Problem $4$: Exploring Neural Network Training $(15$ points$)$

In class, we explored the TensorFlow Playground website to develop an intuitive understanding of how

neural networks function by experimenting with various parameters and observing their effects on

classifying non$-$linear datasets. In this exercise, your goal is to fine$-$tune the parameters to successfully

classify the non$-$linear "spiral" dataset.

Instructions:

Go to the TensorFlow Playground website, select the "Spiral" dataset from the "Data" option

and pick "Classification" from the "Problem Type" menu.

Run the neural network with the default parameters and observe how well or badly it classifies

the dataset. Adjust the number of hidden layers and neurons in each layer to observe how it

impacts the model's ability to classify the data correctly.

Change the activation function of the hidden layers $($e$.$g$.,$ switch between ReLU, Tanh, and

Sigmoid$)$ and observe how the decision boundaries change.

You do not need to play around with the learning rate and regularization at this moment.

Write a brief summary of your observations from the experiments:

Which combinations of parameters $($such as the number of neurons and choice of activation

function$)$ were most effective for classifying the spiral dataset?

How did the choice of activation function affect the model's ability to create non$-$linear

decision boundaries?

How did individual neurons in each hidden layer contribute to the classification?

Lower Layers: Observe how neurons in the initial hidden layers tend to classify the data

into simpler, binary$-$like regions.

Higher Layers: Notice how neurons in deeper layers capture more complex, non$-$linear

trends necessary for accurately classifying the spiral dataset.

Include screenshots of your experiment setups, particularly those configurations that result in

the best performance.