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![Page 1: Jakobson's Grand Unified Theory of Linguistic Cognition Paul Smolensky Cognitive Science Department Johns Hopkins University Elliott Moreton Karen Arnold.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649e4e5503460f94b44b1c/html5/thumbnails/1.jpg)
Jakobson's Grand Unified Theory of Linguistic Cognition
Paul SmolenskyCognitive Science Department
Johns Hopkins University
Elliott MoretonKaren Arnold Donald Mathis
Melanie Soderstrom
Géraldine LegendreAlan Prince
Peter Jusczyk Suzanne Stevenson
with:
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Grammar and Cognition
1. What is the system of knowledge? 2. How does this system of
knowledge arise in the mind/brain? 3. How is this knowledge put to use? 4. What are the physical mechanisms
that serve as the material basis for this system of knowledge and for the use of this knowledge?
(Chomsky ‘88; p. 3)
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Advertisement
The complete story, forthcoming (2003) Blackwell:
The harmonic mind: From neural computation to optimality-theoretic
grammarSmolensky & Legendre
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A Grand Unified Theory for the cognitive science of language is enabled by Markedness:
Avoid α①Structure
• Alternations eliminate α• Typology: Inventories lack α
②Acquisition• α is acquired late
③Processing• α is processed poorly
④Neural• Brain damage most easily disrupts α
Jakobson’s Program
Formalize through OT?
OT
①
③
④
②
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StructureAcquisition UseNeural
Realization
Theoretical. OT (Prince & Smolensky ’91,
’93): – Construct formal grammars directly from
markedness principles– General formalism/ framework for
grammars: phonology, syntax, semantics; GB/LFG/…
– Strongly universalist: inherent typology Empirical. OT:– Allows completely formal markedness-
based explanation of highly complex data
/
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• Theoretical Formal structure enables OT-general:– Learning algorithms
•Constraint Demotion: Provably correct and efficient (when part of a general decomposition of the grammar learning problem)
– Tesar 1995 et seq. – Tesar & Smolensky 1993, …, 2000
•Gradual Learning Algorithm – Boersma 1998 et seq.
Structure Acquisition UseNeural Realization
Initial state
Empirical – Initial state predictions explored
through behavioral experiments with infants
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Structure Acquisition UseNeural
Realization
• Theoretical– Theorems regarding the computational
complexity of algorithms for processing with OT grammars • Tesar ’94 et seq.• Ellison ’94• Eisner ’97 et seq.• Frank & Satta ’98• Karttunen ’98
• Empirical (with Suzanne Stevenson)– Typical sentence processing theory:
heuristic constraints– OT: output for every input; enables
incremental (word-by-word) processing– Empirical results concerning human
sentence processing difficulties can be explained with OT grammars employing independently motivated syntactic constraints
– The competence theory [OT grammar] is the performance theory [human parsing heuristics]
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• Empirical
Structure Acquisition UseNeural
Realization
• Theoretical OT derives from the theory of abstract neural (connectionist) networks – via Harmonic Grammar (Legendre, Miyata,
Smolensky ’90)
For moderate complexity, now have general formalisms for realizing– complex symbol structures as distributed
patterns of activity over abstract neurons– structure-sensitive constraints/rules as
distributed patterns of strengths of abstract synaptic connections
– optimization of Harmony
Construction of a miniature, concrete LAD
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Program
Structure OT
•Constructs formal grammars directly from markedness principles
•Strongly universalist: inherent typology
OT allows completely formal markedness-based explanation of highly complex data
AcquisitionInitial state predictions explored through
behavioral experiments with infants
Neural Realization Construction of a miniature, concrete LAD
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The Great Dialectic
Phonological representations serve two masters
Phonological Representation Lexico
nPhoneti
cs
Phonetic interface
[surface form]
Often: ‘minimize effort (motoric & cognitive)’;
‘maximize discriminability’
Locked in conflict
Lexical interface
/underlying form/
Recoverability: ‘match this invariant
form’
FAITHFULNESSMARKEDNESS
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OT from Markedness Theory
• MARKEDNESS constraints: *α: No α• FAITHFULNESS constraints
– Fα demands that /input/ [output] leave α unchanged (McCarthy & Prince ’95)
– Fα controls when α is avoided (and how)
• Interaction of violable constraints: Ranking – α is avoided when *α ≫ Fα
– α is tolerated when Fα ≫ *α
– M1 ≫ M2: combines multiple markedness dimensions
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OT from Markedness Theory
• MARKEDNESS constraints: *α• FAITHFULNESS constraints: Fα
• Interaction of violable constraints: Ranking – α is avoided when *α ≫ Fα – α is tolerated when Fα ≫ *α – M1 ≫ M2: combines multiple markedness dimensions
