PSY318 Computational Modeling Tom Palmeri. Spring 2014! Mon 1:10-4:00 Wilson 316

Transcription

1 PSY318 Computational Modeling Tom Palmeri Spring 2014!! Mon 1:10-4:00 Wilson 316

2 sheet going around name! department! position! address

3 NO CLASS next week (MLK Day)!! CANCELLED CLASS last week!! Class Presentations: probably Tuesday (Reading Day) after the end of classes (per Dean s Office)

4 What is a model?! What kind of models have you seen?! What are models used for?! Why would we create a model?! Why do you want to learn about modeling?

5 course requirements - readings, attendance, participation (10%) - homework assignments (60%) - final project (30%) auditors and postdocs and others - all graduate students should audit (see Lydia)

6 course web site login : p318 password : p318 can be found from my lab web site, under people, under me, under courses taught

7 required readings Lewandowsky & Farrell textbook pdf files online recommended! Busemeyer & Diederich textbook (available at amazon or elsewhere online)

8 MATLAB who knows it? who has it? all examples and homework assignments will be in MATLAB if someone needs to get access to Matlab, let me know.

9 homework assignments! use Matlab! will be posted on the web site may include some skeleton Matlab code solutions will be posted later

10 final project implement, test, fit, evaluate one or more computational models related to your research (not something you re already doing in your lab) present modeling results (15-20 min) brief description of the model and the situation being evaluated (a couple pages of text)!! include code that I can run this is not a research paper!

11 the who, what, where, when, why, and how of modeling

12 What is a Model?

13 observed stimuli

14 observed stimuli Unobservable Mental/Neural Processes

15 observed stimuli Unobservable Mental/Neural Processes observed behavior

16 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes observed behavior measured behavior cognitive models are abstractions that! explain and predict behavior

17 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes observed behavior measured behavior selection, measurement, summarization

18 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes observed behavior measured behavior selection, measurement, summarization Model

19 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes observed behavior measured behavior selection, measurement, summarization Model predicted behavior

20 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes observed behavior measured behavior selection, measurement, summarization Model predicted behavior

21 observed stimuli Model selection, measurement, summarization Pimo hallmark of cognitive models is that they are derived from basic principles Unobservable of cognition. This observed is what makes cognitive models Mental/Neural different from generic behavior statistical Processes models or empirical curve fitting models. For example, regression models, factor analysis models, structural selection, measurement, equation summarization models, and time series models are generally applicable to data from any field, as long as that data meets the statistical assumptions, such as for example, normality and linearity. These statistical assumptions are not derived from any principles of cognition, and they may even be inconsistent with the known facts of cognition. (Busemeyer & Diederich) measured behavior predicted behavior

22 do we still need models of mechanisms if we can just look at neural mechanisms directly?

23 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes Unobservable Mental/Neural Processes observed behavior measured behavior

24 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes Unobservable Mental/Neural Processes observed behavior measured behavior selection, measurement, summarization Computational Model Stage #1 predicted ERPs Computational Model Stage #2 predicted behavior

25 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes Unobservable Mental/Neural Processes observed behavior measured behavior selection, measurement, summarization Computational Model Stage #1 predicted ERPs

26 Pimo selection, measurement, summarization observed stimuli Unobservable Mental/Neural Processes Unobservable Mental/Neural Processes observed behavior measured behavior selection, measurement, summarization Constraints Model predicted behavior

27

28 Why Model?

29 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Verbal Theory predicted behavior

30 stimuli Unobservable Mental/Neural Processes measured behavior qualitative account stimuli Verbal Theory predicted behavior

31 stimuli Unobservable Mental/Neural Processes measured behavior qualitative account stimuli Verbal Theory predicted behavior

32

33 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior

34 stimuli Unobservable Mental/Neural Processes measured behavior qualitative fit and quantitative fit stimuli Formal Model predicted behavior defined in terms of mathematics and/or computer simulation

35 stimuli stimuli Unobservable Mental/Neural Processes Formal Model measured behavior predicted behavior more, less, faster, slower qualitative fit and quantitative fit precise error rates or response times defined in terms of mathematics and/or computer simulation

36 Formal (i.e., mathematical or computational) theories have a number of advantages that psychologists often overlook. They force the theorist to be explicit, so that assumptions are publicly accessible and the reliability of derivations can be confirmed... (Hintzman, 1990).

