Define the tuning curve, noise and signal correlations.

 

  1. ( a) Define the tuning curve, noise and signal correlations. (each 5 points )

(b) Consider two neurons, with Bell shaped tuning curves. If these two neurons are   positively signal correlation, how does the presence or absence of noise correlations between them neurons influence stimulus-response mutual information? (10 points)

  1. Describe two consequences of the inhibition-excitation balance in a recurrent network. ( each 5 points )
  2. Define the following terms
    • Supervised learning (5)
    • Bistability (5)
    • Basin of attraction (5)
    • Spike-triggered and double-spike triggered averages. (10)

4 . (a) Given the response of a neurons R to stimuli S, how is the stimulus response mutual information defined? (5 points)

Suppose you present 3 stimuli to an animal each 100 times except for the last one which is presented 300 times. Assume that this presentation protocol reflects the prior about the stimuli p(s), and that the following response frequencies were collected

 

Stimulus/

Response

5 spikes 10 spikes 20 spikes
stimulus 1 50 times 50 times 0 times
stimulus 2 50 times 25 times 25 times
stimulus 3 100 times 150 times 50 times
  • What is the entropy of stimulus set? (5 points )
  • What is the entropy of responses? (5 points)
  • What is the stimulus response mutual information? (5)
  • Assume that after these measurements, someone shows one of the stimuli to the animal. Assuming the same stimulus prior as before,
    • What is the maximum likelihood stimulus if the neuron emits 10 spikes (5 points)?
    • What is the maximum a posteriori stimulus (5 points)?

5 . In the network below, neurons shown as squares are binary neurons (0 and 1 output ) with a firing threshold of 2 and are receiving inputs as shown. The neuron shown as circle is a threshold-linear neuron, with the threshold of 1 and gain of 2. The number on each arrow is the weight of the coupling.

  • What is the output? (8 points)
  • What happens to the output if we double all the weights to the binary (square) neurons (2 points)?
  • What happens to the output if we double all weights in the network (5 points)?
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