(1) Learning (2) The proximity principle and

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(1) Learning (2) The proximity principle
and evolutionary learning
Ling 411 17
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Schedule of Presentations
Tu Apr 13 Th Apr 15 Tu Apr 20
Th Apr 22
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Operations in relational networks
REVIEW

• 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

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Operation of the Networkin terms of cortical
columns
Review

• 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

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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

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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

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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

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Learning The Basic Process
Latent nodes
Latent links
Dedicated nodes and links
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Learning The Basic Process
Latent nodes
Let these links get activated
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Learning The Basic Process
Latent nodes
Then these nodes will get activated
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Learning The Basic Process
That will activate these links
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Learning The Basic Process
This node gets enough activation to satisfy its
threshold
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Learning The Basic Process
This node is therefore recruited
These links now get strengthened and the nodes
threshold gets raised
B
A
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Learning The Basic Process
This node is now dedicated to function AB
AB
B
A
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Learning
Next time it gets activated it will send
activation on these links to next level
AB
B
A
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Learning more terms
AB
Child nodes Potential Actual
Parent nodes
B
A
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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

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Learning in cortical networksA 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

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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

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Columns of different sizes
REVIEW

• 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

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

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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

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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?
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Functional columns in phonological recognitionA
hypothesis
REVIEW

• Demisyllable (e.g. /de-/) activates a maxicolumn
• Different functional columns within the
  maxicolumn for syllables with this demisyllable
• /ded/, /deb/, /det/, /dek/, /den/, /del/

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

• 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 well be able to test with
  sensitive brain imaging

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Adjacent maxicolumns in phonological cortex?
REVIEW
de-
A module of contiguous maxicolumns
te-
be-
pe-
Hypercolum
Each of these maxicolumns is divided into
functional columns
ge-
ke-
Note that the entire module responds to -e-
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Adjacent maxicolumns in phonological cortex?
REVIEW
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-
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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
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Learning The Basic Process
Let these links get activated
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Learning The Basic ProcessRefined view
Then these supercolumns get activated
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Learning The Basic ProcessRefined view
That will activate these links
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Learning Refined view
This supercolumn gets enough activation to
satisfy its threshold
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Learning Refined view
This super-column is recruited for function AB
AB
B
A
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LearningRefined view
Next time it gets activated it will send
activation on these links to next level
AB
B
A
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LearningRefined view
Can get subdivided for finer distinctions
AB
B
A
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A further enhancement

• Minicolumns within a supercolumn have mutual
  horizontal excitatory connections
• Therefore, some minicolumns can get activated
  from their neighbors even if they dont receive
  activation from outside

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Learning Refined view
AB
Hypercolumn composed of 3 maxicolumns Can get
subdivided for finer distinctions
B
A
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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
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Learning refined view
And the connection from C to ABC is strengthened
it is no longer latent
ABC
AB
B
A
C
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Learning phonological distinctionsA 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
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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?

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Hypothesis applied to conceptual categories
REVIEW

• 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.

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Locating FunctionsThe 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

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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

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Learning and the Proximity Principle

• Start with the observation
• Related areas tend to be adjacent to each other
• Primary auditory and Wernickes area
• V1 and V2, etc.
• Wernickes area and lexical-conceptual
  information angular gyrus, SMG, MTG
• Thus we have the proximity principle
• Question Why How to explain?

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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

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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

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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

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Limits on intercolumn connectivity

• Number of cortical minicolumns
• If 27 billion neurons in entire cortex
• If avg. 77 neurons per minicolumn
• Then 350 million minicolumns in the cortex
• Extent of available latent connections to other
  columns
• Perhaps 35,000 to 350,000
• Do the math..
• A given column has available latent connections
  to between 1/1000 and 1/10000 of the other
  columns in the cortex

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Locations of available latent connections

• Local
• Surrounding area
• Horizontal connections (grey matter)
• Intermediate
• Short-distance fibers in white matter
• For example from one gyrus to neighboring gyrus
• Long-distance
• Long-distance fiber bundles
• At ends, considerable branching

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The role of long-distance fibers

• Arcuate fasciculus
• Genetically determined
• Limits location of phonological recognition area
• Interhemispheric fibers
• Also genetically determined
• Wernickes area RH homolog of Ws area
• Brocas area RH homolog of Bs area
• Etc.

