3055b8sreHHSV+DkpkRy1nvvV6cc8jUAhl8yYtu8l2M2YRsElTIud1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\u2264 M and \u03c6T1 \u2264 5\n\nsome constants M > m > 0.\nStage II: Converge to the global optimum (Theorem 13): After T1 iterations, we restart the counter,\n\u03b4 ), we have\n\nTheorem 2 (Main Results). Let the GD algorithm de\ufb01ned in Section 2 be initialized with w0 =\n0 and arbitrary a0 \u2208 B0(|1(cid:62)a\u2217|/\u221ak). Then the algorithm converges in two stages:\nStage I: Avoid the spurious local optimum (Theorem 4): We choose \u03b7a = O(1/k2) and \u03b7w =\n(cid:101)O(1/k4). Then there exists T1 = (cid:101)O(1/\u03b7a), such that m \u2264 a(cid:62)T1\n12 \u03c0 hold for\nand choose \u03b7 = \u03b7a = \u03b7w = (cid:101)O(1/k2). Then for any \u03b4 > 0, any t \u2265 T2 = (cid:101)O( 1\n(cid:107)wt \u2212 w\u2217(cid:107)2\nNote that the set {(wt, at) | a(cid:62)t a\u2217 \u2208 [m, M ], \u03c6t \u2264 5\u03c0/12} belongs to be the basin of attraction\naround the global optimum (Lemma 11), where certain regularity condition (partial dissipativity)\nguides the algorithm toward the global optimum. Hence, after the algorithm enters the second stage,\nwe increase the step size \u03b7w of w for a faster convergence. Figure 3 demonstrates the initialization of\n(w, a), and the convergence of GD both on CNN in Du et al. (2017) and our ResNet model.\nWe start our convergence analysis with the de\ufb01nition of partial dissipativity for L.\nDe\ufb01nition 3 (Partial Dissipativity). Given any \u03b4 \u2265 0 and a constant c \u2265 0, \u2207wL is (c, \u03b4)-partially\ndissipative with respect to w\u2217 in a set K\u03b4, if for every (w, a) \u2208 K\u03b4, we have\n\n2 \u2264 \u03b4 and (cid:107)at \u2212 a\u2217(cid:107)2\n\n2 \u2264 5\u03b4.\n\n\u03b7 log 1\n\n\u2207aL is (c, \u03b4)-partially dissipative with respect to a\u2217 in a set A\u03b4, if for every (w, a) \u2208 A\u03b4, we have\n\n(cid:104)\u2212\u2207wL(w, a), w\u2217 \u2212 w(cid:105) \u2265 c(cid:107)w \u2212 w\u2217(cid:107)2\n\n2 \u2212 \u03b4;\n\n(cid:104)\u2212\u2207aL(w, a), a\u2217 \u2212 a(cid:105) \u2265 c(cid:107)a \u2212 a\u2217(cid:107)2\n\n2 \u2212 \u03b4.\n\nMoreover, If K\u03b4 \u2229 A\u03b4 (cid:54)= \u2205, \u2207L is (c, 2\u03b4)-jointly dissipative with respect to (w\u2217, a\u2217) in K\u03b4 \u2229 A\u03b4, i.e.,\nfor every (w, a) \u2208 K\u03b4 \u2229 A\u03b4, we have\n\n(cid:104)\u2212\u2207wL(w, a), w\u2217 \u2212 w(cid:105) + (cid:104)\u2212\u2207aL(w, a), a\u2217 \u2212 a(cid:105) \u2265 c((cid:107)w \u2212 w\u2217(cid:107)2\n\n2 + (cid:107)a \u2212 a\u2217(cid:107)2\n\n2) \u2212 2\u03b4.\n\nThe concept of dissipativity is originally used in dynamical systems (Barrera and Jara, 2015), and\nis de\ufb01ned for general operators. It suf\ufb01ces to instantiate the concept to gradients here for our\nconvergence analysis. The partial dissipativity for perturbed gradients is used in Zhou et al. (2019) to\nstudy the convergence behavior of Perturbed GD. The variational coherence studied in Zhou et al.\n(2017) and one point convexity studied in Li and Yuan (2017) can be viewed as special examples of\npartial dissipativity.\n\n3.1 Stage I: Avoid the Spurious Local Optimum\nWe \ufb01rst show with properly chosen step sizes, GD algorithm can avoid being trapped by the spurious\nlocal optimum. We propose to update w, a using different step sizes. We formalize our result in the\nfollowing theorem.\n\nTheorem 4. Initialize with arbitrary a0 \u2208 B0(|1(cid:62)a\u2217|/\u221ak) and w0 = 0. We choose step sizes\n\n\u03b7a =\n\n\u03c0\n\n20(k + \u03c0 \u2212 1)2 = O(cid:0)1/k2(cid:1) ,\n\nfor some constant C > 0. Then, we have\n\nand \u03b7w = C(cid:107)a\u2217(cid:107)2\n\n2\u03b72\n\na)\n\na = (cid:101)O(\u03b72\n\nfor all t \u2208 [T1, T ], where\n\n\u03c6t \u2264 5\u03c0/12 and 0 \u2264 m \u2264 a(cid:62)t a\u2217 \u2264 M,\n\nT1 = (cid:101)O(1/\u03b7a), T = O(1/\u03b72\n\na), m = (cid:107)a\u2217(cid:107)2\n\n2/5, and M = 3(cid:107)a\u2217(cid:107)2\n\n2 + 2(cid:0)1(cid:62)a\u2217(cid:1)2\n\nProof Sketch. Due to the space limit, we only provide a proof sketch here. The detailed proof is\ndeferred to Appendix B.2. We prove the two arguments in (9) in order. Before that, we \ufb01rst show our\ninitialization scheme guarantees an important bound on a, as stated in the following lemma.\n\nLemma 5. Given a0 \u2208 B0(|1(cid:62)a\u2217|/\u221ak), we choose \u03b7a \u2264 2\u03c0\n\u2264 1(cid:62)a\u22171(cid:62)at \u2212(cid:0)1(cid:62)a\u2217(cid:1)2\n\n\u22123(cid:0)1(cid:62)a\u2217(cid:1)2\n\nk+\u03c0\u22121 . Then for any t > 0,\n\n\u2264 0.\n\n(10)\n\n(9)\n\n.\n\n5\n\n\fUnder the shortcut prior assumption 1 that w0 is close to w\u2217, the update of w should be more\nconservative to provide enough accuracy for a to make progress. Based on Lemma 5, the next lemma\nshows that when \u03b7w is small enough, \u03c6t stays acute (\u03c6t < \u03c0\n2 ), i.e., w is suf\ufb01ciently away from\n\u00afw = \u2212(1/\u221ap) \u2212 v\u2217 .\nLemma 6. Given w0 = 0 and a0 \u2208 B0(|1(cid:62)a\u2217|/\u221ak), we choose \u03b7a <\na = (cid:101)O(\u03b72\nC(cid:107)a\u2217(cid:107)2\n\na) for some absolute constant C > 0. Then for all t \u2264 T = O(1/\u03b72\na),\n\nk+\u03c0\u22121 and \u03b7w =\n\n\u03c6t \u2264 5\u03c0/12.\n\n(11)\n\n2\u03b72\n\n2\u03c0\n\nWe want to remark that (10) and (11) are two of the key conditions that de\ufb01ne the partially dissipative\nregion of \u2207aL , as shown in the following lemma.\nLemma 7. For any (w, a) \u2208 A, \u2207aL satis\ufb01es\n\n5\n\n20(cid:107)a\u2217(cid:107)2\n\n2 or (cid:107)a \u2212 a\u2217/2(cid:107)2\n\n(cid:104)\u2212\u2207aL(w, a), a\u2217 \u2212 a(cid:105) \u2265 (1/10\u03c0)(cid:107)a \u2212 a\u2217(cid:107)2\n2,\n2 \u2265 (cid:107)a\u2217(cid:107)2\n\nwhere A = (cid:8)(w, a) (cid:12)(cid:12)a(cid:62)a\u2217 \u2264 1\n12 \u03c0, \u2212 3(1(cid:62)a\u2217)2 \u2264 1(cid:62)a\u22171(cid:62)a \u2212 (1(cid:62)a\u2217)2 \u2264 0(cid:9).