• Typology: All cross-linguistic variation results from differences in ranking – in how the dialectic is resolved (and in how multiple markedness dimensions are combined)
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OT from Markedness Theory
• MARKEDNESS constraints• FAITHFULNESS constraints• Interaction of violable constraints: Ranking • Typology: All cross-linguistic variation
results from differences in ranking – in resolution of the dialectic
• Harmony = MARKEDNESS + FAITHFULNESS
– A formally viable successor to Minimize Markedness is OT’s Maximize Harmony (among competitors)
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Structure
Explanatory goals achieved by OT• Individual grammars are literally
and formally constructed directly from universal markedness principles
• Inherent Typology : Within the analysis of phenomenon Φ in language L is inherent a typology of Φ across all languages
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Program
Structure OT
• Constructs formal grammars directly from markedness principles
• Strongly universalist: inherent typology OT allows completely formal
markedness-based explanation of highly complex data --- Friday
AcquisitionInitial state predictions explored through
behavioral experiments with infants
Neural Realization Construction of a miniature, concrete LAD
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Structure: Summary
• OT builds formal grammars directly from markedness: MARK, with FAITH
Friday:• Inventories consistent with markedness
relations are formally the result of OT with local conjunction
• Even highly complex patterns can be explained purely with simple markedness constraints: all complexity is in constraints’ interaction through ranking and conjunction: Lango ATR vowel harmony
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Program
Structure OT
• Constructs formal grammars directly from markedness principles
• Strongly universalist: inherent typology OT allows completely formal markedness-
based explanation of highly complex data
AcquisitionInitial state predictions explored
through behavioral experiments with infants
Neural Realization Construction of a miniature, concrete LAD
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Nativism I: Learnability
• Learning algorithm – Provably correct and efficient (under strong
assumptions)
– Sources:• Tesar 1995 et seq. • Tesar & Smolensky 1993, …, 2000
– If you hear A when you expected to hear E, increase the Harmony of A above that of E by minimally demoting each constraint violated by A below a constraint violated by E
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in +possible
Candidates
FaithMark (NPA)
☹ ☞ Einpossibl
e *
A impossibl
e *
Faith
*☺ ☞
If you hear A when you expected to hear E, increase the Harmony of A above that of E by minimally demoting each constraint violated by A below a constraint violated by E
Constraint Demotion Learning
Correctly handles difficult case: multiple violations in E
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Nativism I: Learnability
• M ≫ F is learnable with /in+possible/→impossible– ‘not’ = in- except when followed by …– “exception that proves the rule, M = NPA”
• M ≫ F is not learnable from data if there are no ‘exceptions’ (alternations) of this sort, e.g., if lexicon produces only inputs with mp, never np: then M and F, no M vs. F conflict, no evidence for their ranking
• Thus must have M ≫ F in the initial state, ℌ0
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The Initial State
OT-general: MARKEDNESS ≫ FAITHFULNESS
Learnability demands (Richness of the Base)
(Alan Prince, p.c., ’93; Smolensky ’96a)
Child production: restricted to the unmarked
Child comprehension: not so restricted (Smolensky ’96b)
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Nativism II: Experimental Test
Collaborators Peter Jusczyk Theresa Allocco Language Acquisition (2002)
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Nativism II: Experimental Test
• Linking hypothesis: More harmonic phonological stimuli
⇒ Longer listening time • More harmonic:
M ≻ *M, when equal on F F ≻ *F, when equal on M– When must chose one or the other,
more harmonic to satisfy M: M ≫ F
• M = Nasal Place Assimilation (NPA)
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• X/Y/XY paradigm (P. Jusczyk)
un...b...umb
un...b...umb
Experimental Paradigm
p = .006um...b...umb um...b...iŋgu
iŋ…..gu...iŋgu vs. iŋ…..gu…umb
… … ∃FAITH
• Headturn Preference Procedure (Kemler Nelson et al. ‘95; Jusczyk ‘97)
•Highly general paradigm: Main result
ℜ *FNP
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15.36
12.31
0
2
4
6
8
10
12
14
16
18
20
Faithfulness Markedness M ≫ F
Tim
e (s
ec)
Higher HLower H
4.5 Months (NPA)Higher
HarmonyLower Harmony
um…ber…umber
um…ber… iŋgu
p = .006 (11/16)
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15.2315.36
12.7312.31
0
2
4
6
8
10
12
14
16
18
20
Faithfulness Markedness M ≫ F
Tim
e (s
ec)
Higher HLower H
Higher Harmony
Lower Harmony
um…ber…umber
un…ber…unber
p = .044 (11/16)
4.5 Months (NPA)
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15.2315.36
12.7312.31
0
2
4
6
8
10
12
14
16
18
20
Faithfulness Markedness M ≫ F
Tim
e (s
ec)
Higher HLower H
4.5 Months (NPA) Markedness * Faithfulness
* Markedness Faithfulness
un…ber…umber
un…ber…unber
???
