15-883 Midterm Exam

This exam is open book, open notes. You can also use the library or the Web. And you can ask me if you have questions about any of the problems. But you may not discuss the exam with anyone else.

Please type your answers; handwritten answers will not be accepted. You can hand in hardcopy at the start of class on March 2, or email your answers to dst@cs.cmu.edu.

1. Suppose you are given two sets of vectors, A and B, and told that the vectors in A are "highly orthogonal", but the vectors in B are "not very orthogonal". (a) What does it mean for a set of vectors to be highly or not very orthogonal? (b) How would you test the claim about A and B mathematically? (c) Supposing the claim is true, what are its implications, if you're using a matrix memory model?

2. Both Marr and O'Reilly & McClelland used an architecture or mechanism for making patterns more orthogonal. (a) Describe this "codon" mechanism in a few sentences. (b) Which part of the hippocampus is thought to be particularly suited for implementing this mechanism, and why? (c) In order to store memories and accurately recover them from partial cues, both papers relied on another mechanism. Describe it in a few sentences. [Note: don't summarize the entire paper; you need to extract the essential idea and state it clearly.]

3. Suppose area A projects to area B with modifiable synapses that follow the BCM rule, with an adjustable threshold theta equal to 1.5 times the mean activity level of the postsynaptic cell. (a) Write down the equations that describe how learning progresses. (b) Suppose we give a drug that forces cells in area B to fire at a high rate for an extended period of time, i.e., their mean activity leel is 0.99, while the mean activity of area A cells remains steady at about 0.5. What will happen to the value of theta? (c) What will happen to the synapses onto cells in area B? (d) Suppose we cannot counteract the effect of the drug that is making cells in area B hyperactive; we must simply wait for it to wear off. Given your understanding of the BCM learning rule, what could we do to protect the w_AB synapses while waiting for the drug to wear off?

4. Compare the putative role of acetylcholine in the rat hippocampus with that of serotonin in Aplysia. What are the similarities and differences? (A couple of paragraphs should suffice.)

5. (a) Many areas of the brain are organized as maps, e.g., visual cortex is a map of the visual field, and nearby cells have highly overlapped receptive fields. Similarly, somatosensory cortex forms a map of the body's sensory nerve endings. Why aren't place cells laid out topologically, so that nearby cells in hippocampus have nearby firing fields in the environment? (b) Consider the Samsonovich & McNaughton place cell model. Describe the essential computational idea driving this model. (c) How does the Samsonovich & McNaughton model account for the persistence of place fields in the dark? (d) How does the model provide for the rat having a different map in each environment?