\nPlease refer to Appendix B.2.3 for a detailed proof. Note that with arbitrary initialization of a,\n2 possibly holds at a0. In this case, (w0, a0) falls in A,\na(cid:62)a\u2217 \u2264 1\nand (12) ensures the improvement of a.\nLemma 8. Given (w0, a0) \u2208 A, we choose \u03b7a <\n20(k+\u03c0\u22121)2 . Then there exists \u03c411 = O(1/\u03b7a),\nsuch that 1\n\n(12)\n2, (cid:107)w + 1/\u221ap(cid:107)2 = 1, \u03c6 \u2264\n\n2 or (cid:107)a \u2212 a\u2217/2(cid:107)2\n\n2 \u2265 (cid:107)a\u2217(cid:107)2\n\n20(cid:107)a\u2217(cid:107)2\n\n\u03c0\n\n20(cid:107)a\u2217(cid:107)2\n\n2 \u2264 a(cid:62)\u03c411 a\u2217 \u2264 2(cid:107)a\u2217(cid:107)2\n2.\n\nOne can easily verify that a(cid:62)a\u2217 \u2264 2(cid:107)a\u2217(cid:107)2\n8, we claim that even with arbitrary initialization, the iterates can always enter the region with a(cid:62)a\u2217\npositive and bounded in polynomial time. The next lemma shows that with proper chosen step sizes,\na(cid:62)a\u2217 stays positive and bounded.\n\n2 holds for any a \u2208 B0(|1(cid:62)a\u2217|/\u221ak). Together with Lemma\n\nLemma 9. Suppose 1\n\n20(cid:107)a\u2217(cid:107)2\n\n2 \u2264 a(cid:62)0 a\u2217 \u2264 2(cid:107)a\u2217(cid:107)2\n\n\u2264 0 holds for all t. Choose \u03b7a < 2\u03c0\n\n(cid:0)1(cid:62)a\u2217(cid:1)2\n\n2, \u03c6t \u2264 5\n\n\u03c0\u22121 , then we have for all t \u2265 \u03c412 = (cid:101)O(1/\u03b7a),\n\n12 \u03c0, and \u22123(cid:0)1(cid:62)a\u2217(cid:1)2\n2 + 2(cid:0)1(cid:62)a\u2217(cid:1)2\n\n.\n\n\u2264 1(cid:62)a\u22171(cid:62)at \u2212\n\n(cid:107)a\u2217(cid:107)2\n\n2/5 \u2264 a(cid:62)t a\u2217 \u2264 3(cid:107)a\u2217(cid:107)2\n\nTake T1 = \u03c411 + \u03c412, and we complete the proof.\n\nIn Theorem 4, we choose a conservative \u03b7w. This brings two bene\ufb01ts to the training process: 1). w\nstays away from \u00afw. The update on w is quite limited, since \u03b7w is small. Hence, w is kept suf\ufb01ciently\naway from \u00afw, even if w moves towards \u00afw in every iteration); 2). a continuously updates toward a\u2217.\nTheorem 4 ensures that under the shortcut prior, GD with adaptive step sizes can successfully\novercome the optimization challenge early in training, i.e., the iterate is suf\ufb01ciently away from the\nspurious local optima at the end of Stage I. Meanwhile, (9) actually demonstrates that the algorithm\nenters the basin of attraction of the global optimum, and we next show the convergence of GD.\n\n3.2 Stage II: Converge to the Global Optimum\nRecall that in the previous stage, we use a conservative step size \u03b7w to avoid being trapped by the\nspurious local optimum. However, the small step size \u03b7w slows down the convergence of w in\nthe basin of attraction of the global optimum. Now we choose larger step sizes to accelerate the\nconvergence. The following theorem shows that, after Stage I, we can use a larger \u03b7w, while the\nresults in Theorem 4 still hold, i.e., the iterate stays in the basin of attraction of (w\u2217, a\u2217).\nTheorem 10. We restart the counter of time. Suppose m \u2264 a(cid:62)0 a\u2217 \u2264 M, and \u03c60 \u2264 5\n\u03b7w \u2264 m\n\nk+\u03c0\u22121 . Then for all t > 0, we have\n\nk2 ) and \u03b7a < 2\u03c0\n\n12 \u03c0. We choose\n\nM 2 = (cid:101)O( 1\n\n\u03c6t \u2264 5\u03c0/12\n\nand 0 \u2264 m \u2264 a(cid:62)t a\u2217 \u2264 M.\n\n6\n\n\fProof Sketch. To prove the \ufb01rst argument, we need the partial dissipativity of \u2207wL.\nLemma 11. For any m > 0, \u2207wL satis\ufb01es\n\n(cid:104)\u2212\u2207wL(w, a), w\u2217 \u2212 w(cid:105) \u2265\n\nm\n8 (cid:107)w \u2212 w\u2217(cid:107)2\n2,\n\nfor any (w, a) \u2208 Km, where\n\nKm =(cid:8)(w, a)(cid:12)(cid:12) a(cid:62)a\u2217 \u2265 m, (w + 1/\u221ap)(cid:62)v\u2217 \u2265 0, (cid:107)w + 1/\u221ap(cid:107)2 = 1(cid:9) .\n\nThis condition ensures that when a(cid:62)a\u2217 is positive, w always makes positive progress towards w\u2217, or\nequivalently \u03c6t decreasing. We need not worry about \u03c6t getting obtuse, and thus a larger step size \u03b7w\ncan be adopted. The second argument can be proved following similar lines to Lemma 9. Please see\nAppendix B.3.2 for more details.\n\nNow we are ready to show the convergence of our GD algorithm. Note that Theorem 10 and Lemma\n11 together show that the iterate stays in the partially dissipative region Kw, which leads to the\nconvergence of w. Moreover, as shown in the following lemma, when w is accurate enough, the\npartial gradient with respect to a enjoys partial dissipativity.\nLemma 12. For any \u03b4 > 0, \u2207aL satis\ufb01es\n\n(cid:104)\u2212\u2207aL (w, a) , a\u2217 \u2212 a(cid:105) \u2265\n\n\u03c0 \u2212 1\n2\u03c0 (cid:107)a \u2212 a\u2217(cid:107)2\n\n2 \u2212\n\n1\n5\n\n\u03b4,\n\nfor any (w, a) \u2208 Am,M,\u03b4, where\n\n5\u03c02\n\n2M 2 ,\n\n5(cid:107)a\u2217(cid:107)2\n\n(cid:107)wt \u2212 w\u2217(cid:107)2\n\n2 = m \u2264 a(cid:62)t a\u2217 \u2264 M = 3(cid:107)a\u2217(cid:107)2\n\n2 + 2(cid:0)1(cid:62)a\u2217(cid:1)2 hold for\n\nAs a direct result, a converges to a\u2217. The next theorem formalize the above discussion.\nTheorem 13 (Convergence). Suppose 1\n\n2 \u2264 \u03b4, (cid:107)w + 1/\u221ap(cid:107)2 = 1(cid:9) .\n4(k+\u03c0\u22121)2(cid:111) = (cid:101)O( 1\n\nAm,M,\u03b4 =(cid:8)(w, a)(cid:12)(cid:12) a(cid:62)a\u2217 \u2208 [m, M ], (cid:107)w \u2212 w\u2217(cid:107)2\nall t > 0. For any \u03b4 > 0, choose \u03b7a = \u03b7w = \u03b7 = min(cid:110) m\nfor any t \u2265 T2 = (cid:101)O( 1\nProof Sketch. The detailed proof is provided in Appendix B.4. Our proof relies on the partial\ndissipativity of \u2207wL (Lemma 11) and that of \u2207aL (Lemma 12).\nNote that the partial dissipative region Am,M,\u03b4, depends on the precision of w. Thus, we \ufb01rst show\nthe convergence of w.