A Bayesian Approach to the Reading Process: From Networks to Human Data

A Bayesian ApproachA Bayesian Approachto the Reading Process:to the Reading Process:

From Networks to Human DataFrom Networks to Human Data

David A. MedlerCenter for the Neural Basis of Cognition

Carnegie Mellon University

Bayesian ConnectionsBayesian Connections

• The Bayesian Approach to Cognitive Neuroscience– How do we represent the world?– Bayesian Connectionist Framework.

• Bayesian Generative Networks– Learning letters.– How does context affect learning?– Empirical and Simulation Results.

• Symmetric Diffusion Networks– The Ambiguity Advantage/Disadvantage.

• Closing Remarks

P( )P( )

Representing the WorldRepresenting the World

• Problem: how do we form meaningful internal representations, P(H), given our observations of the external world, P(D)?

• For a given hypothesis, H, and observed data, D, the posterior probability of H given D is computed as:

Bayesian TheoryBayesian Theory

(D)(H)H)(D|

D)|(HP

where– P(H) = prior probability of the hypothesis, H– P(H ) = probability of the data, D– P(D | H) = probability of D given H

• For a given hypothesis, H, and observed data, D, the posterior probability of H given D is computed as:

Bayesian TheoryBayesian Theory

(H)(D)D)|(H

H)(D|P

where– P(H) = prior probability of the hypothesis, H– P(H ) = probability of the data, D– P(D | H) = probability of D given H

Bayesian ConnectionismBayesian Connectionism

Representation LayerP(H)

Mediating Layer

P(D) Surface Layer

Mediating Layer

P(D) Surface Layer

Mediating Layer

P(D) Surface Layer

It was 20 years ago today...It was 20 years ago today...

An Interactive Activation Model of Context Effects in Letter Perception

James L. McClelland & David E. Rumelhart (1981; 1982)

• Word superiority effect– words > pseudowords > nonwords

• The model accounted for the time course of perceptual identification.

Interactive Activation ModelInteractive Activation Model

FeatureLevel

LetterLevel

WordLevel

Interactive Activation ModelInteractive Activation Model

FeatureLevel

LetterLevel

WordLevel

20 Years Later...20 Years Later...

• Interactive Activation (IA) Model has been influential.

• Many positives, but 20 years of negatives.

• Internal representations are hard-coded:

The Interactive Activation Model does not learn!

• Closing Remarks

Bayesian Generative NetworksBayesian Generative Networks

• Initial work is an expansion of the Bayesian Generative Network framework of Lewicki & Sejnowski, 1997.

• It is an unsupervised learning paradigm for multilayered architectures.

• Simplified network equations, added sparse coding constraints, & included a “supervised” component.

P(D) Surface Layer

Mediating Layer

Bayesian Generative NetworksBayesian Generative Networks

P(D) Surface Layer

Mediating Layer

Sparse Coding ConstraintsSparse Coding Constraints

• Modified the basic framework to include “sparse coding” constraints.

• These are a Bayesian prior that constrain the types of representations learned.

• Sparse coding encourages the network to represent any given input pattern with relatively few units.

Step 1: Learning the AlphabetStep 1: Learning the Alphabet

• First stage of the IA model is the mapping between features and letters.

• We use the Rumelhart & Siple (1974) character features.

Network LearningNetwork Learning

• 16 surface units (corresponding to 16 line segments)

• 30 representation units

• Trained for 50 epochs (evaluated at 1, 10, 25 & 50)

• Evaluated:– Generative capability of the network– Internal representations formed

Generating the AlphabetGenerating the Alphabet

1 10 25 50

No Sparse Coding Sparse Coding

Interpreting Weight StructureInterpreting Weight Structure

Network WeightsNetwork Weights

Unit 20Unit 19Unit 18Unit 17Unit 16Unit 15Unit 14Unit 13Unit 12Unit 11

No SparseCoding

SparseCoding

Epoch: 1

No SparseCoding

SparseCoding

Epoch: 10

Network WeightsNetwork Weights25

No SparseCoding

SparseCoding

Epoch:

No SparseCoding

SparseCoding

Epoch:

What We Have LearnedWhat We Have Learned

• In the unsupervised framework, the Bayesian Generative Network is able to learn the alphabet.

• Representations are not necessarily the same as the IA model.– distributed (not localist)– redundant (features are coded several times)

• Having learned the letters, can we now learn words?

Step 2: Learning WordsStep 2: Learning Words

• The second stage of the IA model is the mapping from letters to words.

• Interested in how the Bayesian framework accounts for the development of contextual regularities (i.e., letters within words).

• Look at participants’ learning of context.

Experimental MotivationExperimental Motivation

• Our motivation for the current experiments is the word-superiority effect.

• Specifically, we draw inspiration from the Reicher-Wheeler paradigm.

KQZW--Z-

--S-+ GLUR

---R+ READ

-O--+KQZW

--S-GLUR---P

---RREAD-E--

The TaskThe Task

• The current set of studies was designed to simulate how the word superiority may develop. Specifically we were interested in:– the learning of novel, letter-like stimuli– whether stimuli were learned in parts or wholes– the effects of context on learning.

• Consequently, we created an artificial environment in which we tightly controlled context.

Experimental Design: TrainingExperimental Design: Training

• Reicher-Wheeler task is based the discrimination between two characters.

• Wanted a similar task in which context would interact with a character pair.

a b cd e f

p1 p2 p3

g h i j k l

p1 p2 p3

Experimental Design: TestingExperimental Design: Testing

• Testing: 288 Stimuli

a e c g k l

– 96 Familiar Stimuli:

j e c g k f

– 96 Crossed Stimuli:

• Total of 16 stimuli– Detect change

a b cd b ca e cd e ca b fd b fa e fd e f

Ag h i j h ig k i j k ig h l j h lg k l j k l

a e r g n l

– 96 Novel Stimuli:

AAABBB

BAAABB

CAACBB

• Characters were constructed from the RS features.

• Each character had six line segments with the following constraints:

StimuliStimuli

– characters were continuous

– no two segments formed a straight line

– no character was a mirror image nor rotation of another.

p1 p2 p3

Ap1 p2 p3

Initial SimulationsInitial Simulations

Character 1 Character 2 Character 3

48P(D)

16P(H)

Initial SimulationsInitial Simulations

Character 1 Character 2 Character 3

48P(D)

16P(H)

iii GPTPdiff

Performance was measured by computing a “differentiation value” based on the difference between the generated surface layer representation (Gi) and the target representation (Ti).

Initial Simulation ResultsInitial Simulation Results

1.00E-24

1.00E-22

1.00E-20

1.00E-18

1.00E-16

1.00E-14

1.00E-12

1.00E-10

1.00E-08

1.00E-06

1.00E-04

1.00E-02

1.00E+00

2 2wt 3 3wt 3sp 3sp/wt

Network Architecture

FamiliarCrossedNovel

Simulation ConclusionsSimulation Conclusions

• Regardless of the network architecture, all simulations showed a (slight) difference between the familiar and crossed stimuli.

• No simulation performed well on the novel stimuli in comparison to the other stimuli.

• These results are somewhat counter to what we expected.

• Is the model broken?

• How do participants perform on this task?

Stimulus PresentationStimulus Presentation

500 ms

250 ms

200 ms

250 ms

200 ms

Stimulus PresentationStimulus Presentation

Data AnalysisData Analysis

• Each participant’s reaction time and proportion of “hits” and “correct rejections” were recorded.

• To correct for potential responder biases, the scores were converted to d’ scores using:

Hit Miss

“No”“Yes”

Differ

SameSti

Detect Change?

d’ = ni(Hit) + ni(CR)

• 4 Participants, 10 days each

• 1440 trials per day:– 288 test trials intermixed with 1152 training

trials.

• Three conditions:– Familiar (AAA or BBB)– Crossed (BAA or ABB)– Novel (CAA or CBB)

Experiment 1: One NovelExperiment 1: One Novel

d’ Scoresd’ Scores

1 2 3 4 5 6 7 8 9 10

00.10.20.30.40.50.60.70.80.9

1 2 3 4 5 6 7 8 9 10

Fam-HitFam-FACro-HitCro-FANov-HitNov-FA

Reporting ChangesReporting Changes

100150200250300350400450500

1 2 3 4 5 6 7 8 9 10

Familiar-C

Familiar-S

Cross-C

Cross-S

Novel-C

Novel-S

Reaction TimesReaction Times

Experiment ConclusionsExperiment Conclusions

• Although there is a context effect, it is not as large as we expected, nor as stable.

• There are no significant differences in reaction times for any of the conditions.

• Participants do not perform well in the Novel condition– this is due to a tendency to respond “Change”

to all novel stimuli

Re-Simulation of TaskRe-Simulation of Task

• The network was trained on the same data set that the participants were trained on.

• Network learned on all training/testing trials

• Wanted a similar measure for network performance.

• Used a variant of the Kullback-Leibler divergence measure:

ygygKL

)1(log)1(

)(log)(

1 2 3 4 5 6 7 8 9 10

Network "Days"

Simulation: Difference MeasureSimulation: Difference Measure

1 2 3 4 5 6 7 8 9 10

Network "Days"

Fam-HitFam-FACro-HitCro-FANov-HitNov-FA

Simulation: Report Change?Simulation: Report Change?

Internal RepresentationsInternal Representations

• If we look at the internal representations formed by the network, we get an idea of why it behaves as it does...

Unit 18Unit 17Unit 16Unit 15Unit 14Unit 13

Training “Day”: 1

6Training “Day”:

10Training “Day”:

– The network failed to learn to represent novel items.