37 Formal (i.e., mathematical or computational) theories have a number of advantages that psychologists often overlook. They force the theorist to be explicit, so that assumptions are publicly accessible and the reliability of derivations can be confirmed... (Hintzman, 1990). models are explanations made explicit

38 Formal (i.e., mathematical or computational) theories have a number of advantages that psychologists often overlook. They force the theorist to be explicit, so that assumptions are publicly accessible and the reliability of derivations can be confirmed... (Hintzman, 1990). there can be no hidden assumptions

39 Formal (i.e., mathematical or computational) theories have a number of advantages that psychologists often overlook. They force the theorist to be explicit, so that assumptions are publicly accessible and the reliability of derivations can be confirmed... (Hintzman, 1990). there are no post hoc predictions (though we want to avoid ad hoc assumptions)

40 Formal (i.e., mathematical or computational) theories have a number of advantages that psychologists often overlook. They force the theorist to be explicit, so that assumptions are publicly accessible and the reliability of derivations can be confirmed... (Hintzman, 1990). Models make verifiable predictions

41 To have one s hunches about how a simple combination of processes will behave repeated dashed by one s own computer program is a humbling experience that no experimental psychologist should miss. Surprises are likely when the model has properties that are inherently difficult to understand, such as variability, parallelism, and nonlinearity - all, undoubtedly, properties of the brain. (Hintzman, 1990).

42 To have one s hunches about how a simple combination of processes will behave repeated dashed by one s own computer program is a humbling experience that no experimental psychologist should miss. Surprises are likely when the model has properties that are inherently difficult to understand, such as variability, parallelism, and nonlinearity - all, undoubtedly, properties of the brain. (Hintzman, 1990). Models challenge intuitions

43 .. describing data by means of a model is not an end in itself, but, rather, a preliminary to use of the model as an aid to abstracting generalizable information from the immediate products of research. (Estes, 2002).

44 .. describing data by means of a model is not an end in itself, but, rather, a preliminary to use of the model as an aid to abstracting generalizable information from the immediate products of research. (Estes, 2002). Models explain results

45 .. describing data by means of a model is not an end in itself, but, rather, a preliminary to use of the model as an aid to abstracting generalizable information from the immediate products of research. (Estes, 2002). Models explain results (contrast with machine learning, where developing a model is the goal)

46 .. describing data by means of a model is not an end in itself, but, rather, a preliminary to use of the model as an aid to abstracting generalizable information from the immediate products of research. (Estes, 2002). Models generate predictions

47 models let you see relations between different processes e.g., between different aspects of perception and cognition

48 60 s SCM 70 s Context Model 80 s Instance Theory GCM Poggio & Edelman 90 s TVA ALCOVE EBRW Reisenhuber & Poggio

49 60 s SCM Identification 70 s Context Categorization Model 80 s Instance Theory GCM Poggio & Edelman 90 s TVA ALCOVE EBRW Reisenhuber & Poggio

50 60 s SCM Identification 70 s Context Categorization Model 80 s Instance Theory GCM Poggio Object & Recognition Edelman 90 s TVA ALCOVE EBRW Reisenhuber & Poggio

51 60 s SCM Identification 70 s Context Categorization Model 80 s Instance Automaticity Theory GCM Poggio Object & Recognition Edelman 90 s TVA ALCOVE EBRW Reisenhuber & Poggio

52 60 s SCM Identification 70 s Context Categorization Model 80 s Instance Automaticity Theory GCM Poggio Object & Recognition Edelman 90 s Attention TVA ALCOVE EBRW Reisenhuber & Poggio

53

54 examples from visual cognition

55 Visual Category Learning

56 are these members of! Category A or Category B? at first you ll need to guess,! but I ll provide the right answer.

57 Category A

58

59 Category A

60

61 Category B

62

63 Category A

64

65 Category B

66

67 Category A

68

69 Category A

70

71 Category A

72

73 Category B

74

75 Category A

76

77 Category B

78

79 Category A

80

81 Category A

82

83 Category A

84

85 Category B

86

87 Category B

88

89 Category A

90

91 Categorization Testing

92 A or B

93

94 A or B

95

96 A or B

97

98 A or B

99

100 Dimension 2 Dimension 1

101 Category A Dimension 2 Dimension 1 Category B

102

103 What to model?

104 Why model?

105 Can you model my data?

106 Can you model my data? Why?

107 (I bet your model can t account for my data!)