\n2 + 4(cid:0)1(cid:62)a\u2217(cid:1)2\nLemma 14 (Convergence of wt). Suppose 1\nhold for all t > 0. For any \u03b4 > 0, choose \u03b7 \u2264 m\n\n2 \u2264 \u03b4 and (cid:107)at \u2212 a\u2217(cid:107)2\n\nk2 ), then we have\n\n5(cid:107)a\u2217(cid:107)2\n2 = m \u2264 a(cid:62)t a\u2217 \u2264 M = 3(cid:107)a\u2217(cid:107)2\n2M 2 = (cid:101)O( 1\n\nk2 ), then we have\n\n2 \u2264 5\u03b4\n\n\u03b7 log 1\n\n2 \u2264 \u03b4\n\n\u03b4 ).\n\n\u03b7 log 1\n\nm\u03b7 log 4\n\n\u03b4 = (cid:101)O( 1\n\nfor any t \u2265 \u03c421 = 4\nLemma 14 implies that after \u03c421 iterations, the algorithm enters Am,M,\u03b4. Then we show the conver-\ngence property of a in next lemma.\nLemma 15 (Convergence of at). Suppose m \u2264 a(cid:62)t a\u2217 \u2264 M and (cid:107)wt \u2212 w\u2217(cid:107)2\n2 \u2264 \u03b4 holds for all t. We\n= (cid:101)O( 1\nchoose \u03b7 \u2264\n\nk2 ). Then for all t \u2265 \u03c422 = 4\n2 \u2264 5\u03b4.\n\n4(k+\u03c0\u22121)2 = O( 1\n\n\u03b7 log (cid:107)a0\u2212a\u2217(cid:107)2\n\n(cid:107)at \u2212 a\u2217(cid:107)2\n\n\u03b4 ), we have\n\n\u03b7 log 1\n\n5\u03c02\n\n\u03b4\n\n2\n\n(cid:107)wt \u2212 w\u2217(cid:107)2\n\u03b4 ).\n\nCombine the above two lemmas together, take T2 = \u03c421 + \u03c422, and we complete the proof.\n\nTheorem 13 shows that with larger \u03b7w than in Stage I, GD converges to the global optimum in\npolynomial time. Compared to the convergence with constant probability for CNN (Du et al., 2017),\nAssumption 1 assures convergence even under arbitrary initialization of a. This partially justi\ufb01es the\nimportance of shortcut in ResNet.\n\n7\n\n\fFigure 4: Success rates of converging to the global optimum for GD training ResNet with and without\nSSW and CNN with varying k and and p = 8.\n\n4(cid:107)a\u2217(cid:107)2\n\n4 Numerical Experiment\nWe present numerical experiments to illustrate the convergence of the GD algorithm. We \ufb01rst\ndemonstrate that with the shortcut prior, our choice of step sizes and the initialization guarantee\nthe convergence of GD. We consider the training of a two-layer non-overlapping convolutional\nResNet by solving (7). Speci\ufb01cally, we set p = 8 and k \u2208 {16, 25, 36, 49, 64, 81, 100}. The teacher\nnetwork is set with parameters a\u2217 satisfying 1(cid:62)a\u2217 = 1\n2, and v\u2217 satisfying v\u22171 = cos(7\u03c0/10),\nv\u22172 = sin(7\u03c0/10), and v\u2217j = 0 for j = 3, . . . , p.3 More detailed experimental setting is provided\nin Appendix C. We initialize with w0 = 0 and a0 uniformly distributed over B0(|1(cid:62)a\u2217|/\u221ak). We\nadopt the following learning rate scheme with Step Size Warmup (SSW) suggested in Section\n3: We \ufb01rst choose step sizes \u03b7a = 1/k2 and \u03b7w = \u03b72\na, and run for 1000 iterations. Then, we\nchoose \u03b7a = \u03b7w = 1/k2. We also consider learning the same teacher network using step sizes\n\u03b7w = \u03b7a = 1/k2 throughout, i.e., without step size warmup.\nWe further demonstrate learning the aforementioned teacher network using a student network of\nthe same architecture. Speci\ufb01cally, we keep a\u2217, v\u2217 unchanged. We use the GD in Du et al. (2017)\nwith step size \u03b7 = 0.1, and initialize v0 uniformly distributed over the unit sphere and a uniformly\ndistributed over B0(|1(cid:62)a\u2217|/\u221ak).\n\nFor each combination of k and a\u2217, we repeat 5000 simulations for aforementioned three settings,\nand report the success rate of converging to the global optimum in Table 1 and Figure 4. As can be\nseen, our GD on ResNet can avoid the spurious local optimum, and converge to the global optimum\nin all 5000 simulations. However, GD without SSW can be trapped in the spurious local optimum.\nThe failure probability diminishes as the dimension increase. Learning the teacher network using a\ntwo-layer CNN student network (Du et al., 2017) can also be trapped in the spurious local optimum.\n\nTable 1: Success rates of converging to the global optimum for GD training ResNet with and without\nSSW and CNN with varying k and and p = 8.\n\n16\n\nk\nResNet w/ SSW 1.0000\nResNet w/o SSW 0.7042\nCNN\n0.5348\n\n25\n\n1.0000\n0.7354\n0.5528\n\n36\n\n1.0000\n0.7776\n0.5312\n\n49\n\n1.0000\n0.7848\n0.5426\n\n64\n\n1.0000\n0.8220\n0.5192\n\n81\n\n1.0000\n0.8388\n0.5368\n\n100\n\n1.0000\n0.8426\n0.5374\n\nWe then demonstrate the algorithmic behavior of our GD. We set k = 25 for the teacher network,\nand other parameters the same as in the previous experiment. We initialize w0 = 0 and a0 \u2208\nB0(|1(cid:62)a\u2217|/\u221ak). We start with \u03b7a = 1/k2 and \u03b7w = \u03b72\na. After 1000 iterations, we set the step\nsizes \u03b7a = \u03b7w = 1/k2. The algorithm is terminated when (cid:107)at \u2212 a\u2217(cid:107)2\n2 \u2264 10\u22126.\nWe also demonstrate the GD algorithm without SSW at the same initialization. The step sizes are\n\u03b7a = \u03b7w = 1/k2 throughout the training.\nOne solution path of GD with SSW is shown in the \ufb01rst row of Figure 5. As can be seen, the algorithm\nhas a phase transition. In the \ufb01rst stage, we observe that wt makes very slow progress due to the\n\n2 + (cid:107)wt \u2212 w\u2217(cid:107)2\n\n\u221a\n3v\u2217 essentially satis\ufb01es \u2220(v\u2217, 1/\n\np) = 0.45\u03c0.