– Thus, if the first generated representation is garbage, and the second generated representation is garbage, then the comparison will be garbage

Simulation ConclusionsSimulation Conclusions

• The Bayesian Generative Network qualitatively matched the performance of the participants.

• Furthermore, analysis of the internal structure of the network offers an explanation for the participants’ behaviour.

“change”

Assessing RepresentationsAssessing Representations

• The models predicted that participants in the one novel condition would fail to learn to represent the novel items.

• Unfortunately, we can’t open up a person to see what their internal representation is.

• We can, however, ask them.– Specifically, we can test their recognition of

“novel” items following training and compare these to truly new items.

Experiment 2Experiment 2

• 10 Participants

• Trained on the same data as Experiment 1 but were only run for 2 days.

• At the conclusion of the training, participants were given a “new/old” task in which they saw the 12 old training items, the 6 old novel items, and 12 new items.

• Participants saw a single character, and made the judgement “old” or “new”.

Experiment 2: ResultsExperiment 2: Results

• Participants were about 70% correct at detecting “Old” items.

Stimulus Presented

OldNovelNew

• Participants were no better at recognizing old “Novel” items than truly “New” items.

Learning ContextLearning Context

• The Bayesian Generative Network is able to learn higher order information such as which characters appear in which positions.

• It is able to both simulate and explain the performance of participants trained on a contextual learning task.

• It is able to predict new findings!

• Can we expand the model?

• Closing Remarks

Symmetric Diffusion NetworkSymmetric Diffusion Network

• Symmetric Diffusion Networks (SDN) are a class of networks that explicitly embody many of the implicit assumptions made be the Bayesian Generative Network.

• SDN’s can be viewed as a more general form of the Bayesian Generative Network.

Mediating Layer

P(D) Surface Layer

Mediating Layer

P(D) Surface Layer

Mediating Layer

P(D) Surface Layer

Supervised Learning

Mediating Layer

P(D) Surface Layer

Unsupervised Learning

SDN RepresentationSDN Representation

• One advantage of the SDN is that it is able to learn continuous probability distributions.

• That is, it can learn multiple representations for the same input data. – bat (“flying mammal”) vs. bat (“wooden stick”)

• The SDN can be used to address the ambiguity paradox.

The Ambiguity ParadoxThe Ambiguity Paradox

Lexical Semantic

Unambiguous Ambiguous Non-Word

chargechance

chathe

Unambiguous:Ambiguous:Non-Word:

Is it a word? feeluck

thakeIs it related?

One Possible ExplanationOne Possible Explanation

• “Efficient then Inefficient” Hypothesis(Piercey & Joordens, 2000)– Efficient: The ambiguity advantage results from

a “blend” state.– Inefficient: The ambiguity disadvantage occurs

in relatedness judgements because it takes longer to settle into a correct meaning

An Alternative ExplanationAn Alternative Explanation

• The Symmetric Diffusion Network offers an alternative explanation.

• Lexical Decisions are faster (on average) because there are more “semantic attractors” to fall into.

• Semantic Decisions are slower (on average) because on some proportion of the trials, one must move between “attractors”.

Preliminary ConclusionsPreliminary Conclusions

• Symmetric Diffusion Networks are able to learn ambiguous meanings (in contrast to other models).

• It has provided a plausible theory for the ambiguity paradox.

• It suggests new empirical studies.

• Larger network simulations are underway.

• Closing Remarks

What have we learned?What have we learned?

• Introduced a class of connectionist networks that embody Bayesian principles.

• Using the IA model as inspiration, we:– Compared the letter representations learned

versus the hard-coded representations.– Simulated, explained, & predicted empirical

data on context learning.– Addressed the ambiguity paradox.

The Next 20+ YearsThe Next 20+ Years

• Explore the Bayesian framework and how it relates to connectionism to a fuller extent.– Continue research on learning and how it

interacts with the IA model and aspects of the reading process.

• Make links to neurophysiology– Lexicon vs. Semantic Representations?

(one area or two?)

The “Take Home” MessageThe “Take Home” Message

• We are able to effectively model aspects of the reading process with connectionist networks embodying Bayesian principles!

• These networks are able to qualitatively simulate observed data.

• These networks are able to predict new findings.• Using very simple principles, these networks offer

plausible explanations for a range of behaviours.

Jay McClelland

Michael Lewicki

Tai Sing Lee

Michael Harm

David Noelle

Chris Kello

Darren Piercey

AcknowledgementsAcknowledgements

Ambiguity AdvantageAmbiguity Advantage

“a measure of how likely it is that some event will occur”

“a financial liability”

“a pleading describingsome wrong or offense”

“chance”“chance”

“chance”

“Semantic Space”

“complaint”

“tax”

“charge”“charge”

“a financial liability”“charge”

Ambiguity DisadvantageAmbiguity Disadvantage

“charge”

“complaint”

A Bayesian Approach to the Reading Process: From Networks to Human Data

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