Cognitive Science Computational modelling

1
Cognitive ScienceComputational modelling

• Week 3
• Linear separability
• Configuration files
• Reconstructing Cohens 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
0
Marxist
0
1
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

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