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16.75
15.2315.3614.01
12.7312.31
0
2
4
6
8
10
12
14
16
18
20
Faithfulness Markedness M ≫ F
Tim
e (s
ec)
Higher HLower H
4.5 Months (NPA)Higher
HarmonyLower Harmony
un…ber…umber
un…ber…unber
p = .001 (12/16)
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Program
Structure OT
• Constructs formal grammars directly from markedness principles
• Strongly universalist: inherent typology OT allows completely formal markedness-
based explanation of highly complex data
AcquisitionInitial state predictions explored through
behavioral experiments with infants
Neural Realization Construction of a miniature, concrete
LAD
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The question
• The nativist hypothesis, central to generative linguistic theory:
Grammatical principles respected by all human languages are encoded in the genome.
• Questions:– Evolutionary theory: How could this
happen?– Empirical question: Did this happen?– Today: What — concretely — could it
mean for a genome to encode innate knowledge of universal grammar?
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UGenomics
• The game: Take a first shot at a concrete example of a genetic encoding of UG in a Language Acquisition Device¿ Proteins ⇝ Universal grammatical principles ?
Time to willingly suspend disbelief …
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UGenomics
• The game: Take a first shot at a concrete example of a genetic encoding of UG in a Language Acquisition Device¿ Proteins ⇝ Universal grammatical principles ?
• Case study: Basic CV Syllable Theory (Prince & Smolensky ’93)
• Innovation: Introduce a new level, an ‘abstract genome’ notion parallel to [and encoding] ‘abstract neural network’
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Grammar Innate Constraints
Abstract Neural Network Abstract Genome
Biological Neural Network Biological Genome
= A instantiates B
= A encodes B
Approach: Multiple Levels of Encoding
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UGenome for CV Theory
• Three levels– Abstract symbolic: Basic CV Theory– Abstract neural: CVNet– Abstract genomic: CVGenome
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UGenomics: Symbolic Level
• Three levels– Abstract symbolic: Basic CV
Theory– Abstract neural: CVNet– Abstract genomic: CVGenome
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Grammar Innate Constraints
Abstract Neural Network Abstract Genome
Biological Neural Network Biological Genome
= A instantiates B
= A encodes B
Approach: Multiple Levels of Encoding
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Basic syllabification: Function
• Basic CV Syllable Structure Theory– ‘Basic’ — No more than one segment
per syllable position: .(C)V(C).
• ƒ: /underlying form/ [surface form]• /CVCC/ [.CV.C V C.] /pæd+d/[pædd]
• Correspondence Theory– McCarthy & Prince 1995 (‘M&P’)
• /C1V2C3C4/ [.C1V2.C3 V C4]
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Why basic CV syllabification?
• ƒ: underlying surface linguistic forms• Forms simple but combinatorially
productive • Well-known universals; typical typology• Mini-component of real natural
language grammars• A (perhaps the) canonical model of
universal grammar in OT
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• PARSE: Every element in the input corresponds to an element in the output
• ONSET: No V without a preceding C
• etc.
