Neural network with linear activation functions
Suppose you had a neural network with linear activation functions. That is, for each unit the output is some constant c times the weighted sum of the inputs.
Assume that the network has one hidden layer. For a given assignment to the weights w, write down equations for the value of the units in the output layer as a function of w and the input layer x, without any explicit mention of the output of the hidden layer. Show that there is a network with no hidden units that computes the same function.
Repeat the calculation in part (a), but this time do it for a network with any number of hidden layers.
Suppose a network with one hidden layer and linear activation functions has n input and output nodes and h hidden nodes. What effect does the transformation in part (a) to a network with no hidden layers have on the total number of weights? Discuss the case h << n.
Sample Answer
Analysis of the Stark Law and a Related Court Case
I. Analysis of the Stark Law
State: The Stark Law, formally known as the Physician Self-Referral Law, prohibits physicians from referring Medicare or Medicaid patients to entities for designated health services 1 if the physician or their immediate family has a financial relationship with that entity, unless an exception applies.
Explain: The Stark Law aims to prevent conflicts of interest that could lead to medically unnecessary referrals, driving up healthcare costs for Medicare and Medicaid. It focuses on situations where physicians may benefit financially from referring patients to entities in which they have a financial stake, such as:
- Owning or investing in the entity: For example, a physician referring patients to a laboratory they own.
- Having a family member with a financial interest in the entity: For instance, a physician referring patients to a clinic where their spouse is a partner.