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Structured Representations
Melissa LibertusSepideh SadaghianiKlaus Tichacek
Cognitive ArchitecturesApril 30, 2003
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Symbolic Cognitive Model := System that iscapable of manipulating and composingsymbols and symbol structures
Symbol := physical pattern with associatedprocesses denoting either external or otherinternal symbol structures
Symbolic Cognitive Models
Newell & Simon
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Purely syntactic composition of novelstructures
Interpretation of novel structures
Explicit processes on structures
Important Characteristics of
Symbolic Models
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Central QuestionsAre connectionist models able to composeand interpret novel structures?
Do we have to model hardwired recursionas an example of structured representationat all?
How can we implement recursion in neuralsubstrate?
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Structured RePresentation
Structured Representations
Recursion
Need for models? Implementations
Representational
Challenges
Separational
Challenges
Churchland
Simple
Recurrent
Networks
Ramsey
Stich
Garon
Rumelhart
Todd
Old
Proposals
New
Proposal
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Two Aspects of Recursion
Syntax: Inductive definition ofstructured representations in the mind:
Set of primitive elements Way of combining primitive elements
to complex structures
Way of combining complex structures
to new complex structuresRecursion
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Two Aspects of Recursion
Semantics:
Representation of factual knowledgePropositions
Separate storage for each recursive factHardwired vs online recursion in
memory retrieval
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Representational Challenges
Churchland 1986: Geometrical conception
Distributed representation instead ofrecursively structured representation
No distinction between simple and complex
elementsEncoding as intersection between featuresets forming a point in hyperspace
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Representational Challenges
Marcus Rebuttal:
Not all concepts can be described in terms ofset intersections e.g. small elephant
Ambiguity
e.g. box inside a pot vs pot inside a box
Representation of boolean combinationse.g. nurse and elephant vs
nurse or elephant
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Simple Recurrent Networks Elman, 1995:
Simple recurrent networks can captureeverything that recursion can model
Apparently recursive structures represented
by patterns of hidden units
No explicit process for combining elements
Representational Challenges
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Marcus Rebuttal:
Inablity to generalize
No unique encoding of each recursivestructure
Representational Challenges
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Separational Challenges
Ramsey, Stich & Garon 1990:
No representation of propositions butdistributed encoding of information
Exemplar multilayer perceptron modelfor knowledge about animals
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Rumelhart & Todd 1993:
No representation of propositions butdistributed encoding of information
Exemplar semantic network model forknowledge about animals and plants
Separational Challenges
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Marcus Rebuttal:
Catastrophic interference
Overgeneralization
Separational Challenges
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Review: What features should
implementations include?
separate representational resources for each
propositionpresented in all following implementation
recursive complex structures
representing instances which are present inmultiple propositions avoiding crosstalk
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Structured RePresentation
Temporal
Synchrony
Structured
Space
Semantic
Networks
old
proposals
Structured Representations
Recursion
Need for models? Implementations
Representational
Challenges
Separational
Challenges
Temporal
Synchrony
+
OscillationFrequencies
Switching
NetworksTemporal
Asynchrony
New
proposal
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semantic networks
differ from MLPs: labeled connections between
nodes representing nature of relation
dont confuse with the hierarchical networksrepresenting only concepts: here every possibleproposition is represented
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semantic networks II
easy representation of recursivestructures
Marcus Rebuttal:crosstalk !
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semantic networks Problems1. crosstalk for multiple instances,
because:
each primitive is represented only once
solution: including a proposition node foreach proposition
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semantic networks Problems cont.
2. i building new nodes for each new word iibuilding new connections for each new
fact, rapidly and online! especially problematic
to STM
new nodes:accepting generation! fast enough?assigning values to preexisting
nodesnew connections:
temporal synchronyswitching network
temporal asynchrony
!
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solving problems of new connections temporal synchrony I
no connections at all !!!
each node hasrelation to a node specifying itsrole in the proposition
this relation is given by temporal synchrony
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solving problems of new connections temporal synchrony II
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solving problems of new connections temporal synchrony II
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solving problems of new connections temporal synchrony II
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solving problems of new connections temporal synchrony
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purple !!!
wearingglasses !!
employeeno recursion possible because of crosstalk
problems with multiple instance:
crosstalk like in semantic networks
similar solution with proposition nodes
!!