\n\n8\n\n25AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoseiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0ULvslytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0qpVPbfq3V9U6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/GLjPU=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoseiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0ULvslytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0qpVPbfq3V9U6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/GLjPU=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoseiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0ULvslytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0qpVPbfq3V9U6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/GLjPU=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoseiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0ULvslytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0qpVPbfq3V9U6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/GLjPU=36AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU1GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvSATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVDBssFrFqB1Sj4BIbhhuB7UQhjQKBrWB0O/VbT6g0j+WjGSfoR3QgecgZNVZ6OL/slStu1Z2BLBMvJxXIUe+Vv7r9mKURSsME1brjuYnxM6oMZwInpW6qMaFsRAfYsVTSCLWfzS6dkBOr9EkYK1vSkJn6eyKjkdbjKLCdETVDvehNxf+8TmrCaz/jMkkNSjZfFKaCmJhM3yZ9rpAZMbaEMsXtrYQNqaLM2HBKNgRv8eVl0jyrem7Vu7+o1G7yOIpwBMdwCh5cQQ3uoA4NYBDCM7zCmzNyXpx352PeWnDymUP4A+fzB/SUjPc=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU1GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvSATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVDBssFrFqB1Sj4BIbhhuB7UQhjQKBrWB0O/VbT6g0j+WjGSfoR3QgecgZNVZ6OL/slStu1Z2BLBMvJxXIUe+Vv7r9mKURSsME1brjuYnxM6oMZwInpW6qMaFsRAfYsVTSCLWfzS6dkBOr9EkYK1vSkJn6eyKjkdbjKLCdETVDvehNxf+8TmrCaz/jMkkNSjZfFKaCmJhM3yZ9rpAZMbaEMsXtrYQNqaLM2HBKNgRv8eVl0jyrem7Vu7+o1G7yOIpwBMdwCh5cQQ3uoA4NYBDCM7zCmzNyXpx352PeWnDymUP4A+fzB/SUjPc=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU1GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvSATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVDBssFrFqB1Sj4BIbhhuB7UQhjQKBrWB0O/VbT6g0j+WjGSfoR3QgecgZNVZ6OL/slStu1Z2BLBMvJxXIUe+Vv7r9mKURSsME1brjuYnxM6oMZwInpW6qMaFsRAfYsVTSCLWfzS6dkBOr9EkYK1vSkJn6eyKjkdbjKLCdETVDvehNxf+8TmrCaz/jMkkNSjZfFKaCmJhM3yZ9rpAZMbaEMsXtrYQNqaLM2HBKNgRv8eVl0jyrem7Vu7+o1G7yOIpwBMdwCh5cQQ3uoA4NYBDCM7zCmzNyXpx352PeWnDymUP4A+fzB/SUjPc=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU1GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvSATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVDBssFrFqB1Sj4BIbhhuB7UQhjQKBrWB0O/VbT6g0j+WjGSfoR3QgecgZNVZ6OL/slStu1Z2BLBMvJxXIUe+Vv7r9mKURSsME1brjuYnxM6oMZwInpW6qMaFsRAfYsVTSCLWfzS6dkBOr9EkYK1vSkJn6eyKjkdbjKLCdETVDvehNxf+8TmrCaz/jMkkNSjZfFKaCmJhM3yZ9rpAZMbaEMsXtrYQNqaLM2HBKNgRv8eVl0jyrem7Vu7+o1G7yOIpwBMdwCh5cQQ3uoA4NYBDCM7zCmzNyXpx352PeWnDymUP4A+fzB/SUjPc=49AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoN6KXjxWsR/QhrLZTtqlm03Y3Qgl9B948aCIV/+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RTW1jc2t4rbpZ3dvf2D8uFRS8epYthksYhVJ6AaBZfYNNwI7CQKaRQIbAfj25nffkKleSwfzSRBP6JDyUPOqLHSQ+26X664VXcOskq8nFQgR6Nf/uoNYpZGKA0TVOuu5ybGz6gynAmclnqpxoSyMR1i11JJI9R+Nr90Ss6sMiBhrGxJQ+bq74mMRlpPosB2RtSM9LI3E//zuqkJr/yMyyQ1KNliUZgKYmIye5sMuEJmxMQSyhS3txI2oooyY8Mp2RC85ZdXSeui6rlV775Wqd/kcRThBE7hHDy4hDrcQQOawCCEZ3iFN2fsvDjvzseiteDkM8fwB87nD/qljPs=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoN6KXjxWsR/QhrLZTtqlm03Y3Qgl9B948aCIV/+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RTW1jc2t4rbpZ3dvf2D8uFRS8epYthksYhVJ6AaBZfYNNwI7CQKaRQIbAfj25nffkKleSwfzSRBP6JDyUPOqLHSQ+26X664VXcOskq8nFQgR6Nf/uoNYpZGKA0TVOuu5ybGz6gynAmclnqpxoSyMR1i11JJI9R+Nr90Ss6sMiBhrGxJQ+bq74mMRlpPosB2RtSM9LI3E//zuqkJr/yMyyQ1KNliUZgKYmIye5sMuEJmxMQSyhS3txI2oooyY8Mp2RC85ZdXSeui6rlV775Wqd/kcRThBE7hHDy4hDrcQQOawCCEZ3iFN2fsvDjvzseiteDkM8fwB87nD/qljPs=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoN6KXjxWsR/QhrLZTtqlm03Y3Qgl9B948aCIV/+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RTW1jc2t4rbpZ3dvf2D8uFRS8epYthksYhVJ6AaBZfYNNwI7CQKaRQIbAfj25nffkKleSwfzSRBP6JDyUPOqLHSQ+26X664VXcOskq8nFQgR6Nf/uoNYpZGKA0TVOuu5ybGz6gynAmclnqpxoSyMR1i11JJI9R+Nr90Ss6sMiBhrGxJQ+bq74mMRlpPosB2RtSM9LI3E//zuqkJr/yMyyQ1KNliUZgKYmIye5sMuEJmxMQSyhS3txI2oooyY8Mp2RC85ZdXSeui6rlV775Wqd/kcRThBE7hHDy4hDrcQQOawCCEZ3iFN2fsvDjvzseiteDkM8fwB87nD/qljPs=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoN6KXjxWsR/QhrLZTtqlm03Y3Qgl9B948aCIV/+RN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RTW1jc2t4rbpZ3dvf2D8uFRS8epYthksYhVJ6AaBZfYNNwI7CQKaRQIbAfj25nffkKleSwfzSRBP6JDyUPOqLHSQ+26X664VXcOskq8nFQgR6Nf/uoNYpZGKA0TVOuu5ybGz6gynAmclnqpxoSyMR1i11JJI9R+Nr90Ss6sMiBhrGxJQ+bq74mMRlpPosB2RtSM9LI3E//zuqkJr/yMyyQ1KNliUZgKYmIye5sMuEJmxMQSyhS3txI2oooyY8Mp2RC85ZdXSeui6rlV775Wqd/kcRThBE7hHDy4hDrcQQOawCCEZ3iFN2fsvDjvzseiteDkM8fwB87nD/qljPs=64AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkqMeiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0cFnrlytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0rqoem7Vu69V6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/YbjPg=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkqMeiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0cFnrlytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0rqoem7Vu69V6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/YbjPg=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkqMeiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0cFnrlytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0rqoem7Vu69V6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/YbjPg=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkqMeiF49V7Ae0oWy2k3bpZhN2N0IJ/QdePCji1X/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0cFnrlytu1Z2DrBIvJxXI0eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtVTSCLWfzS+dkjOrDEgYK1vSkLn6eyKjkdaTKLCdETUjvezNxP+8bmrCaz/jMkkNSrZYFKaCmJjM3iYDrpAZMbGEMsXtrYSNqKLM2HBKNgRv+eVV0rqoem7Vu69V6jd5HEU4gVM4Bw+uoA530IAmMAjhGV7hzRk7L86787FoLTj5zDH8gfP5A/YbjPg=81AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEaI9FLx6r2A9oQ9lsJ+3SzSbsboQS+g+8eFDEq//Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ7dzvPKHSPJaPZpqgH9GR5CFn1Fjpoe4NyhW36i5A1omXkwrkaA7KX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFpfOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzVh3c+4TFKDki0XhakgJibzt8mQK2RGTC2hTHF7K2FjqigzNpySDcFbfXmdtK+qnlv17q8rjZs8jiKcwTlcggc1aMAdNKEFDEJ4hld4cybOi/PufCxbC04+cwp/4Hz+APSZjPc=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEaI9FLx6r2A9oQ9lsJ+3SzSbsboQS+g+8eFDEq//Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ7dzvPKHSPJaPZpqgH9GR5CFn1Fjpoe4NyhW36i5A1omXkwrkaA7KX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFpfOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzVh3c+4TFKDki0XhakgJibzt8mQK2RGTC2hTHF7K2FjqigzNpySDcFbfXmdtK+qnlv17q8rjZs8jiKcwTlcggc1aMAdNKEFDEJ4hld4cybOi/PufCxbC04+cwp/4Hz+APSZjPc=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEaI9FLx6r2A9oQ9lsJ+3SzSbsboQS+g+8eFDEq//Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ7dzvPKHSPJaPZpqgH9GR5CFn1Fjpoe4NyhW36i5A1omXkwrkaA7KX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFpfOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzVh3c+4TFKDki0XhakgJibzt8mQK2RGTC2hTHF7K2FjqigzNpySDcFbfXmdtK+qnlv17q8rjZs8jiKcwTlcggc1aMAdNKEFDEJ4hld4cybOi/PufCxbC04+cwp/4Hz+APSZjPc=AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEaI9FLx6r2A9oQ9lsJ+3SzSbsboQS+g+8eFDEq//Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ7dzvPKHSPJaPZpqgH9GR5CFn1Fjpoe4NyhW36i5A1omXkwrkaA7KX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFpfOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzVh3c+4TFKDki0XhakgJibzt8mQK2RGTC2hTHF7K2FjqigzNpySDcFbfXmdtK+qnlv17q8rjZs8jiKcwTlcggc1aMAdNKEFDEJ4hld4cybOi/PufCxbC04+cwp/4Hz+APSZjPc=100AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKcyKoMegF48RzQOSJcxOepMhs7PLzKwQQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrTKUwltJvr7C2vrG5Vdwu7ezu7R+UD4+aJsk0xwZPZKLbITMohcKGFVZiO9XI4lBiKxzdzvzWE2ojEvVoxykGMRsoEQnOrJMefEp75Qqt0jnIKvFzUoEc9V75q9tPeBajslwyYzo+TW0wYdoKLnFa6mYGU8ZHbIAdRxWL0QST+alTcuaUPokS7UpZMld/T0xYbMw4Dl1nzOzQLHsz8T+vk9noOpgIlWYWFV8sijJJbEJmf5O+0MitHDvCuBbuVsKHTDNuXTolF4K//PIqaV5UfVr17y8rtZs8jiKcwCmcgw9XUIM7qEMDOAzgGV7hzZPei/fufSxaC14+cwx/4H3+AFaIjSk=AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKcyKoMegF48RzQOSJcxOepMhs7PLzKwQQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrTKUwltJvr7C2vrG5Vdwu7ezu7R+UD4+aJsk0xwZPZKLbITMohcKGFVZiO9XI4lBiKxzdzvzWE2ojEvVoxykGMRsoEQnOrJMefEp75Qqt0jnIKvFzUoEc9V75q9tPeBajslwyYzo+TW0wYdoKLnFa6mYGU8ZHbIAdRxWL0QST+alTcuaUPokS7UpZMld/T0xYbMw4Dl1nzOzQLHsz8T+vk9noOpgIlWYWFV8sijJJbEJmf5O+0MitHDvCuBbuVsKHTDNuXTolF4K//PIqaV5UfVr17y8rtZs8jiKcwCmcgw9XUIM7qEMDOAzgGV7hzZPei/fufSxaC14+cwx/4H3+AFaIjSk=AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKcyKoMegF48RzQOSJcxOepMhs7PLzKwQQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrTKUwltJvr7C2vrG5Vdwu7ezu7R+UD4+aJsk0xwZPZKLbITMohcKGFVZiO9XI4lBiKxzdzvzWE2ojEvVoxykGMRsoEQnOrJMefEp75Qqt0jnIKvFzUoEc9V75q9tPeBajslwyYzo+TW0wYdoKLnFa6mYGU8ZHbIAdRxWL0QST+alTcuaUPokS7UpZMld/T0xYbMw4Dl1nzOzQLHsz8T+vk9noOpgIlWYWFV8sijJJbEJmf5O+0MitHDvCuBbuVsKHTDNuXTolF4K//PIqaV5UfVr17y8rtZs8jiKcwCmcgw9XUIM7qEMDOAzgGV7hzZPei/fufSxaC14+cwx/4H3+AFaIjSk=AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKcyKoMegF48RzQOSJcxOepMhs7PLzKwQQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrTKUwltJvr7C2vrG5Vdwu7ezu7R+UD4+aJsk0xwZPZKLbITMohcKGFVZiO9XI4lBiKxzdzvzWE2ojEvVoxykGMRsoEQnOrJMefEp75Qqt0jnIKvFzUoEc9V75q9tPeBajslwyYzo+TW0wYdoKLnFa6mYGU8ZHbIAdRxWL0QST+alTcuaUPokS7UpZMld/T0xYbMw4Dl1nzOzQLHsz8T+vk9noOpgIlWYWFV8sijJJbEJmf5O+0MitHDvCuBbuVsKHTDNuXTolF4K//PIqaV5UfVr17y8rtZs8jiKcwCmcgw9XUIM7qEMDOAzgGV7hzZPei/fufSxaC14+cwx/4H3+AFaIjSk=kAAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipORmUK27VXYCsEy8nFcjRGJS/+sOYpRFKwwTVuue5ifEzqgxnAmelfqoxoWxCR9izVNIItZ8tDp2RC6sMSRgrW9KQhfp7IqOR1tMosJ0RNWO96s3F/7xeasIbP+MySQ1KtlwUpoKYmMy/JkOukBkxtYQyxe2thI2poszYbEo2BG/15XXSvqp6btVrXlfqt3kcRTiDc7gED2pQh3toQAsYIDzDK7w5j86L8+58LFsLTj5zCn/gfP4A0oWM7w==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipORmUK27VXYCsEy8nFcjRGJS/+sOYpRFKwwTVuue5ifEzqgxnAmelfqoxoWxCR9izVNIItZ8tDp2RC6sMSRgrW9KQhfp7IqOR1tMosJ0RNWO96s3F/7xeasIbP+MySQ1KtlwUpoKYmMy/JkOukBkxtYQyxe2thI2poszYbEo2BG/15XXSvqp6btVrXlfqt3kcRTiDc7gED2pQh3toQAsYIDzDK7w5j86L8+58LFsLTj5zCn/gfP4A0oWM7w==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipORmUK27VXYCsEy8nFcjRGJS/+sOYpRFKwwTVuue5ifEzqgxnAmelfqoxoWxCR9izVNIItZ8tDp2RC6sMSRgrW9KQhfp7IqOR1tMosJ0RNWO96s3F/7xeasIbP+MySQ1KtlwUpoKYmMy/JkOukBkxtYQyxe2thI2poszYbEo2BG/15XXSvqp6btVrXlfqt3kcRTiDc7gED2pQh3toQAsYIDzDK7w5j86L8+58LFsLTj5zCn/gfP4A0oWM7w==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipORmUK27VXYCsEy8nFcjRGJS/+sOYpRFKwwTVuue5ifEzqgxnAmelfqoxoWxCR9izVNIItZ8tDp2RC6sMSRgrW9KQhfp7IqOR1tMosJ0RNWO96s3F/7xeasIbP+MySQ1KtlwUpoKYmMy/JkOukBkxtYQyxe2thI2poszYbEo2BG/15XXSvqp6btVrXlfqt3kcRTiDc7gED2pQh3toQAsYIDzDK7w5j86L8+58LFsLTj5zCn/gfP4A0oWM7w==SuccessRateAAAB83icbVDLSgNBEJz1GeMr6tHLYBA8hd1c9Bj04jE+8oBkCbOT3mTI7Owy0yOEkN/w4kERr/6MN//GSbIHTSxoKKq66e6KMikM+v63t7a+sbm1Xdgp7u7tHxyWjo6bJrWaQ4OnMtXtiBmQQkEDBUpoZxpYEkloRaObmd96Am1Eqh5xnEGYsIESseAMndR9sJyDMfSeIfRKZb/iz0FXSZCTMslR75W+uv2U2wQUcsmM6QR+huGEaRRcwrTYtQYyxkdsAB1HFUvAhJP5zVN67pQ+jVPtSiGdq78nJiwxZpxErjNhODTL3kz8z+tYjK/CiVCZRVB8sSi2kmJKZwHQvtDAUY4dYVwLdyvlQ6YZRxdT0YUQLL+8SprVSuBXgrtquXadx1Egp+SMXJCAXJIauSV10iCcZOSZvJI3z3ov3rv3sWhd8/KZE/IH3ucPuRWRdQ==AAAB83icbVDLSgNBEJz1GeMr6tHLYBA8hd1c9Bj04jE+8oBkCbOT3mTI7Owy0yOEkN/w4kERr/6MN//GSbIHTSxoKKq66e6KMikM+v63t7a+sbm1Xdgp7u7tHxyWjo6bJrWaQ4OnMtXtiBmQQkEDBUpoZxpYEkloRaObmd96Am1Eqh5xnEGYsIESseAMndR9sJyDMfSeIfRKZb/iz0FXSZCTMslR75W+uv2U2wQUcsmM6QR+huGEaRRcwrTYtQYyxkdsAB1HFUvAhJP5zVN67pQ+jVPtSiGdq78nJiwxZpxErjNhODTL3kz8z+tYjK/CiVCZRVB8sSi2kmJKZwHQvtDAUY4dYVwLdyvlQ6YZRxdT0YUQLL+8SprVSuBXgrtquXadx1Egp+SMXJCAXJIauSV10iCcZOSZvJI3z3ov3rv3sWhd8/KZE/IH3ucPuRWRdQ==AAAB83icbVDLSgNBEJz1GeMr6tHLYBA8hd1c9Bj04jE+8oBkCbOT3mTI7Owy0yOEkN/w4kERr/6MN//GSbIHTSxoKKq66e6KMikM+v63t7a+sbm1Xdgp7u7tHxyWjo6bJrWaQ4OnMtXtiBmQQkEDBUpoZxpYEkloRaObmd96Am1Eqh5xnEGYsIESseAMndR9sJyDMfSeIfRKZb/iz0FXSZCTMslR75W+uv2U2wQUcsmM6QR+huGEaRRcwrTYtQYyxkdsAB1HFUvAhJP5zVN67pQ+jVPtSiGdq78nJiwxZpxErjNhODTL3kz8z+tYjK/CiVCZRVB8sSi2kmJKZwHQvtDAUY4dYVwLdyvlQ6YZRxdT0YUQLL+8SprVSuBXgrtquXadx1Egp+SMXJCAXJIauSV10iCcZOSZvJI3z3ov3rv3sWhd8/KZE/IH3ucPuRWRdQ==AAAB83icbVDLSgNBEJz1GeMr6tHLYBA8hd1c9Bj04jE+8oBkCbOT3mTI7Owy0yOEkN/w4kERr/6MN//GSbIHTSxoKKq66e6KMikM+v63t7a+sbm1Xdgp7u7tHxyWjo6bJrWaQ4OnMtXtiBmQQkEDBUpoZxpYEkloRaObmd96Am1Eqh5xnEGYsIESseAMndR9sJyDMfSeIfRKZb/iz0FXSZCTMslR75W+uv2U2wQUcsmM6QR+huGEaRRcwrTYtQYyxkdsAB1HFUvAhJP5zVN67pQ+jVPtSiGdq78nJiwxZpxErjNhODTL3kz8z+tYjK/CiVCZRVB8sSi2kmJKZwHQvtDAUY4dYVwLdyvlQ6YZRxdT0YUQLL+8SprVSuBXgrtquXadx1Egp+SMXJCAXJIauSV10iCcZOSZvJI3z3ov3rv3sWhd8/KZE/IH3ucPuRWRdQ==0AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AeRmMtA==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AeRmMtA==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AeRmMtA==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AeRmMtA==0.2AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4CkkR9Fj04rGi/YA2lM120i7dbMLuRiihP8GLB0W8+ou8+W/ctjlo64OBx3szzMwLU8G18bxvZ219Y3Nru7RT3t3bPzisHB23dJIphk2WiER1QqpRcIlNw43ATqqQxqHAdji+nfntJ1SaJ/LRTFIMYjqUPOKMGis9eG6tX6l6rjcHWSV+QapQoNGvfPUGCctilIYJqnXX91IT5FQZzgROy71MY0rZmA6xa6mkMeogn586JedWGZAoUbakIXP190ROY60ncWg7Y2pGetmbif953cxE10HOZZoZlGyxKMoEMQmZ/U0GXCEzYmIJZYrbWwkbUUWZsemUbQj+8surpFVzfc/17y+r9ZsijhKcwhlcgA9XUIc7aEATGAzhGV7hzRHOi/PufCxa15xi5gT+wPn8AVUAjSg=AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4CkkR9Fj04rGi/YA2lM120i7dbMLuRiihP8GLB0W8+ou8+W/ctjlo64OBx3szzMwLU8G18bxvZ219Y3Nru7RT3t3bPzisHB23dJIphk2WiER1QqpRcIlNw43ATqqQxqHAdji+nfntJ1SaJ/LRTFIMYjqUPOKMGis9eG6tX6l6rjcHWSV+QapQoNGvfPUGCctilIYJqnXX91IT5FQZzgROy71MY0rZmA6xa6mkMeogn586JedWGZAoUbakIXP190ROY60ncWg7Y2pGetmbif953cxE10HOZZoZlGyxKMoEMQmZ/U0GXCEzYmIJZYrbWwkbUUWZsemUbQj+8surpFVzfc/17y+r9ZsijhKcwhlcgA9XUIc7aEATGAzhGV7hzRHOi/PufCxa15xi5gT+wPn8AVUAjSg=AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4CkkR9Fj04rGi/YA2lM120i7dbMLuRiihP8GLB0W8+ou8+W/ctjlo64OBx3szzMwLU8G18bxvZ219Y3Nru7RT3t3bPzisHB23dJIphk2WiER1QqpRcIlNw43ATqqQxqHAdji+nfntJ1SaJ/LRTFIMYjqUPOKMGis9eG6tX6l6rjcHWSV+QapQoNGvfPUGCctilIYJqnXX91IT5FQZzgROy71MY0rZmA6xa6mkMeogn586JedWGZAoUbakIXP190ROY60ncWg7Y2pGetmbif953cxE10HOZZoZlGyxKMoEMQmZ/U0GXCEzYmIJZYrbWwkbUUWZsemUbQj+8surpFVzfc/17y+r9ZsijhKcwhlcgA9XUIc7aEATGAzhGV7hzRHOi/PufCxa15xi5gT+wPn8AVUAjSg=AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4CkkR9Fj04rGi/YA2lM120i7dbMLuRiihP8GLB0W8+ou8+W/ctjlo64OBx3szzMwLU8G18bxvZ219Y3Nru7RT3t3bPzisHB23dJIphk2WiER1QqpRcIlNw43ATqqQxqHAdji+nfntJ1SaJ/LRTFIMYjqUPOKMGis9eG6tX6l6rjcHWSV+QapQoNGvfPUGCctilIYJqnXX91IT5FQZzgROy71MY0rZmA6xa6mkMeogn586JedWGZAoUbakIXP190ROY60ncWg7Y2pGetmbif953cxE10HOZZoZlGyxKMoEMQmZ/U0GXCEzYmIJZYrbWwkbUUWZsemUbQj+8surpFVzfc/17y+r9ZsijhKcwhlcgA9XUIc7aEATGAzhGV7hzRHOi/PufCxa15xi5gT+wPn8AVUAjSg=0.4AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ68NzLfrXmud4cZJX4BalBgUa/+tUbJCyLURomqNZd30tNkFNlOBM4rfQyjSllYzrErqWSxqiDfH7qlJxZZUCiRNmShszV3xM5jbWexKHtjKkZ6WVvJv7ndTMTXQc5l2lmULLFoigTxCRk9jcZcIXMiIkllClubyVsRBVlxqZTsSH4yy+vktaF63uuf39Zq98UcZThBE7hHHy4gjrcQQOawGAIz/AKb45wXpx352PRWnKKmWP4A+fzB1gIjSo=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ68NzLfrXmud4cZJX4BalBgUa/+tUbJCyLURomqNZd30tNkFNlOBM4rfQyjSllYzrErqWSxqiDfH7qlJxZZUCiRNmShszV3xM5jbWexKHtjKkZ6WVvJv7ndTMTXQc5l2lmULLFoigTxCRk9jcZcIXMiIkllClubyVsRBVlxqZTsSH4yy+vktaF63uuf39Zq98UcZThBE7hHHy4gjrcQQOawGAIz/AKb45wXpx352PRWnKKmWP4A+fzB1gIjSo=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ68NzLfrXmud4cZJX4BalBgUa/+tUbJCyLURomqNZd30tNkFNlOBM4rfQyjSllYzrErqWSxqiDfH7qlJxZZUCiRNmShszV3xM5jbWexKHtjKkZ6WVvJv7ndTMTXQc5l2lmULLFoigTxCRk9jcZcIXMiIkllClubyVsRBVlxqZTsSH4yy+vktaF63uuf39Zq98UcZThBE7hHHy4gjrcQQOawGAIz/AKb45wXpx352PRWnKKmWP4A+fzB1gIjSo=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ68NzLfrXmud4cZJX4BalBgUa/+tUbJCyLURomqNZd30tNkFNlOBM4rfQyjSllYzrErqWSxqiDfH7qlJxZZUCiRNmShszV3xM5jbWexKHtjKkZ6WVvJv7ndTMTXQc5l2lmULLFoigTxCRk9jcZcIXMiIkllClubyVsRBVlxqZTsSH4yy+vktaF63uuf39Zq98UcZThBE7hHHy4gjrcQQOawGAIz/AKb45wXpx352PRWnKKmWP4A+fzB1gIjSo=0.6AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE1GPRi8eK1hbaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLK6tr6RnmzsrW9s7tX3T941EmmGDZZIhLVDqlGwSU2DTcC26lCGocCW+HoZuq3nlBpnsgHM04xiOlA8ogzaqx077kXvWrNc70ZyDLxC1KDAo1e9avbT1gWozRMUK07vpeaIKfKcCZwUulmGlPKRnSAHUsljVEH+ezUCTmxSp9EibIlDZmpvydyGms9jkPbGVMz1IveVPzP62QmugpyLtPMoGTzRVEmiEnI9G/S5wqZEWNLKFPc3krYkCrKjE2nYkPwF19eJo9nru+5/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step size \u03b7w, while a(cid:62)t a\u2217 gradually increases. This implies the algorithm avoids being attracted\nby the spurious local optimum. In the second stage, wt and at both continuously evolve towards the\nglobal optimum.\nThe second row of Figure 5 illustrates the trajectory of GD without SSW being trapped by the\nspurious local optimum. Speci\ufb01cally, (wt, at) converges to ( \u00afw, \u00afa) as we observe that \u03c6t converges to\n\u03c0, and (cid:107)wt \u2212 w\u2217(cid:107)2\n5 Discussions\n\n2 converges to 4(cid:107)v\u2217(cid:107)2\n2.\n\nFigure 5: Algorithmic behavior of GD on ResNet. The\nhorizontal axis corresponds to the number of iterations.\n\nDeep ResNet. Our two-layer network\nmodel is largely simpli\ufb01ed compared with\ndeep and wide ResNets in practice, where\nthe role of the shortcut connection is more\ncomplicated. It is worth mentioning that\nthe empirical results in Veit et al. (2016)\nshow that ResNet can be viewed as an en-\nsemble of smaller networks, and most of\nthe smaller networks are shallow due to the\nshortcut connection. They also suggest that\nthe training is dominated by the shallow\nsmaller networks. We are interested in in-\nvestigating whether these shallow smaller\nnetworks possesses similar benign proper-\nties to ease the training as our two-layer\nmodel.\nMoreover, our student network and the teacher network have the same degree of freedom. We have\nnot considered deeper and wider student networks. It is also worth an investigation that what is the\nrole of shortcut connections in deeper and wider networks.\nFrom GD to SGD. A straightforward extension is to investigate the convergence of SGD with\nmini-batch. We remark that when the batch size is large, the effect of the noise on gradient is limited\nand SGD mimics the behavior of GD. When the batch size is small, the noise on gradient plays a\nsigni\ufb01cant role in training, which is technically more challenging.