Explain the advantages and disadvantages of using Newton’s method versus a first-order method like SGD for optimizing the neural network’s loss function, including any specific considerations for your team’s use case.
Newton’s method can provide faster convergence to optimal solutions but requires access to the Hessian matrix of the loss function. In contrast, first-order methods like SGD are typically faster and easier to implement but may converge slowly to suboptimal solutions.
Propose an extension of RMSProp with Nesterov momentum to handle this multi-term objective function. Explain how you would adapt the algorithm’s parameters and what tradeoffs you would consider.
To extend RMSProp to handle a multi-term objective function, we can modify the algorithm to accumulate gradients from each term separately and then combine them using the weighted sum of individual gradients. This approach allows us to maintain the benefits of RMSProp while adapting to the specific structure of our objective function.
Propose an optimization technique to eliminate redundant common subexpressions in the back-propagation process. Explain how it improves computational efficiency without compromising model accuracy.
Apply a technique like dynamic reordering or memoization to store and reuse computed intermediate values, eliminating redundant computation of common subexpressions. This can be achieved by analyzing the graph structure and identifying opportunities for caching intermediate results.