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.

Explain the Extended Least Squares Assumptions?

What does it mean if the assumptions of ordinary least squares estimator are not met? -Why is this a concern?

Figure 1 shows the results of the statistical test without interaction term between Region and Design (aov1), and the statistical test with interaction term between Region and Design (aov2) as R output for this problem. Figure 1. R output of model results for two statistical models, one without an interaction term between Design and Region (aov1) and one with interaction term between Design and Region (aov2). aovi F) 83.42 5.56e-13 *** 22.27 8. 80e-08 *** 42495 signif. codes: 0 ****' 0.001 ***' 0.01 **' 0.05 '.' 0.1 ''1 aov2 F) þesign Region þesign:Region 6 Residuals 3 94638 8248 34247 31546 22.107 4. 34e-07 *** 0. 963 1375 1427 0.47 24 --- signif. codes: O *** 0.001 0. 01 * 0.05 .' 0.1'1 Using a significant at the significance level alpha = 0.05, based on Figure 1 which statement is correct? %D The model without interaction (aov1) shows that the factors Design and Region are not significant with regards to their impact on survey responses at the selected significance level. The model…