1. Cognitive Science Computational modelling
Week 3
Linear separability
Configuration files
Reconstructing Cohen’s model of autism

2. Objectives of this workshop
To gain more familiarity with Tlearn
To learn how to set up a network in Tlearn
To train and evaluate a backprop network learning "Exclusive OR"
To appreciate the difficulty of analysing network performance
To train and evaluate a backprop network model of "autism"

3. "Exclusive OR“ & hidden units
"John is a Tory or John is a Marxist"
Either Tory, or Marxist, but not both.
Compositional

4. Linear separability XOR truth table as a graph
2 dimensions (one for each input)
Plot the corresponding target output
Tory 1 1 1
Marxist

5. Exercise Draw the corresponding graph for ‘and’ e.g.
Sue likes Radiohead and chocolate cake
Is ‘and’ linearly separable?

6. Number of inputs: 2 i1, i2
Number of hidden: ? two? #1, #2
Number of outputs: 1 #3
xor-1501.wts
contains the weights saved after 1501 learning trials with the set of training patterns
For exercise
follow from p117, Chapter 5

7. Cohen's model of learning in autism
Too many and too few neurons and/or connections
- Some things hard to learn
- Poor generalisation
Model looks at effect of
irrelevant inputs
extra hidden units
Rote learning good
Distracted by task-irrelevant aspects of the situation
Poor generalisation: eg change teacher or environment, don’t perform well
Too many eg hippocampus; too few eg cerebellum

8. Happy face
mouth up -1 … 1 (+ve = smile)
eyebrows 0 … -1 (-ve = smile*)
*roughly
See Figure 11.3, but note that the vertical axis has the wrong values

9. Reconstructing Cohen Re-create input patterns
Re-create the target for each input pattern
Put those patterns into .data and .teach files
Create configuration file

10. Input patterns 5 input values in each pattern 1st : mouth
2nd : eyebrow
3rd, 4th, 5th : mimic task-irrelevant features of the situation

11. Values for ‘xtra’ inputs
Random numbers
should be noise
easy way to do it is using SPSS …
then “Save as…” comma delimitted

12. Overview Create training pattern inputs with 5 input values, n = 16
- and corresponding targets in a .teach file
Create 8 more in a separate .data file [why?] nb no .teach file needed for these
Create configuration file
Train; every so many trials, test both the training set & the configuration set

13. Overview ctd Do it all again, with just one irrelevant xtra input
Hint: you only need to make small changes to some of the files you already have

14. Overview concluded Evaluate the results Quantitatively
error as learning progresses, on training set
error as learning progresses, generalisation
compare results for 1 irrelevant v 3 irrelevant
Qualitatively
Mapping parameters onto theory
eg number of inputs; what does it stand for from the theory
Mapping to cognitive performance
Mapping to biology