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

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"

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

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

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

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

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

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

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

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

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

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

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

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