108 Can you model my data? Why?

109 What do you hope to learn from modeling?

110 Do people learn visual categories by abstracting the prototype of each category? On the genesis of abstract ideas Posner & Keele (1968)

111 Enhanced performance on unseen category prototypes implies prototype abstraction

112 Enhanced performance on unseen category prototypes implies prototype abstraction

113 Enhanced performance on unseen category prototypes implies prototype abstraction

114 Enhanced performance on unseen category prototypes implies prototype abstraction Old Prototype New

115 Enhanced performance on unseen category prototypes implies prototype abstraction prototype enhancement Accuracy Proto Old New

116 What can you learn from modeling?

117 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Model predicted behavior

118 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Model predicted behavior model data (predicted)

119 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Model predicted behavior model data (predicted) data (observed)

120 stimuli Unobservable Mental/Neural Processes measured behavior data (observed) stimuli Model predicted behavior data (predicted) model data (predicted) data (observed)

121 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Model predicted behavior model data (predicted) data (observed) model???

122 Enhanced performance on unseen category prototypes implies prototype abstraction prototype model prototype enhancement

123 Enhanced performance on unseen category prototypes implies prototype abstraction prototype model prototype enhancement prototype enhancement

124 Enhanced performance on unseen category prototypes implies prototype abstraction prototype model prototype enhancement prototype enhancement prototype model???

125 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data (predicted) data (observed) model??? confirmation tells you that the model could be right

126 A model can show the sufficiency of a hypothetical mechanism

127 Logical Fallacy: Affirming the Consequent If Bill Gates owns Fort Knox, then he is rich. Bill Gates is rich. Therefore, Bill Gates owns Fort Knox.! If I have the flu, then I have a sore throat. I have a sore throat. Therefore, I have the flu.! If he wins the lottery, he will buy a new car. He is buying a new car. Therefore, he won the lottery.!

128 A model can show the sufficiency of a hypothetical mechanism show that a mechanism can work

129 A model can show the sufficiency of a hypothetical mechanism show that a mechanism can work

130 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data (predicted) data (observed) model??? confirmation tells you that the model could be right

131 All models are wrong!

132 All models are wrong! It is logically impossible to discover the RIGHT model because there are always an infinite number of possible models explaining the same data

133 All models are wrong! It is logically impossible to discover the RIGHT model because there are always an infinite number of possible models explaining the same data

134 All models are wrong! It is logically impossible to discover the RIGHT mechanism because there are always an infinite number of possible mechanisms explaining the same data

135 All models are wrong! It is logically impossible to discover the RIGHT cognitive process because there are always an infinite number of possible cognitive processes explaining the same data

136 All models are wrong! It is logically impossible to discover the RIGHT neural mechanism because there are always an infinite number of possible neural mechanisms explaining the same data

137 All theories are wrong! It is logically impossible to discover the RIGHT theory because there are always an infinite number of possible theories explaining the same data

138 All theories are wrong! It is logically impossible to discover the RIGHT verbal theory because there are always an infinite number of possible verbal theories explaining the same data

139 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data (predicted)

140 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data (predicted) NOT data (observed)

141 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data (predicted) NOT data (observed) model???

142 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data (predicted) NOT data (observed) NOT model Your model has been falsified.

143 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data (predicted) NOT data (observed) NOT model Your model has been falsified. (But maybe you can fix it )

144 Logical Inference: Denying the Consequent (Modus Tollens) If Bill Gates owns Fort Knox, then he is rich. Bill Gates is not rich. Therefore, Bill Gates does not own Fort Knox.! If I have the flu, then I have a sore throat. I do not have a sore throat. Therefore, I do not have the flu.! If he wins the lottery, he will buy a new car. He is not buying a new car. Therefore, he did not win the lottery.!

145 All models are wrong! It is logically impossible to discover the RIGHT model because there are always an infinite number of possible models explaining the same data

146 All models are wrong! But you can reject whole classes of models.

147 All models are wrong! And use principles like parsimony or a rational analysis to favor the simplest explanation (theory/model) of the data

148 All models are wrong! And use principles like parsimony or a rational analysis to favor the simplest explanation (theory/model) of the data! And favor models that allow us to see new relationships and make new predictions that can be tested

149 Enhanced performance on unseen category prototypes implies prototype abstraction prototype model prototype enhancement prototype enhancement prototype model

150 Enhanced performance on unseen category prototypes implies prototype abstraction prototype model prototype enhancement prototype enhancement prototype model

151 ! What about exemplar models? schema abstraction in a multiple- trace memory model Hintzman (1986)

152 ! What about exemplar models? exemplar model prototype enhancement

153 ! What about exemplar models? exemplar model prototype enhancement prototype enhancement

154 ! What about exemplar models? exemplar model prototype enhancement prototype enhancement exemplar model

155 ! What about exemplar models? exemplar model prototype enhancement prototype enhancement exemplar model

