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McCulloch Pitts Neurons (page 2)

Author: Michael Marsalli
Additional Credits:
Funding
This module was supported by National Science Foundation Grants #9981217 and #0127561.

So far we have only considered signals coming from the bird's receivers that are added to the other signals coming from the other receivers. These types of signals are called excitatory because they excite the neuron toward possibly sending its own signal. The more excitatory signals a neuron receives, the closer the total will be to the neuron's threshold, and so the closer the neuron will be to sending its signal. So as the neuron receives more and more excitatory signals, it gets more and more excited, until the threshold is reached, and the neuron sends out its own signal. But there is another kind of signal that has the opposite effect on a neuron. These other signals are called inhibitory signals, and they have the effect of inhibiting the neuron from sending a signal. When a neuron receives an inhibitory signal, it becomes less excited, and so it takes more excitatory signals to reach the neuron's threshold. In effect, inhibitory signals subtract from the total of the excitatory signals, making the neuron more relaxed, and moving the neuron away from its threshold.

MCP neurons with an inhibitory signal

Now let's look at an example of an MCP neuron with an inhibitory signal. Let's consider a a particular type of bird, say a robin. Now the robin, which has red feathers on its breast, is safe around any red objects, including red creatures such as a cardinal. Suppose our robin's brain has a neuron with two receivers connected to the robin's eyes. Normally our robin will flee from any other creature it sees. If the robin sees another creature, an excitatory signal will be sent to the first receiver, which will try to cause the bird to flee. So the first receiver is a creature detector, and it excites our bird to fleeing. However, if the creature that the robin sees has red on it, an inhibitory signal will be sent to the second receiver, which will prevent the bird from fleeing. So the second receiver is a red detector, and it inhibits our bird from fleeing.

Suppose our robin sees a black cat. What would happen? The creature detector would send an excitatory signal to the neuron, and the red detector would send no signal. So the bird would flee.

Suppose our robin sees a cardinal. The creature detector would send an excitatory signal to the neuron, and the red detector would send an inhibitory signal. So the bird would not flee, because the inhibitory signal would "cancel" the excitatory signal.

Here is a table that summarizes how this MCP neuron with the excitatory and inhibitory signals would work in several cases.

Table 4

Object

Creature?

Red?

Flee?

Black Cat

Yes

No

Yes

Male
Cardinal

Yes

Yes

No

Hot Dog

No

Yes

No



Exercise 4. What would a row of Table 4 look like if the object were another robin? What would a row look like if the object were a violet?

Now we'll see how these new ideas of excitatory and inhibitory signals work when the MCP neuron compares these signals to its threshold. As before, we'll use a 1 if an excitatory signal is sent, and a 0 if no excitatory signal is sent. But now we'll use a -1 when an inhibitory signal is sent, and a 0 if no inhibitory signal is sent. Because we are using a -1 for an inhibitory signal, when we add an inhibitory signal to the total of all signals received, the effect of the inhibitory signal on the total is to subtract a 1. (Recall that adding a -1 is the same as subtracting a 1.) So when an MCP neuron computes the total effect of its signals, it will add a 1 to the total for each of the excitatory signals and add a -1 to the total for each of its inhibitory signals. If the total of excitatory signals and inhibitory signals is greater than or equal to the threshold, then the MCP neuron will send a 1. If the total of excitatory signals and inhibitory signals is less than the threshold, then the MCP neuron will send a 0.

(We note that this is not how McCulloch and Pitts handled the effect of an inhibitory signal, but we have changed their approach in order to ease the transition to modern neural networks. In fact, for McCulloch and Pitts, if a neuron receives an inhibitory signal, then it will not send out a signal, i.e. the effect of any inhibitory signal is to cause the neuron to send a 0.)

Let's look at an example. Suppose we have an MCP neuron connected to a creature detector that sends an excitatory signal and a red detector that sends an inhibitory signal. Let's also suppose the threshold is 1. We could have chosen another number for the threshold. Now for each object in Table 4, we can compute the total of the signals by adding a 1 for each excitatory signal and a -1 for each inhibitory signal. Then we compare the total to the threshold.

If the robin sees a black cat, then the creature detector, which is excitatory, sends a 1, because the cat is a creature. The red detector, which is inhibitory, sends a 0 , because the cat is not red. Because there is one excitatory signal and no inhibitory signal, the total is 1 + 0 = 1 We compare this total of 1 to the threshold. Because the total of 1 is equal to the threshold of 1, the MCP neuron will send a 1, and so the robin will flee.

If the robin sees a male cardinal, then the creature detector, which is excitatory, sends a 1, because the cardinal is a creature. The red detector, which is inhibitory, sends a -1, because the cardinal is red. Because there is one excitatory signal and one inhibitory signal, the total is 1 + -1 = 0. We compare this total of 0 to the threshold. Because 0 is less than the threshold of 1, the MCP neuron will send a 0, and so the robin will not flee.

If the robin sees a hot dog, then the creature detector, which is excitatory, sends a 0, because the hot dog is not a creature. The red detector, which is inhibitory, sends a -1, because the hot dog is red. Because there is no excitatory signal and one inhibitory signal, the total is 0 + -1 = -1. We compare this total of -1 to the threshold. Because -1 is less than the threshold of 1 , the MCP neuron will send a 0, and so the robin will not flee.

Exercise 5. Find the signal this MCP neuron sends when the robin sees a blue marble.

We can summarize how this MCP neuron works in the table below.

Table 5

Object

Creature?

Excitatory

Red?

Inhibitory

 Total

 Greater than or equal to threshold of 1?

Flee?

Black Cat

1

0

 1

 Yes

1

Male Cardinal

1

-1

 0

 No

0

Hot Dog

0

-1

-1

 No

0


Copyright: 2006