Dynamic computational networks

1. Dynamic computational networks John Goldsmith University of Chicago April 2005

2. Work done in collaboration with Gary Larson (Wheaton College) Other work by Bernard Laks and his students (Paris X)

3. Two models in neurocomputing: 1. In space: lateral inhibition Work done jointly with Gary Larson. Discrete unit modeling. 2. In time: neural oscillation

4. The structure of linguistic time • Language is not merely a sequence of one unit after another – at any level. • In phonology, we have known since classical times about syllables and feet – whatever they are. What are they?

5. One view of syllables • The Panini-Saussure view: Language is uttered in waves of increasing and decreasing sonority. Syllables are units that begin with a sequence of rising sonority, and end with a sequence of falling sonority.

6. Pike-Hockett-Fudge-Selkirk • The alternative to the wave view of the syllable was proposed by Pike (Pike and Pike 1947), who proposed: • To apply Bloomfield’s syntactic model of immediate constitutents to phonology. • Bloomfield was not amused. • Hockett 1955 (among others) took this as a central fact about phonology: that all apparent phonological sequences were really hierarchical structure.

7. Accent • Metrical theory (Liberman 1975) came in two flavors: • Hierarchical theory (Liberman and Prince 1977) • Metrical Grid (Prince 1982) • The grid model emphasized the rise and fall of an unnamed quantity. • Halle (et collaborator) attempted to integrate constituency and the grid.

8. Immediate constituents (ICs) • So the granddaddy of the constituent theory of syllables and feet is the structuralist theory of IC. • ICs were reformulated by Harris and by Chomsky as Phrase-Structure Grammars. • What’s the central idea of PSGs? (and why should we care?)

9. PSGs • Basic message: The structure in language does not pass from one terminal element to another, but flows up and down a tree. • The structural link between two adjacent elements is expressible directly iff they are sisters:

10. a ‘det’ can be followed by an N because there is a rule NPdet N; the generalization is through the mother category. This relationship is unchanged if there is a linearly intervening element:

11. PSGs are not designed to deal with relationships between adjacent terminal elements. That’s a hypothesis about the nature of syntax.

12. PSGs • are designed to deal with structurally defined positions that can be recursively elaborated indefinitely. • They are unnecessary for accounting for material that can be indefinitely expanded in a linear sense (i.e., flat structure).

13. PSGs • Not good at dealing with distinct functions assigned to the same distributional categories in different positions (i.e., marking pre-verbal NPs as subjects, post-verbal NPs as objects; distinguishing the functions of post verbal NPs; etc.)

14. Note what GPSG did: • Split up PS rules into mother-daughter relations (immediate constituency) and left-right relationships. • And in phonology?

15. What kind of structure do phonological representations need? • Proposal: They need to be able to identify local peaks and global peaks of two quantities: sonority and accent. • We need to build a model in which that computation is accomplished, and no other.

16. Original motivation for this particular model • Dell and Elmedlaoui’s analysis of Tashlhiyt Berber: • There, the generalization appears to be that segments compete with their neighbors with respect to sonority, so to speak. • In most cases, a segment is a syllable nucleus if and only if (iff) its sonority is greater than that of both of its neighbors.

17. We take that to be the central operation: search for elements for which a function takes on a peak value w.r.t. its neighbors. (discrete versions of 1st and 2nd derivative). • To this, we add another hypothesis: that the value of the function may be influenced by its context.

18. Its context? • Sonority: the inherent sonority of a segment may be influenced by its environment. The segments to its left and right may increase or decrease its sonority. Derived sonority is a function of both the inherent sonority and the sonority of the neighbors. • Accent:

19. Accent • The accent on an element is a function of both its inherent accentability (weight of the syllable = sum of the sonorities of the syllable or the coda) and its context: • Context? A stressed syllable destresses syllables on either side; • An unstressed syllable stresses syllables on either side. • All part of the same computational system.