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Two Factors in Localization

• Genetic factors determine general area for a
  particular type of knowledge
• Within this general area the learning-based
  proximity factors select a more narrowly defined
  location
• Thus the exact localization depends on experience
  of the individual
• When part of the system is damaged,
  learning-based factors can take over and result
  in an abnormal location for a function
  plasticity

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Genetically determined proximity

• Genetically-determined proximity would have
  developed over a long period of evolution
• Many features are shared with other mammals
• This process could be called evolutionary
  learning
• According to standard evolutionary theory..
• A process of trial-and-error
• Trial
• Produce varieties
• Error
• Most varieties will not survive/reproduce
• The others the best among them are selected
• Other genetic factors supplement proximity
• Long-distance fiber bundles

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Some innate factors relating to localization

• Primary areas
• Long-distance fiber bundles

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Innate factors relating to primary areas

• Location
• Genetically determined locations
• But there are exceptions
• Malformation
• Damage
• Structure
• Genetically determined structures adapted to
  sensory modality (they have to be where they are)
• Heterotypical structures
• Found in primary areas
• Primary visual
• Primary auditory

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A Heterotypical (i.e., genetically built-in)
structureVisual motion perception
REVIEW
An area in the posterior bank of the superior
temporal sulcus of a macaque monkey (V-5) A
heterotpical area Albright et al. 1984
400-500 µ
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A Heterotypical structureAuditory areas in a
cats cortex
REVIEW
A1
AAF Anterior auditory field A1 Primary
auditory field PAF Posterior auditory
field VPAF Ventral posterior
auditory field
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Innate factors relating to localization

• The primary areas
• Long-distance fiber bundles
• Interhemispheric via corpus callosum
• Longitudinal from front to back
• Arcuate fasciculus is part of the superior
  longitudinal fasciculus
• They allow for exceptions to proximity
• Areas closely related yet not neighboring

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Applying the proximity principle

• For both types (genetic and experience-based) we
  can make predictions of where various functions
  are most likely to be located, based on the
  proximity principle
• Brocas area near the inferior precentral gyrus
• Wernickes area near the primary auditory area
• Such predictions are possible even in cases where
  we dont know whether genetics or learning is
  responsible
• maybe both

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Implications of the proximity principle

• System level
• Functionally related subsystems will tend to be
  close to one another
• Neighboring subsystems will probably have related
  functions
• Cortical column level
• Nodes for similar functions should be physically
  close to one another
• Nodes that are physically close to one another
  probably have similar functions
• Therefore..
• Neighboring nodes are likely to be competitors
• They need to have mutually inhibitory connections

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Deriving location from proximity hypothesis

• The cortex has to provide for decoding speech
  input
• Speech input enters the cortex in the primary
  auditory area
• Results of the decoding (recognition of
  syllables etc.) are represented in Wernickes
  area
• Why is Wernickes area where it is?

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Speech Recognition in the Left Hemisphere
Phonological Production
Phonological Recognition
Primary Auditory Area
Wernickes Area
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Exercise Location of Wernickes area

• Why is phonological recognition in the posterior
  superior temporal gyrus?
• Alternatives to consider
• Anterior to primary auditory cortex
• Advantage would be close to phonological
  production
• Inferior to primary auditory cortex
• (There are two reasons)

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Answer Location of Wernickes area

• Wernickes area pretty much has to be where it is
  to take advantage of the arcuate fasciculus
• The location of W.s area makes it close to
  angular gyrus, likely area for noun lemmas
  (morphemes and complex morphemes)
• Also, close to SMG, presumed area for
  phonological monitoring
• (Why?
• Because it is adjacent to primary somatosensory
  area)

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More exercises

• Explaining likely locations of morphemes
• verb morphemes in the frontal lobe
• noun morphemes in the angular gyrus and/or middle
  temporal gyrus
• The dorsal (where) pathway of visual perception

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Experience-based proximity

• Can be expected to be operative
• more at higher (more abstract) levels, less at
  lower levels
• for areas of knowledge that have developed too
  recently for evolution to have played a role
• Reading
• Writing
• Higher mathematics
• Physics, computer technology, etc.

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Innate features that support language

• Columnar structure
• Coding of frequencies in Heschls gyrus
• Arcuate fasciculus
• Interhemispheric connections (via corpus
  callosum) e.g., connect Wernickes area with RH
  homolog
• Spread of myelination from primary areas to
  successively higher levels
• Left-hemisphere dominance for grammar etc.

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