This is an important slide wherein we can learn how and why machine learning algorithms work and why do linear models fail. So we discussed multiple classes, the problem here is classification. For example, we are showing two classes: class 1 and class 2, both represented with two colors. It's very simple to classify the set with separate lines. This can be classified by drawing a separate straight line between these two classes. Such problems can be solved using traditional models too and machine learning models might not be required. But, since this is a two-dimensional problem, this can be solved easily. How about multidimensional problems? For such problems, the non-linear models or existing mathematical problems fail. Suppose we have an N gate here in two dimensional space, we have I1 and I2. When input is 0 0, then output should be equal to 0. When the input is 0 1, output should be 0. When the input is 1 0, output should be 0. When input is 1 1, output should be 1. This means output should be 1 only when both inputs are equal to 1. This is fairly straightforward, then where is the problem? It exists in XOR gate; wherein, the desired output is 0 1 1 0. Here, we are unable to differentiate nor classify it with a separate line. This is where the third dimension comes into play and we will see the use of artificial neural networks. With the hidden layers in artificial neural networks we are able to solve the three dimensional problems. Nowadays, data is so uncertain, as the dimensions keep increasing it becomes more complicated and difficult to solve by dense models. This is the reason we are going for artificial neural networks for such multidimensional problems.