How do block diagonal and Kronecker product approximations improve the efficiency of second-order methods in neural network optimization, and what are the trade-offs involved in using these approximations?

Second-order optimization methods, such as Newton's method and its variants, are highly effective for neural network training due to their ability to leverage curvature information to provide more accurate updates to the model parameters. These methods typically involve the computation and inversion of the Hessian matrix, which represents the second-order derivatives of the loss function

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