\nRelated Work. Li and Yuan (2017) study ResNet-type two-layer neural networks with the output\nweight known (a = 1), which is equivalent to assuming a(cid:62)t a\u2217 > 0 for all t in our analysis. Thus,\ntheir analysis does not have Stage I (a(cid:62)0 a\u2217 < 0). Moreover, since they do not need to optimize a,\nthey only need to handle the partial dissipativity of \u2207Lw with \u03b4 = 0 (one-point convexity). In our\nanalysis, however, we also need to handle the the partial dissipativity of \u2207La with \u03b4 (cid:54)= 0, which\nmakes our proof more involved.\nInitialization. Our analysis shows that GD converges to the global optimum, when w is initialized\nat zero. Empirical results in Li et al. (2016) and Zhang et al. (2019) also suggest that deep ResNet\nworks well, when the weights are simply initialized at zero or using the Fixup initialization. We are\ninterested in building a connection between training a two-layer ResNet and its deep counterpart.\nStep Size Warmup. Our choice of step size \u03b7w is related to the learning rate warmup and layerwise\nlearning rate in the existing literature. Speci\ufb01cally, Goyal et al. (2017) presents an effective learning\nrate scheme for training ResNet on ImageNet for less than 1 hour. They start with a small step size,\ngradually increase (linear scale) it, and \ufb01nally shrink it for convergence. Our analysis suggests that in\nthe \ufb01rst stage, we need smaller \u03b7w to avoid being attracted by the spurious local optimum. This is\nessentially consistent with Goyal et al. (2017). Note that we are considering GD (no noise), hence,\nwe do not need to shrink the step size in the \ufb01nal stage. While Goyal et al. (2017) need to shrink the\nstep size to control the noise in SGD. Similar learning rate schemes are proposed by Smith (2017).\nOn the other hand, we incorporate the shortcut prior, and adopt a smaller step size for the inner layer,\nand a larger step size for the outer layer. Such a choice of step size is shown to be helpful in both\ndeep learning and transfer learning (Singh et al., 2015; Howard and Ruder, 2018), where it is referred\nto as differential learning rates or discriminative \ufb01ne-tuning. It is interesting to build a connection\nbetween our theoretical discoveries and these empirical observations.\n\n9\n\nStage II startsStep size warmup1a>ta\u21e4katk2ka\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>ta\u21e4katk2ka\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\u21e1AAACAHicbVDLSsNAFL2pr1pfVZduBlvBVUnqQpcFNy4rmLbQhjKZTNqhk0mYmQgldOMPuNU/cCdu/RN/wO9wkmahrQcuHM65L46fcKa0bX9ZlY3Nre2d6m5tb//g8Kh+fNJTcSoJdUnMYznwsaKcCepqpjkdJJLiyOe0789uc7//SKVisXjQ84R6EZ4IFjKCtZHc5ihhzXG9YbfsAmidOCVpQInuuP49CmKSRlRowrFSQ8dOtJdhqRnhdFEbpYommMzwhA4NFTiiysuKZxfowigBCmNpSmhUqL8nMhwpNY980xlhPVWrXi7+6wUqX7hyXYc3XsZEkmoqyPJ4mHKkY5SngQImKdF8bggmkpn/EZliiYk2mdVMMM5qDOuk1245V632fbvR6ZQRVeEMzuESHLiGDtxBF1wgwOAZXuDVerLerHfrY9lascqZU/gD6/MHWFWWpg==4kv\u21e4k22AAACE3icbZDLSsNAFIYn9VbrLSq4cTNYBHFRkljQZcGNywr2Am0aJpNJO3QyCTOTQol9DF/Arb6BO3HrA/gCPoeTNgtt/WHg4z/nzDn8fsKoVJb1ZZTW1jc2t8rblZ3dvf0D8/CoLeNUYNLCMYtF10eSMMpJS1HFSDcRBEU+Ix1/fJvXOxMiJI35g5omxI3QkNOQYqS05Zkn9T5rE6HgZHAJ+yJHzxk4nlm1atZccBXsAqqgUNMzv/tBjNOIcIUZkrJnW4lyMyQUxYzMKv1UkgThMRqSnkaOIiLdbH7/DJ5rJ4BhLPTjCs7d3xMZiqScRr7ujJAayeVabv5bC2T+4dJ2Fd64GeVJqgjHi+VhyqCKYR4QDKggWLGpBoQF1fdDPEICYaVjrOhg7OUYVqHt1OyrmnNfrzYaRURlcArOwAWwwTVogDvQBC2AwSN4Bi/g1Xgy3ox342PRWjKKmWPwR8bnDwnrnXE=kwtw\u21e4k22AAACGHicbVDLSgMxFM3UV62vUZfdBIsggmVmFOyy4MZlBfuAPoZMJtOGZh4kdyyldOFv+ANu9Q/ciVt3/oDfYabtQlsPXDicc29u7vESwRVY1peRW1vf2NzKbxd2dvf2D8zDo4aKU0lZncYili2PKCZ4xOrAQbBWIhkJPcGa3vAm85sPTCoeR/cwTlg3JP2IB5wS0JJrFjuiwSTgkQv4Ao9657gjM8F1eo5rlqyyNQNeJfaClNACNdf87vgxTUMWARVEqbZtJdCdEAmcCjYtdFLFEkKHpM/amkYkZKo7mR0xxada8XEQS10R4Jn6e2JCQqXGoac7QwIDtexl4r+er7IHl7ZDUOlOeJSkwCI6Xx6kAkOMs5SwzyWjIMaaECq5/j+mAyIJBZ1lQQdjL8ewShpO2b4sO3dXpWplEVEeFdEJOkM2ukZVdItqqI4oekTP6AW9Gk/Gm/FufMxbc8Zi5hj9gfH5A1UCnx8=kata\u21e4k22AAACGHicbVDLSgMxFM3UV62vqstugkUQwTIzCnZZcOOygn1Apx0yaaYNzWSG5I5QShf+hj/gVv/Anbh15w/4HWbaLrT1wIXDOffm5p4gEVyDbX9ZubX1jc2t/HZhZ3dv/6B4eNTUcaooa9BYxKodEM0El6wBHARrJ4qRKBCsFYxuMr/1wJTmsbyHccK6ERlIHnJKwEh+seSJJlOAiQ/4ApPeOfZUJvhuz/WLZbtiz4BXibMgZbRA3S9+e/2YphGTQAXRuuPYCXQnRAGngk0LXqpZQuiIDFjHUEkipruT2RFTfGqUPg5jZUoCnqm/JyYk0nocBaYzIjDUy14m/uv1dfbg0nYIq90Jl0kKTNL58jAVGGKcpYT7XDEKYmwIoYqb/2M6JIpQMFkWTDDOcgyrpOlWnMuKe3dVrlUXEeVRCZ2gM+Sga1RDt6iOGoiiR/SMXtCr9WS9We/Wx7w1Zy1mjtEfWJ8/DCKe8w==kwtw\u21e4k22AAACGHicbVDLSgMxFM3UV62vUZfdBIsggmVmFOyy4MZlBfuAPoZMJtOGZh4kdyyldOFv+ANu9Q/ciVt3/oDfYabtQlsPXDicc29u7vESwRVY1peRW1vf2NzKbxd2dvf2D8zDo4aKU0lZncYili2PKCZ4xOrAQbBWIhkJPcGa3vAm85sPTCoeR/cwTlg3JP2IB5wS0JJrFjuiwSTgkQv4Ao9657gjM8F1eo5rlqyyNQNeJfaClNACNdf87vgxTUMWARVEqbZtJdCdEAmcCjYtdFLFEkKHpM/amkYkZKo7mR0xxada8XEQS10R4Jn6e2JCQqXGoac7QwIDtexl4r+er7IHl7ZDUOlOeJSkwCI6Xx6kAkOMs5SwzyWjIMaaECq5/j+mAyIJBZ1lQQdjL8ewShpO2b4sO3dXpWplEVEeFdEJOkM2ukZVdItqqI4oekTP6AW9Gk/Gm/FufMxbc8Zi5hj9gfH5A1UCnx8=kata\u21e4k22AAACGHicbVDLSgMxFM3UV62vqstugkUQwTIzCnZZcOOygn1Apx0yaaYNzWSG5I5QShf+hj/gVv/Anbh15w/4HWbaLrT1wIXDOffm5p4gEVyDbX9ZubX1jc2t/HZhZ3dv/6B4eNTUcaooa9BYxKodEM0El6wBHARrJ4qRKBCsFYxuMr/1wJTmsbyHccK6ERlIHnJKwEh+seSJJlOAiQ/4ApPeOfZUJvhuz/WLZbtiz4BXibMgZbRA3S9+e/2YphGTQAXRuuPYCXQnRAGngk0LXqpZQuiIDFjHUEkipruT2RFTfGqUPg5jZUoCnqm/JyYk0nocBaYzIjDUy14m/uv1dfbg0nYIq90Jl0kKTNL58jAVGGKcpYT7XDEKYmwIoYqb/2M6JIpQMFkWTDDOcgyrpOlWnMuKe3dVrlUXEeVRCZ2gM+Sga1RDt6iOGoiiR/SMXtCr9WS9We/Wx7w1Zy1mjtEfWJ8/DCKe8w==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 w/o SSW Convergence to the spurious local optimum \fReferences\nBAHDANAU, D., CHO, K. and BENGIO, Y. (2014). Neural machine translation by jointly learning to\n\nalign and translate. arXiv preprint arXiv:1409.0473 .\n\nBALDUZZI, D., FREAN, M., LEARY, L., LEWIS, J., MA, K. W.-D. and MCWILLIAMS, B.\n(2017). The shattered gradients problem: If resnets are the answer, then what is the question? In\nProceedings of the 34th International Conference on Machine Learning-Volume 70. JMLR. org.