Syllabification: Constraints (Con)
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UGenomics: Neural Level
• Three levels– Abstract symbolic: Basic CV Theory– Abstract neural: CVNet– Abstract genomic: CVGenome
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Grammar Innate Constraints
Abstract Neural Network Abstract Genome
Biological Neural Network Biological Genome
= A instantiates B
= A encodes B
Approach: Multiple Levels of Encoding
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CVNet Architecture
/C1 C2/ [C1 V C2]
CV
/ C1 C2 /
[
C1
V
C2
]
‘1’
‘2’
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Connection substructure
Local: fixed, gene-tically determinedContent of constraint 1
Global: variable during learningStrength of constraint 1
1
s1
1c
2
is2
2c
Network weight:
Network input: ι = WΨ a
φψ ΦΨ
1
WconN
ii
i
sc
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PARSE
C
V
3 3
3
3
33
1
11
1
1
1
3 3
3
3
33
3 3
3
3
33
• All connection coefficients are +2
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ONSET• All connection coefficients are 1
C
V
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Crucial Open Question(Truth in Advertising)
• Relation between strict domination and neural networks?
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CVNet Dynamics
• Boltzmann machine/Harmony network– Hinton & Sejnowski ’83 et seq. ; Smolensky ‘83 et
seq.
– stochastic activation-spreading algorithm: higher Harmony more probable
– CVNet innovation: connections realize fixed symbol-level constraints with variable strengths
– learning: modification of Boltzmann machine algorithm to new architecture
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Learning Behavior
• A simplified system can be solved analytically
• Learning algorithm turns out to ≈ si
() = [# violations of constrainti
P ]
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UGenomics: Genome Level
• Three levels– Abstract symbolic: Basic CV Theory– Abstract neural: CVNet– Abstract genomic: CVGenome
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Grammar Innate Constraints
Abstract Neural Network Abstract Genome
Biological Neural Network Biological Genome
= A instantiates B
= A encodes B
Approach: Multiple Levels of Encoding
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Connectivity geometry• Assume 3-d grid geometry
V
C
‘E’
‘N’
‘back’
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C
V
ONSETx0 segment: | S S VO| N S x0
• VO segment: N&S S VO
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• Correspondence units grow north & west and connect with input & output units.
• Output units grow east and connect
Connectivity: PARSE• Input units grow south and connect
C
V
3 3
3
3
3 3
1
1 1
1
1
1
3 3
3
3
3 3
3 3
3
3
3 3
C
V
3 3
3
3
3 3
1
1 1
1
1
1
3 3
3
3
3 3
3 3
3
3
3 3
C
V
3 3
3
3
3 3
3 3
3
3
3 3
1
1 1
1
1
1
3 3
3
3
3 3
3 3
3
3
3 3
3 3
3
3
3 3
3 3
3
3
3 3
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To be encoded• How many different kinds of units are
there? • What information is necessary (from
the source unit’s point of view) to identify the location of a target unit, and the strength of the connection with it?
• How are constraints initially specified? • How are they maintained through the
learning process?
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Unit types
• Input units C V• Output units C V x• Correspondence units C V• 7 distinct unit types• Each represented in a distinct sub-
region of the abstract genome• ‘Help ourselves’ to implicit
machinery to spell out these sub-regions as distinct cell types, located in grid as illustrated
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Direction of projection growth
• Topographic organizations widely attested throughout neural structures– Activity-dependent growth a possible
alternative
• Orientation information (axes)– Chemical gradients during development– Cell age a possible alternative
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Projection parameters
• Direction• Extent
– Local– Non-local
• Target unit type• Strength of connections encoded
separately
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Connectivity Genome
