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Jamie Alexandre. =. ≠. jason. you. a. cookie. would. like. Grammatical Complexity The Chomsky Hierarchy. Grammatical Complexity The Chomsky Hierarchy. Recursion. Something containing an instance of itself. Recursion in Language.

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Jamie alexandre

JamieAlexandre


Jamie alexandre

=


Jamie alexandre

jason

you

a

cookie

would

like


Grammatical complexity the chomsky hierarchy

Grammatical ComplexityThe Chomsky Hierarchy


Grammatical complexity the chomsky hierarchy1

Grammatical ComplexityThe Chomsky Hierarchy


Recursion

Recursion

  • Something containing an instance of itself.


Recursion in language

Recursion in Language

The dog the cat the rat grabbed rode walked down the street.

The dog the cat rode walked down the street.

The dog walked down the street.


Recursion stack memory

Recursion: “Stack” Memory

The dog the cat the rat grabbed rode walked down the street.

DOG

CAT

RAT

GRAB

RIDE

WALK


Recursion stack memory1

Recursion: “Stack” Memory

The dog the cat the rat grabbed rode walked down the street.

GRAB

RIDE

WALK

“Infinite competence…”

RAT

CAT

DOG

“Limited performance…”


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?


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SRN

Simple Recurrent Network (Elman, 1990)

  • Some ability to use longer contexts

  • Incremental learning: no looking back

  • No “rules”: distributed representation


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PCFG

Probabilistic Context-Free Grammar

  • Easily handles recursive structure, long-range context

  • Hierarchical, “rule”-based representation

  • More computationally complex, non-incremental learning

0.8

0.65

0.35

0.1

S  NP VP

N’ AdjP N’

N’ N

Adjgreen


Serial reaction time srt study

Serial ReactionTime (SRT) Study

  • Buttons flash in short sequences

    • “press the button as quickly as possible when it lights up”

  • Dependent measure: RT

    • time from light on  correct button pressed

  • Subjects seem to be making sequential predictions

    RT ∝ P(button|context)

    also: RT ∝ -log(P(button|context))

    (“surprisal”, e.g. Hale, 2001; Levy, 2008)


Training the humans

Training the Humans

  • Eight subjects per experimental condition

  • Same sequences, different mappings

  • Broken into 16 blocks, with breaks

  • About an hour of button-pressing total

  • Emphasized speed, while minimizing errors


Training the models

Training the Models

  • Trained on exactly the same sequences as the humans, but not fit to human data

  • Predictions at every point based solely on sequences seen prior to that

  • Results in sequence of probabilities

    • correlated with sequence of human RTs, through surprisal (negative log probability)


Analysis

Analysis


Analysis1

Analysis


A case study in recursion palindromes

A Case Study in Recursion: Palindromes

A C L Q L C A

(Sequences of length 5 through 15; total of 3728 trials per subject)


Did you notice any patterns

“Did you notice any patterns?”

PCFG

PCFG

SRN

SRN

Subjects with no awareness of pattern:

“No”, “None”, “Not really” (n=5)

Those with explicit awareness of pattern:

“Circular pattern”, “Mirror pattern” (n=3)

PCFG(explicit task performance)

SRN(implicit task performance)

Will this replicate?


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Implicit, didn't notice (n=8)

0.6

PCFG

SRN

0.5

0.4

0.3

Correlation (Surprisal vs RT)

0.2

0.1

0

-0.1

2

4

6

8

10

12

14

16

Block


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  • Differences between individuals?

    • or actually between modes of processing?

  • What if we explicitly train subjects on the pattern?

  • First half implicit, second half explicit


Explicit training worksheet

Explicit Training Worksheet

“This is the middle button in every sequence (and itonlyoccurs in the middle position, halfway through the sequence):

This means that as soon as you see this button, you know that the sequence will start to reverse.

Here are some example sequences of various lengths:


And quiz sheet

And Quiz Sheet

“Now, complete these sequences using the same pattern (crossing out any unneeded boxes at the end of a sequence):


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Fully explicit from middle (n=8)

0.6

PCFG

0.5

SRN

0.4

0.3

Correlation (Surprisal vs RT)

0.2

0.1

0

-0.1

2

4

6

8

10

12

14

16

Block

(explicit instruction given here)


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Before explicit instruction

After


Context free vs context sensitive

Context-free vs Context-sensitive

A  A

B  B

C  C

D  D

1

2

2

1

1

2

1

2


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Explicit Instruction

(after block 4)

CFG:

CSG:


Methods

Methods

  • Four conditions, with 8 subjects in each

    • Implicit context-free grammar (CFG)

    • Implicit context-sensitive grammar (CSG)

    • Explicit context-free grammar (CFG)

    • Explicit context-sensitive grammar (CSG)

  • Total of 640 sequences (4,120 trials) per subject

    • Sequences of length 4, 6, 8, and 10

    • Around 1.5 hours of button-pressing

    • In blocks 9-16, 5% of the trials were “errors”

A1 B1 C1 C2 B2 A2

D2


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Blocks 1-4Blocks 5-8Blocks 9-12 (errors thicker)Blocks 13-16 (errors thicker)


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**

**

**

(6ms)

(27ms)

(2ms)

(11ms)

RT (ms)


Conclusions

Conclusions

  • Explicit/Implicit processing

    • Implicit performance correlated with the predictions made by an SRN (a connectionist model)

    • Explicit performance correlated with the predictions made by a PCFG (a rule-based model)

  • Grammatical complexity

    • Able to process context-free, recursive structures at a very rapid timescale

    • More limited ability to process context-sensitive structures


Future directions

Future Directions

  • Longer training

  • More complex grammars

    • Determinism

  • Other response measures

    • EEG: more sensitive than RTs to initial stages of learning

  • Field studies in Switzerland or Brazil…?


Broader goals

Broader Goals

  • L2-learning pedagogy


Thankyous

Thankyous!

MentorshipJeff ElmanRoger LevyMarta Kutas

AdviceMicah Bregman

Ben Cipollini

Vicente Malave Nathaniel Smith

Angela Yu

Rachel Mayberry

Tom Urbach

Andrea, Seana and the 3rd Year Class!

Research Assistants

Frances Martin (2010)

Ryan Cordova (2009)

Wai Ho Chiu (2009)


Agl and language

AGL and Language

Areas associated with syntax may be involved

Bahlmann, Schubotz, and Friederici (2008). Hierarchical artificial grammar processing engages Broca's area. NeuroImage, 42(2):525-534.

P600-like effects can be seen in AGL

Christiansen, Conway, & Onnis (2007). Neural Responses to Structural Incongruencies in Language and Statistical Learning Point to Similar Underlying Mechanisms.

“violations in an artificial grammar can elicit late positivities qualitatively and topographically comparable to the P600 seen with syntactic violations in natural language”


Sanity check effect is local

Sanity Check: Effect is Local


Context free grammar

Context-free Grammar

The dog the cat the rat grabbed rode walked.

S  NP VP

NP  NNP  N S

N  the dogN  the catN  the rat

VP  grabbedVP  rodeVP  walked


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