156 We can pit competing models against one another Platt, J.R. (1964). Strong inference. Science, 146,

157 Medin & Schaffer (1978)

158 Medin & Schaffer (1978) prototype model A1 > A2 similarity to the prototype exemplar model A2 > A1 within- and betweencategory similarity

159 Medin & Schaffer (1978) prototype model A1 > A2 exemplar model A2 > A1 A2 > A1 (observed) A2 > A1 (observed)

160 Medin & Schaffer (1978) prototype model A1 > A2 exemplar model A2 > A1 NOT A1 > A2 A2 > A1

161 Medin & Schaffer (1978) prototype model A1 > A2 exemplar model A2 > A1 NOT A1 > A2 A2 > A1 prototype model falsified exemplar model confirmed

162 Models provide alternative explanations

163 Do long- term visual recognition memory and categorization depend on overlapping neural mechanism? Accuracy Knowlton & Squire (1993) Control Amnesic Categorization Recognition

164 Do long- term visual recognition memory and categorization depend on overlapping neural mechanism? Accuracy Knowlton & Squire (1993) Control Amnesic n.s. * Categorization Recognition

165 Single-factor models in which classification judgments derive from, or in any way depend on, long-term declarative memory do not account for the finding that amnesic patients perform well on the classification tasks The learning of categories: Parallel brain systems for item memory and category knowledge Knowlton & Squire (1993)

166 Accuracy Knowlton & Squire (1993) Control Amnesic Categorization Recognition multiple memory systems dissociation single system no dissociation

167 Accuracy Knowlton & Squire (1993) Control Amnesic Categorization Recognition multiple memory systems dissociation single system no dissociation dissociation dissociation

168 Accuracy Knowlton & Squire (1993) Control Amnesic Categorization Recognition multiple memory systems dissociation single system no dissociation dissociation dissociation multiple memory systems confirmed single system falsified

169 Accuracy Knowlton & Squire (1993) Control Amnesic Categorization Recognition multiple memory systems dissociation single system? no dissociation dissociation dissociation multiple memory systems confirmed single system falsified

170 Accuracy Knowlton & Squire (1993) Control Amnesic Categorization multiple memory systems dissociation Recognition dissociation Isn t it intuitively obvious? single system? dissociation no dissociation multiple memory systems confirmed single system falsified

171 predictions from an exemplar model that assumes overlapping representations for recognition and categorization Accuracy Nosofsky & Zaki (1998) Control Amnesic Categorization Recognition

172 Knowlton & Squire (1993) Nosofsky & Zaki (1998) Control Amnesic Control Amnesic Accuracy Accuracy Categorization Recognition Categorization Recognition multiple memory systems dissociation single system dissociation dissociation dissociation multiple memory systems confirmed single system confirmed

173 Why does a model fit data?

174 shape shading size I II III IV V VI Learning and memorization of classikications Shepard, Hovland, & Jenkins (1961)

175 shape shading size II A A A A B B B B Learning and memorization of classikications Shepard, Hovland, & Jenkins (1961)

176 III shape shading size I II IV VI < < < V Learning and memorization of classikications Shepard, Hovland, & Jenkins (1961)

177 III shape shading size I II IV VI < < < singledimension XOR V unique identification Learning and memorization of classikications Shepard, Hovland, & Jenkins (1961)

178 I < II < III, IV, V < VI Learning and memorization of classikications Shepard, Hovland, & Jenkins (1961)

179 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI Learning and memorization of classikications Shepard, Hovland, & Jenkins (1961)

180 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI Shepard, Hovland, & Jenkins (1961)

181 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI Shepard, Hovland, & Jenkins (1961)

182 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) We ve learned that ALCOVE can account for the data

183 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) But why can ALCOVE account for the data?

184 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI

185 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI test a competing theory

186 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI test a competing theory I < III, IV, V < II, VI

187 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI break the model! test a special case

188 Nosofsky, Gluck, Palmeri, McKinley, and Glauthier (1994) I < II < III, IV, V < VI break the model! test a special case I < III, IV, V < II < VI

189 Models motivate new research

190 I < II < III, IV, V < VI Separable Dimensions Integral Dimensions P(Error) I II III IV V VI I II III IV V VI Block Block

191 I < II < III, IV, V < VI Nosofsky & Palmeri (1996) I < III, IV, V < II < VI Separable Dimensions Integral Dimensions I II III IV V VI I II III IV V VI P(Error) Block Block Come full circle Empirical evaluation

192 Models have free parameters

193 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model data

194 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model parameters data response mapping (φ) learning rate (λ w ) sensitivity (c) attn. learning rate (λ α )

195 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model φ, λ w, c, λ α data response mapping (φ) learning rate (λ w ) sensitivity (c) attn. learning rate (λ α )

