 A LAD for OT

1.  A LAD for OT Markedness in acquisition: • Hypothesis: Universal markedness principles are genetically encoded, learning is search among UG-permitted grammars. • Question:Is this even conceivable? • Collaborators: Melanie Soderstrom Donald Mathis Oren Schwartz University of Amsterdam

2. V COns CCod ‘1’ ‘2’ CVNet Architecture /C1 C2/[C1 V C2] / C1 C2 / [ COns1 V CCod2 ] University of Amsterdam

3.  s1 Local: fixed, gene-tically determined Content of constraint 1 Global: variable during learning Strength of constraint 1  Connection substructure Network weight: Network input: ι = WΨ a s2 i 2 1 University of Amsterdam

4. V COns CCod PARSE (MAX) University of Amsterdam

5. V 1 COns CCod 1 1 NOCODA University of Amsterdam

6. CVNet Dynamics • Boltzmann machine/Harmony network • Learning: modification of Boltzmann machine algorithm to new architecture • Algorithm minimizes distance to correct output distribution • Stochastic activation algorithm: during processing, higher Harmony  more probable • Final state: local maximum guaranteed; if slow enough, global maximum probable University of Amsterdam

7. Learning Behavior • CVNet can only learn grammars consisting exactly of the CV-theory constraints Con with differential strengths • No guarantee of strict domination • A simplified system can be solved analytically • Learning algorithm turns out to ≈ Dsi() = e [# violations of constrainti P] University of Amsterdam

8. 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? University of Amsterdam

9. Unit types • Input units C V • Output units COns V CCod • 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 University of Amsterdam

10. COns V CCod ‘N’ ‘E’ ‘back’ Connectivity geometry Assume 3-d grid geometry University of Amsterdam

11. V COns CCod 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 3 3 3 Constraint: PARSE • Input units grow south and connect • Output units grow east and connect • Correspondence units grow north & west and connect with input & output units. University of Amsterdam

12. V COns CCod 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 +1 1 3 3 3 3 3 3 3 3 1 +1 3 3 3 3 3 3 3 3 Constraint: ONSET • Short connections grow north from V units and connect to COns unit University of Amsterdam

13. 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 University of Amsterdam

14. Projection parameters • Direction • Extent • Local • Non-local • Target unit type • Strength of connections encoded separately University of Amsterdam

15. Connectivity Genome • Contributions from ONSET and PARSE: • Key: University of Amsterdam

16. Learning Behavior • Simplified system can be solved analytically • Learning algorithm turns out to ≈ Dsi() = e [# violations of constrainti P] University of Amsterdam