Abstract Neuron

w2 wnw1

w0

i0=1

o u t p u t y

i2 ini1. . .

i n p u t i

n

i

iiiwnet0

y 1 if net > 00 otherwise{

Computing with Abstract Neurons

McCollough-Pitts Neurons were initially used to model pattern classification

size = small AND shape = round AND color = green AND Location = on_tree => Unripe_fruit

linking classified patterns to behavior size = large OR motion = approaching => move_away size = small AND location = above => move_above

McCollough-Pitts Neurons can compute logical functions. AND, NOT, OR

Computing logical functions: the OR function

• Assume a binary threshold activation function.

• What should you set w01, w02 and w0b to be so that you can get the right answers for y0?

i1 i2 y0

0 0 0

0 1 1

1 0 1

1 1 1

x0 f

i1 w01

y0i2

b=1

w02

w0b

Many answers would work

y = f (w01i1 + w02i2 + w0bb)

recall the threshold function

the separation happens when w01i1 + w02i2 + w0bb = 0

move things around and you get

i2 = - (w01/w02)i1 - (w0bb/w02)

i2

i1

Decision Hyperplane

The two classes are therefore separated by the `decision' line which is defined by putting the activation equal to the threshold.

It turns out that it is possible to generalise this result to Threshold Units with n inputs.

In 3-D the two classes are separated by a decision-plane.

In n-D this becomes a decision-hyperplane.

Linearly separable patterns

Linearly Separable PatternsPERCEPTRON is an architecture which can solve this type of decision boundary problem. An "on" response in the output node represents one class, and an "off" response represents the other.

The XOR function

i1 i2 y

0 0 0

0 1 1

1 0 1

1 1 0

The Input Pattern Space

 

The Decision planes

 

Multiple Layers

I1 I2

1.50.5

0.5

-11

1 11

1

y

Multiple Layers

I1 I2

1.50.5

0.5

-11

1 11

1

0 1

y

Multiple Layers

I1 I2

1.50.5

0.5

-11

1 11

1

1 1

y

Computing other relations

The 2/3 node is a useful function that activates its outputs (3) if any (2) of its 3 inputs are active

Such a node is also called a triangle node and will be useful for lots of representations.

Triangle nodes and McCullough-Pitts Neurons?

Object (B) Value (C)

Relation (A)

A B C

“They all rose”

triangle nodes:

when two of the abstract neurons fire, the third also fires

model of spreading activation

Basic Ideas behind the model

Parallel activation streams. Top down and bottom up activation combine to

determine the best matching structure. Triangle nodes bind features of objects to values Mutual inhibition and competition between

structures Mental connections are active neural connections

5 levels of Neural Theory of Language

Cognition and Language

Computation

Structured Connectionism

Computational Neurobiology

Biology

MidtermQuiz Finals

Neural Development

Triangle NodesNeural Net and learning

abst

ract

ion

Pyscholinguistic experiments

Psychological Studies

Eva Mok

CS182/CogSci110/Ling109

Spring 2006

Read the list

ORANGE BROWN GREENYELLOWBLUERED

Name the print color

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Name the print color

RED GREENBLUEBROWNORANGEYELLOW

The Stroop Test

Form and meaning interact in comprehension, production and

learning

Top down and bottom up information Bottom-up: stimulus driving processing Top-down: knowledge and context driving

processing When are these information integrated?

Modular view: Staged serial processing Interaction view: Information is used as

soon as available

Tanenhaus et al. (1979) [also Swinney, 1979]

Word / non-word forced choice

Modeling the task with triangle nodes

Reaction times in milliseconds after: “They all rose”

flower 685 659

stood 677 623

desk(control)

711 652

0 delay 200ms. delay

(facilitation)

(facilitation) (facilitation)

(no facilitation)

When is context integrated? Prime: spoken sentences ending in

homophones

They all rose vs. They bought a rose Probe: stood and flower

No offset: primes both stood and flower 200 ms offset: only primes appropriate sense

Modularity? Or weak contextual constraints?

Eye trackingcomputerEye camera

Scene camera

Allopenna, Magnuson & Tanenhaus (1998)

“Pick up the beaker”

Adapted from Jim Magnuson, “Interaction in language processing: Pragmatic constraints on lexical access”

Do rhymes compete? Cohort (Marlsen-Wilson): onset similarity is primary because

of the incremental (serial) nature of speech Cat activates cap, cast, cattle, camera, etc. Rhymes won’t compete

NAM (Neighborhood Activation Model; Luce): global similarity is primary Cat activates bat, rat, cot, cast, etc. Rhymes among set of strong competitors

TRACE (McClelland & Elman): global similarity constrained by incremental nature of speech Cohorts and rhymes compete, but with different time

course

Adapted from Jim Magnuson, “Interaction in language processing: Pragmatic constraints on lexical access”