196 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model φ, λ w, c, λ α data response mapping (φ) learning rate (λ w ) sensitivity (c) attn. learning rate (λ α )

197 stimuli stimuli Unobservable Mental/Neural Processes Formal Model measured behavior predicted behavior minimize SSE model φ, λ w, c, λ α data response mapping (φ) learning rate (λ w ) sensitivity (c) attn. learning rate (λ α )

198 stimuli stimuli Unobservable Mental/Neural Processes Formal Model measured behavior predicted behavior minimize SSE model 2.1,.21, 1.8,.04 data response mapping (φ) learning rate (λ w ) sensitivity (c) attn. learning rate (λ α )

199 Free parameters reflect unknown properties

200 free parameters exist in formal models because they are mathematical expressions even verbal theories have parameters but they are hidden

201 e.g., a verbal theory might say that people are biased to make one response over another HOW MUCH MORE bias? e.g., a verbal theory might say that you pay more attention to one stimulus than another stimulus HOW MUCH MORE attention?

202 With enough free parameters you can fit anything There s one sense that this is true for models that have more parameters than data points.! But sometimes this is said dismissively of any model that has any free parameters (which basically means any model).

203 Is a model falsifiable?

204 stimuli stimuli Unobservable Mental/Neural Processes Formal Model measured behavior predicted behavior minimize SSE model 2.1,.21, 1.8,.04 data response mapping (φ) learning rate (λ w ) sensitivity (c) attn. learning rate (λ α )

205 stimuli stimuli Unobservable Mental/Neural Processes Formal Model measured behavior predicted behavior minimize SSE model 2.1,.21, 1.8,.04 data model 3.2,.71, 2.1,.42 NOT data

206 stimuli Unobservable Mental/Neural Processes measured behavior stimuli Formal Model predicted behavior model 2.1,.21, 1.8,.04 data model 3.2,.71, 2.1,.42 NOT data The model is unfalsifiable!

207 Medin & Schaffer (1978) prototype model A1 > A2 exemplar model A2 > A1 NOT A1 > A2 A2 > A1 prototype model falsified exemplar model confirmed

208 Medin & Schaffer (1978) 1 0 A2 0 1 A1 prototype model A1 > A2 exemplar model A2 > A1 NOT A1 > A2 A2 > A1 prototype model falsified exemplar model confirmed

209 Medin & Schaffer (1978) 1 A2 1 0 A2 0 1 A1 0φ, λw, c, λα A1 0 1

210 Medin & Schaffer (1978) 1 A2 1 0 A2 0 1 A1 0.01,.01,.01,.01 A1 0 1

211 Medin & Schaffer (1978) 1 A2 1 0 A2 0 1 A1 0.01,.01,.01,.02 A1 0 1

212 Medin & Schaffer (1978) A A2 0 1 A1 0.16,.43,.33,.92 A1 0 1

213 Medin & Schaffer (1978) 0 1 A2 0 1 A1 exemplar model

214 Medin & Schaffer (1978) 0 1 A2 0 1 A1 mixed model exemplar model

215 In my opinion the theory here is the logically simplest relativistic field theory that is at all possible. But this does not mean that nature might not obey a more complex theory. More complex theories have frequently been proposed In my view, such more complicated systems and their combinations should be considered only if there exist physical-empirical reasons to do so. Albert Einsten (1921)

216 A model should be as simple as possible, but not simpler. (a version of Occam s Razor)

217 Medin & Schaffer (1978) 1 0 A2 A1 0 1 mixed model exemplar model

218 Medin & Schaffer (1978) 1 0 A2 A1 0 1 mixed model exemplar model

219 Linking models with neural data

220 Training Items Transfer Items Decoding the brain s algorithm for categorization from its neural implementation Mack, Preston, & Love (2013) Does the brain represent learned categories by abstracting prototypes or learning exemplars?

221 Training Items Transfer Items

222 Training Items Transfer Items PA A4 A5 A2 A1 B1 PB A3 B2 B3 B4 Prototype Model Exemplar Model

223 Training Items Transfer Items PA A4 A5 A2 A1 B1 PB A3 B2 B3 B4 Prototype Model Exemplar Model

224 Training Items Transfer Items PA A4 A5 A2 A1 B1 PB A3 B2 B3 B4 Prototype Model Exemplar Model

225 Training Items Transfer Items Latent Model State representational match PA A4 A5 A2 A1 B1 PB A3 B2 B3 B4 Prototype Model Exemplar Model

226 Training Items Transfer Items

227 Training Items Transfer Items

228 Training Items Transfer Items

229