20. Syllabification and accent are not part of a general, all-purpose phonological computational engine.

21. Dynamic computational nets • Brief demonstration of the program • Some background on (some aspects of) metrical theory • This network model as a minimal computational model of the solution we’re looking for. • Its computation of familiar cases • Interesting properties of this network: inversion and learnability • Link to neural circuitry

22. Dynamic computational nets • Brief demonstration of the program • Some background on (some aspects of) metrical theory • This network model as a minimal computational model of the solution we’re looking for. • Its computation of familiar cases • Interesting properties of this network: inversion and learnability • Link to neural circuitry

23. Let’s look at the program --

25. Dynamic computational nets • Brief demonstration of the program • Some background on (some aspects of) metrical theory • This network model as a minimal computational model of the solution we’re looking for. • Its computation of familiar cases • Interesting properties of this network: inversion and learnability • Link to neural circuitry

26. Dynamic computational network Final activation Initial activation b a

28. P(i) is the Positional activation assigned to a syllable by virtue of being (first, last) syllable of the word. That activation does not “go away” computationally.

29. Beta = -.9: rightward spread of activation

30. Alpha = -.9; leftward spread of activation

32. Dynamic computational nets • Brief demonstration of the program • Some background on (some aspects of) metrical theory • This network model as a minimal computational model of the solution we’re looking for. • Its computation of familiar cases • Interesting properties of this network: inversion and learnability • Link to neural circuitry

33. Examples (Hayes) Pintupi (Hansen and Hansen 1969, 1978; Australia): “syllable trochees”: odd-numbered syllables (rightward); extrametrical ultima: S s S s s S s S s S s S s s S s S s S s S s S s S s s

34. Weri (Boxwell and Boxwell 1966, Hayes 1980, HV 1987) • Stress the ultima, plus • Stress all odd numbered syllables, counting from the end of the word

35. Warao (Osborn 1966, HV 1987) Stress penult syllable; plus all even-numbered syllables, counting from the end of the word. (Mark last syllable as extrametrical, and run.)

36. Maranungku (Tryon 1970) Stress first syllable, and All odd-numbered syllables from the beginning of the word.

37. Garawa (Furby 1974) (or Indonesian, …) • Stress on Initial syllable; • Stress on Penult; • Stress on all even-numbered syllables, counting leftward from the end; but • “Initial dactyl effect”: no stress on the second syllable permitted.

38. Two other potential parameters to explore: • Penult activation • Bias = uniform activation for all units

39. Why penult? • Why not: in most cases, • negative Penult activation = positive Final activation, • positive Penult activation = negative Final activation But...

40. Two reasons to consider Penult... (in addition to the fact that it’s easily learnable): • One source for Antepenult patterns • Explanation of two patterns of cyclic stress assignment

41. Two kinds of cyclic assignment Indonesian type: Stress the penult: … s s S s add a suffix: ….s s s S ] s add a suffix: ….s s s s ] S ] s

42. [ S s S s S ] òtogògráfi Versus [ [ S s s s S s ] ] kòn tin u a sí ña (A. Cohn) I = 0.65 Pen = -1.0 alpha = -.4 beta = -0.2 [ [ s s s 0.31 -0.72 -0.85 ] ]

43. Greek • a. [ s1 s2 s3 ] • Inherent 0 0 -1 • Derived -0.2 0.5 -1 • b. [ s1 s2 s3 s4 ] • Inherent 0 0 0 -1 • Derived 0.06 -0.2 0.5 -1 • c. [ [ s1 s2 s3] s4 ] • Inherent 0 0 -1 -1 • Derived -0.12 0.25 -0.5 -1

44. Other type (Greek,…) ..s s S s add a suffix: …s s S s ] s (stress doesn’t shift) add another suffix: …s s s s] S ] s

45. Q-sensitive: Latin stress rule Stress penult if it is heavy; otherwise, stress the antepenult.

46. Q-sensitive systems: an example:ultima or penult

47. An analysis a=-0.2, b = 0.8 Heavy syllables get D = 2.0 If bias > 0 Yapese If bias < 0 Rotuman

48. Dynamic computational nets • Brief demonstration of the program • Some background on (some aspects of) metrical theory • This network model as a minimal computational model of the solution we’re looking for. • Its computation of familiar cases • Interesting properties of this network: inversion and learnability • Link to neural circuitry

49. = Network M Input (underlying representation) is a vector Dynamics: (1) Output is S*: equilibrium state of (1), which by definition is: Quite a surprise! Hence:

50. Please note... • This is not a system where you input a vector U, and watch in the limit