Problem 8: Sample Complexity of Learning with Neural Tangent Kernel (NTK) Statement: Using the Neural Tangent Kernel framework, derive the sample complexity required for a neural network to generalize well on a given learning task. Prove how the sample complexity depends on factors such as the network's depth, width, and the properties of the target function. Key Points for the Proof: • Introduce the Neural Tangent Kernel and its relevance to neural network training dynamics. • Link the NTK to generalization performance and sample complexity. Analyze how architectural parameters influence the NTK and, consequently, the sample complexity. . Provide bounds that relate network properties to the number of samples needed for accurate learning.

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