• Contributions from ONSET and PARSE:
Source:
CI VI CO VO CC VC xo
Projec-tions:
S LCC S L VC E L CC E L VC
N&S S VO
N S x0
N L CI
W L CO
N L VI
W L VO
S S VO
Key: Direction Extent Target
N(orth) S(outh)E(ast) W(est)F(ront) B(ack)
L(ong) S(hort)
Input: CI VI
Output: CO VO x(0)
Corr: VC CC
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CVGenome: Connectivity C-I V-I C-C V-C C-O V-O x
D E T D E T D E T D E T D E T D E T D E T
IDENTITY F Sh V-C B Sh C-C LINEARITY N/E L C-C&V-C N/E L C-C&V-C
S/W L C-C&V-C S/W L C-C&V-C INTEGRITY S L C-C S L V-C
N L C-C N L V-C UNIFORMITY E L C-C E L V-C
W L C-C W L V-C OUTPUTID F Sh V-O B Sh C-O F Sh C-O
B Sh x B Sh x F Sh V-O NOOUTGAPS N Sh x* N Sh x* S Sh C-O&V-O
RESPOND CORRESPOND S L C-C S L V-C N L C-I N L V-I E L C-C E L V-C
W L C-O W L V-O PARSE S L C-C S L V-C N L C-I N L V-I E L C-C E L V-C
W L C-O W L V-O FILL-V S L V-C N L V-I
W L V-O E L V-C FILL-C S L C-C N L C-I E L C-C
W L C-O ONSET N Sh V-O S Sh 1rst V-O
S Sh V-O N Sh 1rst x
NOCODA N Sh C-O N Sh C-O S Sh C-O S Sh x
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Encoding connection strength
• For each constraint i , need to ‘embody’
– Constraint strength si
– Connection coefficients (Φ Ψ cell types)
• Product of these is contribution of i to the Φ Ψ connection weight
φψ ΦΨ
1
WconN
ii
i
sc
ic
Network-level specification
—
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Φ
Ψ
Processing
11 0R c
[P1] ∝ s1
1 1 11 1w [ ]P R s c
W = wii
22 0R c
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Φ
Ψ
Development1 1
1R G c
1 1 0G c 1 1
1L G c
2 22R G c
2 2 0G c
2 22L G c
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Φ
Ψ
Learning
2 22 2 2[ ]P K L G c
1 11 1 1
When and are simultaneously active,
[ ] is P K L G c
1 11L G c
11 1K L c
1 1[ ]P K
(during phase P+; reverse during P )
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CVGenome: Connection Coefficients
Constraint From To Strength Constraint From To Strength IDENTITY C-C V-C 1 PARSE C-C&V-C bias 3
LINEARITY C-C&V-C C-C&V-C 1 C-I&V-I bias 1 INTEGRITY C-C&V-C C-C&V-C 1 C-I&C-O C-C 2
UNIFORMITY C-C C-C 1 V-I&V-O V-C 2 OUTPUTID C-O&V-O&x C-O&V-O&x 2 FILL-V V-C bias 3
NOOUTGAPS x C-O&V-O 1 V-O bias 1 RESPOND C-O&V-O&x bias 1 V-I&V-O V-C 2
CORRESPOND C-C&V-C bias 2 FILL-C C-C bias 3 C-C C-I&C-O 1 C-O bias 1 V-C V-I&V-O 1 C-I&C-O C-C 2
NOCODA C-O C-O&x 1 ONSET V-O V-O&x 1
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C-C:
CORRESPOND:
Abstract Gene Map
General Developmental Machinery Connectivity Constraint Coefficients
S L CC S L VC F S VC N/E L CC&VC S/W L CC&VC
direction extent target
C-I: V-I:
G
CO&V&x B 1 CC&VC B 2 CC CI&CO 1 VC VI&VO 1
RESPOND:
G
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UGenomics
• Realization of processing and learning algorithms in ‘abstract molecular biology’, using the types of interactions known to be biologically possible and genetically encodable
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UGenomics
• Host of questions to address– Will this really work?– Can it be generalized to distributed nets?– Is the number of genes [77=0.26%]
plausible?– Are the mechanisms truly biologically
plausible?– Is it evolvable?
How is strict domination to be handled?
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Hopeful Conclusion
• Progress is possible toward a Grand Unified Theory of the cognitive science of language– addressing the structure, acquisition, use, and
neural realization of knowledge of language– strongly governed by universal grammar– with markedness as the unifying principle– as formalized in Optimality Theory at the
symbolic level– and realized via Harmony Theory in abstract
neural nets which are potentially encodable genetically
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€Thank you for your attention
(and indulgence)
Hopeful Conclusion
• Progress is possible toward a Grand Unified Theory of the cognitive science of language
Still lots of promissory notes, butall in a common currency — Harmony ≈ unmarkedness; hopefullythis will promote further progress by facilitating integration of the sub-disciplines of cognitive science