The objective is to develop a basic neural$-$network to classify fashion images from the

Fashion$-$MNIST dataset. Fashion$-$MNIST database is a collection of images for various fashion

items, and the task is to create a neural network that can accurately classify these items into

different categories.

$1.$ Data Loading and Preprocessing: In this step, load the dataset that contains $28$x$28$ pixel

grayscale images, each representing a specific fashion item $($e$.$g$.,$ shoes, t$-$shirts, etc.$).$

Analyze the test$-$train images with labels in order to identify the unique images and name

them.

$2.$ Neural Network Model: The neural network will feature a simple architecture with two

to three hidden layers. One has to implement the forward pass using ReLU activation for

the hidden layers and softmax for the output layer.

$3.$ Model training and Evaluation: Train the neural network using both Stochastic

Gradient Descent $($SGD$)$ to implement the training loop, forward pass, and

backpropagation. After training, assess the model's performance on the test set, using

accuracy as the evaluation metric.

$4.$ Visualization and Improvements: Visualize the misclassified examples and report their

numbers for each category. Additionally, explore at least $6$ improvements such as tuning

parameters like a$)$ epochs and batch$-$size, b$)$ modifying the model architecture and

activation function, and c$)$ employing advanced optimization $($Adam optimizer or more$)$

techniques.

$5.$ Regularization: Now retrain separate ML models using L$1$ and L$2$ regularizers in the

loss function respectively. Make accuracy plots for no regularization, L$1$ and L$2.$ Could

you provide insights into which model performs better and your reasoning behind the

conclusion? Note: All models should have the same architecture