TRACE predicts different time course for cohorts and rhymes

Adapted from Jim Magnuson, “Interaction in language processing: Pragmatic constraints on lexical access”

TRACE predictions match eye-tracking data

Adapted from Jim Magnuson, “Interaction in language processing: Pragmatic constraints on lexical access”

Natural contexts are used continuously Conclusion from this and other eye-tracking

studies: When constraints from natural contexts are

extremely predictive, they are integrated as quickly as we can measure

Suggests rapid, continuous interaction among Linguistic levels Nonlinguistic context

Even for processes assumed to be low-level and automatic

Constrains processing theories, also has implications for, e.g., learnability

Adapted from Jim Magnuson, “Interaction in language processing: Pragmatic constraints on lexical access”

Eye movement paradigm More sensitive than conventional

paradigms More naturalistic Simultaneous measures of multiple items Transparently linkable to computational

model

Adapted from Jim Magnuson, “Interaction in language processing: Pragmatic constraints on lexical access”

Eye-tracker without headsets

http://www.bcs.rochester.edu/infanteyetrack/eyetrack.html

Recap: Goals of psycholinguistic studies Direct goal: finding out what affect

sentence processing Indirect goal: getting at how words,

syntax, concepts are represented in the brain

Modeling: testing out these hypotheses with computational models

Areas studied in psycholinguistics Lexical access / lexical structure Syntactic structure Referent selection The role of working memory Disfluencies

Disfluencies and new information Disfluencies: pause, repetition, restart Often just seen as production /

comprehension difficulties Arnold, Fagnano, and Tanenhaus (2003)

How are disfluent references interpreted? Componenets to referent selection

lexical meaning discourse constraints

Candle, camel, grapes, salt shaker

a. DISCOURSE-OLD CONTEXT: Put the grapes below the candle. DISCOURSE-NEW CONTEXT: Put the grapes below the camel.

b. FLUENT: Now put the candle below the salt shaker. DISFLUENT: Now put theee, uh, candle below the salt shaker.

Predictions on 4 conditions: (Target = candle)

Disfluent/New, Fluent/Given: Target Put the grapes below the camel.

Now put theee, uh, candle below the salt shaker. Put the grapes below the candle.

Now put the candle below the salt shaker.

Disfluent/Given, Fluent/New: Competitor Put the grapes below the candle.

Now put theee, uh, candle below the salt shaker. Put the grapes below the camel.

Now put the candle below the salt shaker.

Disfluencies affect what we look at

Percentage of fixations on all new objects from 200 to 500 ms after the onset of “the”/“theee uh” (i.e. before the onset of the head noun)

Target is preferred in two conditions

Percentage of target fixations minus percentage competitor fixations in each condition. Fixations cover 200–500 ms after the onset of the head noun.

A lot of information is integrated in sentence processing!

Stroop test [i.e. color words]: form, meaning

Tanenhaus et al (1997) [i.e. “they all rose”]: phonology, meaning, syntactic category

Allopena et al (1998) [i.e. cohorts & rhymes]:phonology, visual context

Arnold et al (2003) [i.e. “theee, uh, candle”]:discourse information, visual context

Producing words from pictures or from other words

A comparison of aphasic lexical access from two different input modalities

Gary Dell with

Myrna Schwartz, Dan Foygel, Nadine Martin, Eleanor Saffran, Deborah Gagnon, Rick Hanley, Janice Kay, Susanne Gahl, Rachel Baron, Stefanie Abel, Walter Huber

A 2-step Interactive Model of Lexical Access in Production

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Semantic Features

Adapted from Gary Dell, “Producing words from pictures or from other words”

1. Lemma Access: Activate semantic features of CAT

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Semantic Features

Adapted from Gary Dell, “Producing words from pictures or from other words”

1. Lemma Access: Activation spreads through network

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

1. Lemma Access: Most active word from proper category is selected and linked to syntactic frame

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

NP

N

2. Phonological Access: Jolt of activation is sent to selected word

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

NP

N

2. Phonological Access: Activation spreads through network

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

NP

N

2. Phonological Access: Most activated phonemes are selected

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

Syl

On Vo Co

Modeling lexical access errors Semantic error Formal error (i.e. errors related by form) Mixed error (semantic + formal) Phonological access error

Semantic error: Shared features activate semantic neighbors

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

NP

N

Formal error: Phoneme-word feedback activates formal neighbors

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

NP

N

Mixed error: neighbors activated by both top-down & bottom-up sources

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

NP

N

Phonological access error: Selection of incorrect phonemes

FOG DOG CAT RAT MAT

f r d k m ae o t g

Onsets Vowels Codas

Adapted from Gary Dell, “Producing words from pictures or from other words”

Syl

On Vo Co

I’ve shown you... Behavioral experiments, and A connectionist model with the goal of understanding how

language is represented and processed in the brain

Next time: Lisa will talk about imaging experiments