\n\nBARRERA, G. and JARA, M. (2015). Thermalisation for stochastic small random perturbations of\n\nhyperbolic dynamical systems. arXiv preprint arXiv:1510.09207 .\n\nBARTLETT, P. L., EVANS, S. N. and LONG, P. M. (2018). Representing smooth functions as\ncompositions of near-identity functions with implications for deep network optimization. arXiv\npreprint arXiv:1804.05012 .\n\nDU, S. S., LEE, J. D., TIAN, Y., POCZOS, B. and SINGH, A. (2017). Gradient descent learns\none-hidden-layer cnn: Don\u2019t be afraid of spurious local minima. arXiv preprint arXiv:1712.00779\n.\n\nGLOROT, X. and BENGIO, Y. (2010). Understanding the dif\ufb01culty of training deep feedforward\nneural networks. In Proceedings of the thirteenth international conference on arti\ufb01cial intelligence\nand statistics.\n\nGOODFELLOW, I., POUGET-ABADIE, J., MIRZA, M., XU, B., WARDE-FARLEY, D., OZAIR, S.,\nCOURVILLE, A. and BENGIO, Y. (2014). Generative adversarial nets. In Advances in neural\ninformation processing systems.\n\nGOYAL, P., DOLL\u00c1R, P., GIRSHICK, R., NOORDHUIS, P., WESOLOWSKI, L., KYROLA, A.,\nTULLOCH, A., JIA, Y. and HE, K. (2017). Accurate, large minibatch sgd: Training imagenet in 1\nhour. arXiv preprint arXiv:1706.02677 .\n\nGRAVES, A., MOHAMED, A.-R. and HINTON, G. (2013). Speech recognition with deep recurrent\nneural networks. In 2013 IEEE international conference on acoustics, speech and signal processing.\nIEEE.\n\nHARDT, M. and MA, T. (2016). Identity matters in deep learning. arXiv preprint arXiv:1611.04231 .\n\nHE, K., ZHANG, X., REN, S. and SUN, J. (2015). Delving deep into recti\ufb01ers: Surpassing human-\nlevel performance on imagenet classi\ufb01cation. In Proceedings of the IEEE international conference\non computer vision.\n\nHE, K., ZHANG, X., REN, S. and SUN, J. (2016a). Deep residual learning for image recognition. In\n\nProceedings of the IEEE conference on computer vision and pattern recognition.\n\nHE, K., ZHANG, X., REN, S. and SUN, J. (2016b). Identity mappings in deep residual networks.\n\narXiv preprint arXiv:1603.05027 .\n\nHOWARD, J. and RUDER, S. (2018). Universal language model \ufb01ne-tuning for text classi\ufb01cation.\n\narXiv preprint arXiv:1801.06146 .\n\nHUANG, G., LIU, Z., VAN DER MAATEN, L. and WEINBERGER, K. Q. (2017). Densely connected\nconvolutional networks. In Proceedings of the IEEE conference on computer vision and pattern\nrecognition.\n\nIOFFE, S. and SZEGEDY, C. (2015). Batch normalization: Accelerating deep network training by\n\nreducing internal covariate shift. arXiv preprint arXiv:1502.03167 .\n\nKRIZHEVSKY, A., SUTSKEVER, I. and HINTON, G. E. (2012). Imagenet classi\ufb01cation with deep\n\nconvolutional neural networks. In Advances in neural information processing systems.\n\nLECUN, Y. A., BOTTOU, L., ORR, G. B. and M\u00dcLLER, K.-R. (2012). Ef\ufb01cient backprop. In\n\nNeural networks: Tricks of the trade. Springer, 9\u201348.\n\n10\n\n\fLI, H., XU, Z., TAYLOR, G., STUDER, C. and GOLDSTEIN, T. (2018). Visualizing the loss\n\nlandscape of neural nets. In Advances in Neural Information Processing Systems.\n\nLI, S., JIAO, J., HAN, Y. and WEISSMAN, T. (2016). Demystifying resnet. arXiv preprint\n\narXiv:1611.01186 .\n\nLI, Y. and YUAN, Y. (2017). Convergence analysis of two-layer neural networks with relu activation.\n\nIn Advances in Neural Information Processing Systems.\n\nLONG, J., SHELHAMER, E. and DARRELL, T. (2015). Fully convolutional networks for semantic\n\nsegmentation. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR).\n\nSINGH, B., DE, S., ZHANG, Y., GOLDSTEIN, T. and TAYLOR, G. (2015). Layer-speci\ufb01c adaptive\nIn 2015 IEEE 14th International Conference on Machine\n\nlearning rates for deep networks.\nLearning and Applications (ICMLA). IEEE.\n\nSMITH, L. N. (2017). Cyclical learning rates for training neural networks. In 2017 IEEE Winter\n\nConference on Applications of Computer Vision (WACV). IEEE.\n\nSMITH, L. N. and TOPIN, N. (2018). Super-convergence: Very fast training of residual networks\n\nusing large learning rates .\n\nSRIVASTAVA, R. K., GREFF, K. and SCHMIDHUBER, J. (2015). Training very deep networks. In\n\nAdvances in neural information processing systems.\n\nVEIT, A., WILBER, M. J. and BELONGIE, S. (2016). Residual networks behave like ensembles of\n\nrelatively shallow networks. In Advances in Neural Information Processing Systems.\n\nYOUNG, T., HAZARIKA, D., PORIA, S. and CAMBRIA, E. (2018). Recent trends in deep learning\n\nbased natural language processing. ieee Computational intelligenCe magazine 13 55\u201375.\n\nYU, X., YU, Z. and RAMALINGAM, S. (2018). Learning strict identity mappings in deep residual\nnetworks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.\n\nZHANG, H., DAUPHIN, Y. N. and MA, T. (2019). Fixup initialization: Residual learning without\n\nnormalization. arXiv preprint arXiv:1901.09321 .\n\nZHOU, M., LIU, T., LI, Y., LIN, D., ZHOU, E. and ZHAO, T. (2019). Toward understanding the\nimportance of noise in training neural networks. In International Conference on Machine Learning.\n\nZHOU, Z., MERTIKOPOULOS, P., BAMBOS, N., BOYD, S. and GLYNN, P. W. (2017). Stochastic\nmirror descent in variationally coherent optimization problems. In Advances in Neural Information\nProcessing Systems.\n\n11\n\n\f", "award": [], "sourceid": 4313, "authors": [{"given_name": "Tianyi", "family_name": "Liu", "institution": "Georgia Institute of Technolodgy"}, {"given_name": "Minshuo", "family_name": "Chen", "institution": "Georgia Tech"}, {"given_name": "Mo", "family_name": "Zhou", "institution": "Duke University"}, {"given_name": "Simon", "family_name": "Du", "institution": "Institute for Advanced Study"}, {"given_name": "Enlu", "family_name": "Zhou", "institution": "Georgia Institute of Technology"}, {"given_name": "Tuo", "family_name": "Zhao", "institution": "Gatech"}]}