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تسجيل مستخدم جديدTowards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
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Gradient descent yields zero training loss in polynomial time for deep neural networks despite non-convex nature of the objective function. The behavior of network in the infinite width limit trained by gradient descent can be described by the Neural Tangent Kernel (NTK) introduced in cite{Jacot2018Neural}. In this paper, we study dynamics of the NTK for finite width Deep Residual Network (ResNet) using the neural tangent hierarchy (NTH) proposed in cite{Huang2019Dynamics}. For a ResNet with smooth and Lipschitz activation function, we reduce the requirement on the layer width $m$ with respect to the number of training samples $n$ from quartic to cubic. Our analysis suggests strongly that the particular skip-connection structure of ResNet is the main reason for its triumph over fully-connected network.
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Residual Network (ResNet) is undoubtedly a milestone in deep learning. ResNet is equipped with shortcut connections between layers, and exhibits efficient training using simple first order algorithms. Despite of the great empirical success, the reaso
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Deep residual network architectures have been shown to achieve superior accuracy over classical feed-forward networks, yet their success is still not fully understood. Focusing on massively over-parameterized, fully connected residual networks with R
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Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a significantly wor
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