Q$1)$ Perceptron Trees: To exploit the desirable properties of decision tree classifiers and perceptrons, Adam came up with a new algorithm called "perceptron trees", which combines features from both. Perceptron trees are similar to decision trees, however each leaf node is a perceptron, instead of a majority vote.

To create a perceptron tree, the first step is to follow a regular decision tree learning algorithm $($such as ID$3)$ and perform splitting on attributes until the specified maximum depth is reached. Once maximum depth has been reached, at each leaf node, a perceptron is trained on the remaining attributes which have not been used up in that branch. Classification of a new example is done via a similar procedure. The example is first passed through the decision tree based on its attribute values. When it reaches a leaf node, the final prediction is made by running the corresponding perceptron at that node.

Assume that you have a dataset with $6$ binary attributes $($A$,$ B$,$ C$,$ D$,$ E$,$ F$)$ and two output labels $(-1$ and $1).$ A perceptron tree of depth $2$ on this dataset is given below. Weights of the perceptron are given in the leaf nodes. Assume bias $=1$ for each perceptron:

Figure $1$: Perceptron Tree of max depth$=2$

Predict the output labels for the following two samples:

a$)x=(1,1,0,1,0,1)$

b$)x=(0,1,0,1,0,1)$