1. Where are we? What’s left? HW 7 due on Wednesday Finish learning this week. Exam #4 next Monday Final Exam is a take-home handed out next Friday in class Scheduled Final Exam meeting – turn in your exam, your team’s final paper, and your final timecard

2. What are these?

3. Truth table for an OR gate Truth table for an AND gate AND gate and OR gate ABQ 000 010 100 111 ABQ 000 011 101 111

4. ICS6114 Biological Inspiration Brain vs. Computers The Perceptron Multilayer networks Some Applications Artificial Neural Networks

5. Biological inspiration Animals are able to react adaptively to changes in their external and internal environment, and they use their nervous system to perform these behaviours. An appropriate model/simulation of the nervous system should be able to produce similar responses and behaviours in artificial systems. The nervous system is build by relatively simple units, the neurons, so copying their behavior and functionality should be the solution.

6. Brain and Machine The Brain –Pattern Recognition –Association –Complexity –Noise Tolerance The Machine –Calculation –Precision –Logic

7. The contrast in architecture The Von Neumann architecture uses a single processing unit; –Tens of millions of operations per second –Absolute arithmetic precision The brain uses many slow unreliable processors acting in parallel

8. The Structure of Neurons 10 11 neurons of at least 20 types. 10 14 synapses 1-10 ms cycle time Signals are noisy “spike trains” of electrical potential Neurons die off frequently (never replaced) Compensates for problems by massive parallelism

9. A neuron only fires if its input signal exceeds a certain amount (the threshold) in a short time period. Synapses vary in strength –Good connections allowing a large signal –Slight connections allow only a weak signal. –Synapses can be either excitatory or inhibitory. The Structure of Neurons

10. The spikes travelling along the axon of the pre- synaptic neuron trigger the release of neurotransmitter substances at the synapse. The neurotransmitters cause excitation or inhibition in the dendrite of the post-synaptic neuron. The integration of the excitatory and inhibitory signals may produce spikes in the post-synaptic neuron. The contribution of the signals depends on the strength of the synaptic connection.

11. Translating this to ANN The McCullogh-Pitts model: spikes are interpreted as spike rates; synaptic strength are translated as synaptic weights; excitation means positive product between the incoming spike rate and the corresponding synaptic weight; inhibition means negative product between the incoming spike rate and the corresponding synaptic weight;

12. The McCulloch-Pitts “Unit” Each neuron has a threshold value Each neuron has weighted inputs from other neurons The input signals form a weighted sum If the activation level exceeds the threshold, the neuron “fires”

13. The Activation Function (a)Is a step function or threshold function (b)Is sigmoid function [ 1/(1+e-x) ] Changing the bias weight Wo,I moves the threshold location.

14. Any Boolean function can be implemented using a McCulloch and Pitts perceptron -0.5

15. What function does perceptron #1 represent? 0.8 0.7 0.6

16. What function does perceptron #2 represent? 0.8 0.3 0.2 0.8

17. What function does perceptron #3 represent? 0.8 - 0.8 0.3 0.6- 0.4