$(40$ points$)$ Implement the neural network model with the architecture specified as below.

multilayer neural network model with two fully connected hidden layers with $1,024$ neurons each; do NOT use convolutional layers. The last layer should have $10$ neurons for the $10$ classes in CIFAR$-10$ dataset.

activation function: ReLU, except for the last layer, which should use the sigmoid activation function.

Loss function: Crossentropy loss

mini$-$batch size: $64$

$1$

Train the model using the four optimization algorithms mentioned above for $200$ epochs. Use the CIFAR$-10$ dataset for training the model.

Plot the training losses of the four algorithm. Explain the convergence behavior of each optimization algorithm based on the plots. Which optimization algorithm reaches the lowest training loss?