(1) Learning (2) The proximity principle and “evolutionary learning”

1. Ling 411 – 17 (1) Learning(2) The proximity principle and “evolutionary learning”

2. Schedule of Presentations Tu Apr 13 Th Apr 15 Tu Apr 20 Th Apr 22

3. REVIEW Operations in relational networks • Relational networks are dynamic • Activation moves along lines and through nodes • Links have varying strengths • A stronger link carries more activation, other things being equal • All nodes operate on two principles: • Integration • Of incoming activation • Broadcasting • To other nodes

4. Review Operation of the Networkin terms of cortical columns • The linguistic system operates as distributed processing of multiple individual components • “Nodes” in an abstract model • These nodes are implemented as cortical columns • Columnar Functions • Integration: A column is activated if it receives enough activation from other columns • Can be activated to varying degrees • Can keep activation alive for a period of time • Broadcasting: An activated column transmits activation to other columns • Exitatory – contribution to higher level • Inhibitory – dampens competition at same level

5. Additional operations: Learning • Links get stronger when they are successfully used (Hebbian learning) • Learning consists of strengthening them • Hebb 1948 • Threshold adjustment • When a node is recruited its threshold increases • Otherwise, nodes would be too easily satisfied

6. Requirements that must be assumed(implied by the Hebbian learning principle) • Links get stronger when they are successfully used (Hebbian learning) • Learning consists of strengthening them • Prerequisites: • Initially, connection strengths are very weak • Term: Latent Links • They must be accompanied by nodes • Term: Latent Nodes • Latent nodes and latent connections must be available for learning anything learnable • The Abundance Hypothesis • Abundant latent links • Abundant latent nodes

7. Support for the abundance hypothesis • Abundance is a property of biological systems generally • Cf.: Acorns falling from an oak tree • Cf.: A sea tortoise lays thousands of eggs • Only a few will produce viable offspring • Cf. Edelman: “silent synapses” • The great preponderance of cortical synapses are “silent” (i.e., latent) • Electrical activity sent from a cell body to its axon travels to thousands of axon branches, even though only one or a few of them may lead to downstream activation

8. Learning – The Basic Process Latent nodes Latent links Dedicated nodes and links

9. Learning – The Basic Process Latent nodes Let these links get activated

10. Learning – The Basic Process Latent nodes Then these nodes will get activated

11. Learning – The Basic Process That will activate these links

12. Learning – The Basic Process This node gets enough activation to satisfy its threshold

13. Learning – The Basic Process This node is therefore recruited These links now get strengthened and the node’s threshold gets raised B A

14. Learning – The Basic Process This node is now dedicated to function AB AB B A

15. Learning Next time it gets activated it will send activation on these links to next level AB B A

16. Learning: more terms AB Child nodes Potential Actual Parent nodes B A

17. Learning: Deductions from the basic process • Learning is generally bottom-up. • The knowledge structure as learned by the cognitive network is hierarchical — has multiple layers • Hierarchy and proximity: • Logically adjacent levels in a hierarchy can be expected to be locally adjacent • Excitatory connections are predominantly from one layer of a hierarchy to the next • Higher levels will tend to have larger numbers of nodes than lower levels

18. Learning in cortical networks:A Darwinian process • A trial-and-error process: • Thousands of possibilities available • The abundance hypothesis • Strengthen those few that succeed • “Neural Darwinism” (Edelman) • The abundance hypothesis • Needed to allow flexibility of learning • Abundant latent nodes • Must be present throughout cortex • Abundant latent connections of a node • Every node must have abundant latent links

19. Learning – Enhanced understanding • This “basic process” is not the full story • The nodes of this depiction: • Are they minicolumns, maxicolumns, or what? • Most likely, a bundle of contiguous columns • Perhaps usually a maxicolumn or hypercolumn

20. REVIEW Columns of different sizes • Minicolumn • Basic anatomically described unit • 70-110 neurons (avg 75-80) • Diameter barely more than that of pyramidal cell body (30-50 μ) • Maxicolumn (term used by Mountcastle) • Diameter 300-500 μ • Bundle of 100 or more contiguous minicolumns • Hypercolumn – up to 1 mm diameter • Can be long and narrow rather than cylindrical • Bundle of contiguous maxicolumns • Functional column • Intermediate between minicolumn and maxicolumn • A contiguous group of minicolumns

21. REVIEW Hypercolums: Modules of maxicolumns A homotypical area in the temporal lobe of a macaque monkey

22. Functional columns vis-à-vis minicolumns and maxicolumns • Maxicolumn • About 100 minicolumns • About 300-500 microns in diameter • Functional column • A group of one to several contiguous minicolumns within a maxicolumn • Established during learning • Initially it might be an entire maxicolumn

23. Learning in a system with columns of different sizes • At early learning stage, maybe a whole hypercolumn gets recruited • Later, maxicolumns for further distinctions • Still later, functional columns as subcolumns within maxicolumns • New term: Supercolumn – a group of minicolumns of whatever size, hypercolumn, maxicolumn, functional column • Links between supercolumns will thus consist of multiple fibers

24. Question on cortical columns E-mail from Kelly Banneyer: …. I understand that a minicolumn is the smallest unit and maxicolumns are composed of minicolumns and functional columns are intermediate in size while hypercolumns are composed of several maxicolumns. I wonder if there can exist a minicolumn or functional column in the brain that is not part of a larger type of column. For example, I know that there exists hierarchical structure, but is there maybe some concept so exact and unrelated to anything else that a mini/functional column exists that is not part of a maxicolumn?

