Softmax for Multi-Class Classification (3 marks) A new cell type is added to the experiment which represents the cells affected with virus that were cured by the vaccine. Let's call them Type C. Now, along with the diameter of the stain, we will consider the depth of the stain color as a feature, which can be represented as 12. The softmax function is a multi-class generalization of the logistic sigmoid: p(CX) = exp(ar) (6) exp(a;) Consider a case where the activation functions as are linear functions of the input features. The weights and bias details are provided in the table below. Table 1: Weights and bias for input features Type A | Type B | Type C 2 5 5 2 bias 5 10 1.5 5 1 where 1 = diameter of the stain 1. = depth of the stain color Answer the following questions. (a) Write the equations for activation functions and class probabilities for Type A Type B and Type C cells. (b) Find the class probabilities for Type A Type B and Type C cells for a sample cell with diame- ter=10 and depth=2. What will be the predicted type for the mentioned sample cell? Softmax for Multi-Class Classification (3 marks) A new cell type is added to the experiment which represents the cells affected with virus that were cured by the vaccine. Let's call them Type C. Now, along with the diameter of the stain, we will consider the depth of the stain color as a feature, which can be represented as 12. The softmax function is a multi-class generalization of the logistic sigmoid: p(CX) = exp(ar) (6) exp(a;) Consider a case where the activation functions as are linear functions of the input features. The weights and bias details are provided in the table below. Table 1: Weights and bias for input features Type A | Type B | Type C 2 5 5 2 bias 5 10 1.5 5 1 where 1 = diameter of the stain 1. = depth of the stain color Answer the following questions. (a) Write the equations for activation functions and class probabilities for Type A Type B and Type C cells. (b) Find the class probabilities for Type A Type B and Type C cells for a sample cell with diame- ter=10 and depth=2. What will be the predicted type for the mentioned sample cell