Suggestions for exam questions

1. After graduation you join the FBI and are assigned the task of writing a system to recognize fuzzy photographs of active criminals. You have a database of clear photographs available to you. Describe a connectionist architecture to accomplish this task. Be specific about the network architecture, how you would represent the photographs, and how you would train the system.

   When you present your implementation plans to the boss she is concerned that connectionist systems are not as powerful or as efficient as more traditional methods. Either give a convincing argument to win her over to using neural networks or describe how you would implement a symbolic system to accomplish the task instead.

2. Consider a connectionist network with three inputs and one output unit using the step activation function. Such a perceptron model can only solve problems from the class of linearly separable functions. For each of the following problems explain whether the function is linearly separable. You may want to use three dimensional pictures of cubes to visualize whether the functions are linearly separable. If a function is separable, give a set of weights and thresholds that solve the problem. Otherwise, determine the minimum multi-layer network to solve the problem and indicate appropriate weights and thresholds.
   1. The output unit turns on only when exactly one of the three inputs is on.
      Patterns 1 0 0, 0 1 0, and 0 0 1 turn on the output unit.
   2. The output unit turns on when more than one input is on.
      Patterns 1 1 1, 1 1 0, 1 0 1, and 0 1 1 turn on the output unit.
   3. The output unit turns on when inputs two and three are on.
      Patterns 1 1 1 and 0 1 1 turn on the output unit.
   4. The output unit turns on when exactly one or two inputs are on.
      Patterns 1 0 0, 0 1 0, 0 0 1, 1 1 0, 1 0 1, 0 1 1 turn on the output unit.
   5. The output unit turns on when the activation of input one equals the activation of input three.
      Patterns 0 0 0, 0 1 0, 1 1 1, and 1 0 1 turn on the output unit.