25. REVIEW Functional columns in phonological recognition:A hypothesis • Demisyllable (e.g. /de-/) activates a maxicolumn • Different functional columns within the maxicolumn for syllables with this demisyllable • /ded/, /deb/, /det/, /dek/, /den/, /del/

26. REVIEW Functional columns in phonological recognitionA hypothesis [de-] deb ded den de- det del dek A maxicolumn (ca. 100 minicolumns) Divided into functional columns (Note that all respond to /de-/)

27. REVIEW Phonological hypercolumns (a hypothesis) • Maybe we have • Hypercolumn of contiguous maxicolumns for /e/ • With maxicolumns for /de-/, /be-/, etc. • Each such maxicolumn subdivided into functional columns for different finals • /det/, /ded/, /den/, /deb/, /dem/. /dek/ • (N.B.: This is just a hypothesis) • Maybe someday soon we’ll be able to test with sensitive brain imaging

28. REVIEW Adjacent maxicolumns in phonological cortex? A module of contiguous maxicolumns de- te- be- pe- Hypercolum Each of these maxicolumns is divided into functional columns ge- ke- Note that the entire module responds to [-e-]

29. REVIEW Adjacent maxicolumns in phonological cortex? de- te- deb ded den de- det del dek A module of six contiguous maxicolumns be- pe- ge- ke- The entire maxicolumn responds to [de-] The entire module responds to [-e-]

30. Revisit the diagram: Each node of the diagram represents a group of minicolumns – a supercolumn Latent super-columns Bundles of latent links Dedicated super-columns and links

31. Learning – The Basic Process Let these links get activated

32. Learning – The Basic Process:Refined view Then these supercolumns get activated

33. Learning – The Basic Process:Refined view That will activate these links

34. Learning – Refined view This supercolumn gets enough activation to satisfy its threshold

35. Learning – Refined view This super-column is recruited for function AB AB B A

36. Learning:Refined view Next time it gets activated it will send activation on these links to next level AB B A

37. LearningRefined view Can get subdivided for finer distinctions AB B A

38. A further enhancement • Minicolumns within a supercolumn have mutual horizontal excitatory connections • Therefore, some minicolumns can get activated from their neighbors even if they don’t receive activation from outside

39. Learning: Refined view AB Hypercolumn composed of 3 maxicolumns Can get subdivided for finer distinctions B A

40. Learning: refined view If, later, C is activated along with A and B, then maxicolumn ABC is recruited for ABC ABC AB B A C

41. Learning: refined view And the connection from C to ABC is strengthened –it is no longer latent ABC AB B A C

42. Learning phonological distinctions:A hypothesis de- te- deb ded den de- det del dek 1. In learning, this hypercolumn gets established first, responding to [-e-] be- pe- ge- ke- 3. The maxicolumn gets divided into functional columns 2. It gets subdivided into maxicolumns for demisyllables

43. Remaining problems – lateral inhibition • When a hypercolumn is first recruited, no lateral inhibition among its internal subdivisions • Later, when finer distinctions are learned, they get reinforced by lateral inhibition • Problem: How does this work?

44. REVIEW Hypothesis applied to conceptual categories • A whole maxicolumn gets activated for the category • Example: DRINKING-VESSEL • Different functional columns within the maxicolumn for subcategories • CUP, GLASS, etc. • Adjacent maxicolumns for categories related to DRINKING VESSEL • BOWL, JAR, etc.

45. Locating Functions:The Proximity Principle • Related functions tend to be in close proximity • If very closely related, they tend to be adjacent  • Areas which integrate properties of different subsystems (e.g., different sensory modalities) tend to be in locations intermediate between those subsystems

46. Consequences of the Proximity Principle • Nodes in close competition will tend to be neighbors • And their mutual competition is preordained even though the properties they are destined to integrate will only be established through the learning process • Therefore, inhibitory connections should exist predominantly among nodes of the same hierarchical level • The presence of their mutual inhibitory connections could be genetically specified

47. Learning and the Proximity Principle • Start with the observation: • Related areas tend to be adjacent to each other • Primary auditory and Wernicke’s area • V1 and V2, etc. • Wernicke’s area and lexical-conceptual information – angular gyrus, SMG, MTG • Thus we have the ‘proximity principle’ • Question: Why – How to explain?

48. Two aspects of the proximity principle • A node that integrates a combination of properties of different subsystems can be expected to lie in a location intermediate between those subsystems • A node that integrates a combination of properties of the same subsystem should be within the same subsystem, and maximally close to the properties it integrates

49. How to Explain the Proximity Principle? • Factors responsible for observations of proximity in cortical structure • Economic necessity • Genetic factors • Experience – provides details of localization within the limits imposed by genetic factors

50. Proximity: Economic necessity • Question: Could a given column be connected to any other column anywhere in the cortex? • That would require a huge number of available latent connections • Way more than are present • Hence there are strict limits on intercolumn connectivity • Therefore, proximity is necessary just for economy of representation