1. slides created by Leon Barrett
CS 182 Sections 101 & 102
slides created by Leon Barrett
with thanks to
Eva Mok and Joe Makin
Feb. 1, 2008

2. Annoucements a1 is due at 5pm on Tuesday
Remember to submit it electronically
a2 out on Tuesday

3. Where we stand Last Week Neural development Connectionist modeling
Coming up
Psycholinguistics
Brain imaging
Neural nets and Backprop

4. a1 questions?

5. Flexor-
Crossed
Extensor
Reflex
(Sheridan
1900)
Reflex
Circuits
With
Inter-neurons
Painful Stimulus

6. Neural development How do neurons develop?
Pre-neuron cells split into neurons
Neurons migrate
Neuron axons follow chemical clues to destinations
Pruning of synapses
What is a chemical gradient? How does a neuron use one?
changing concentration; neuron uses this as a guide

7. Neural development What is the neural plate? the neural tube?
The neural plate is a layer of cells that will become neurons
In early development, the embryo curls up laterally, so the neural plate is curled into a tube
What is a critical period? Can you name one?
A period outside of which certain learning cannot occur
There are critical periods at least for:
Language
Vision

8. Neural Tube formation

9. Neural development
When you consume alcohol, thousands of neurons die. How does your brain deal with this?
Duplicated, inhibited connections
New neurons don't (usually) grow, but new connections can grow
Humans come pre-wired for learning
Some plasticity
Activity dependent fine tuning
Long term memory
Pre-wiring biases the way we learn

10. Neural modeling Why model neurons? to understand them and the brain
to try to accomplish what they do
Why model them in different ways?
to do those different things
science: modeling at different levels allows different types of understanding

11. Neuron models What is a McCullough-Pitts neuron?
Calculate “activation” by weighted sum of inputs
Use a function to map activation to output
What sorts of output functions does it use?
Linear – why is this bad?
Threshold
Sigmoid – smoothed threshold

12. The McCullough-Pitts Neuronxi f yj
wij yi
xi = ∑j wij yj
yi = f(xi)
ti : target
yj: output from unit j
Wij: weight on connection from j to i
xi: weighted sum of input to unit i

13. Let’s try an example: the AND function
w01 y0 i2
b=1
w02
w0b 1 y0 i2 i1
Assume you have a threshold function centered at the origin
What should you set w01, w02 and w0b to be so that you can get the right answers for y0?

14. Many answers would work
y = f (w01i1 + w02i2 + w0bb)
recall the threshold function
the separation happens when w01i1 + w02i2 + w0bb = 0
move things around and you get
i2 = - (w01/w02)i1 - (w0bb/w02) i2 i1

15. Neuron models
If neurons spike, what biological feature do non-integer values correspond to?
Firing rate
What is unbiological about the McCullough-Pitts model?
Time is ignored
Weights are unlimited
Hugely simplifies computations
Some people propose that real neurons do complicated quantum-mechanical things

16. Neuron models
How does a Sigma-Pi neuron differ from a McCullough-Pitts neuron?
It multiplies sets of inputs

17. Sigma-Pi units

18. Sigma-Pi Unit