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temporal synchrony with oscillationfrequencies recursion
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Employee
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temporal synchrony with oscillationfrequenciesrecursion
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Employee
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temporal synchrony - Problems
Marcus Rebuttal:
memory capacities are limited: in temporal synchrony:
by the number of distinctable phases
in temp. synchrony with oscillationfrequencies:
by the number of distinctable harmonicperiods
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switching networks
solving problem of new connections
a switch connects the existing pointers of twonodes to each other
a new pointer just one! is built, only if a node isadded
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switching networks problems
Marcus Rebuttal:
memory capacities limited by number of
switches
no assymmetrydirection within a connection
each pointer connected only once
no multiple instances representable
no recursive structures! Temporal asynchrony
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Temporal asynchrony solving problem of new connections
preexisting connections, where learning adjuststheir weights
consistent with Hebbian Learning
bindings recovered by temporal information
coping with recursion
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Temporal asynchrony problems
Marcus Rebuttal:
cant deal with multiple instances
eachproposition nodewould needpreexisting connections to all possible
fillers!
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Mapping propositions to a
structuredspace I
1. onedimensional space
2. ndimensional space
J.Pollacks Approach: RAAM
RAAM: Recursive AutoAssociative Memory
A device to represent any binary tree structure
using a autoassociative network recursively
perfect representation of recursion
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Mapping propositions to a
structuredspace II
three layer network with2k output nodesk hidden nodes2k input nodes
Compressor: transforms atree to its representation
Reconstructor: transformsrepresentation back to thetree
Compressor
Reconstructor
selfsupervised: target output = input
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Mapping propositions to a
structuredspace III
the semantic treesfor each proposition
internal representationof the trees
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Mapping propositions to a
structuredspace IV
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Mapping propositions to a
structuredspace Problems
Marcus Rebuttal:
each node in the hidden layer must be able to
represent too many distinctable values
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Structured RePresentation
ComparisonTreelets
New
proposal
old
proposals
Structured Representations
Recursion
Need for models? Implementations
Representational
Challenges
Separational
Challenges
Registers Encoding LimitsAdvantages
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Registers see chapter 3
used to store information permanently
established by multistable device
multistable = more than one stable statecould be constructed in neural substrate by
cells which feed back into themselves
selfexcitatory cell assembliesintracellular by modulation of gene expressions
rapidly updateable =learn on a single trial
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Treelets
preorganized
hierarchical arrangement of register sets.
register set = ordered set of registers = single register
,, = set of registers
like prestructured templates
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Parts of a Treelet
Two types of pointers.But: Marcus never
explicitly explains why.
Register set Individualregister
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Treelets in the Mind
large stock of empty treelets
representing knowledge by
filling in an empty treeletadjusting values in existing treelets
a whole treelet encodes complex information
one single register set encodes asimpl
element
number of registers is predetermined and static
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Simple Elements
e.g.: cat, Mary, love,
possible representations
purely arbitrary and randomly
1, 1, 0, 0, 1, 0, 1,
according to semantic features
+furry, +fourlegged, haswings, features do not refer to properties of a particularinstance
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Encoding in a Treelet:
Simple Elements
similar to ASCIIcode
all occurrences of an instance receive the samecoding
every internal representation is identical
simple elements are like atoms
probably decomposable
make up more complex structures
like molecules
recursion
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11010
11100 11001
00011
00010 00001
11011 11101
Arbitrary coding in the
register sets.
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Fact #3
subject predicate
box
inside pot
relation object
The only example
Marcus gives!
Encoding in a Treelet
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Encoding in a Treelet:Complex Structures
account for various degrees of complexity by
treelets which vary in size
preexisting pointers are attached to adjacentregister sets
use of several fixedlength treelets
united by some sort of coding mechanismExample:
lions, the scariest mammals in the jungle, often liearound doing nothing
E di i T l t
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Encoding in a Treelet:Complex Structures II
both mechanisms could be possible
but use of fixedlength treelets seems more plausible
supported by findings from Bransford and Franks1971
recognize sentences exact order / structure
new, never heard sentences were composed out ofactually heard parts
E l f B f d &
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Example from Bransford &Franks
The ants ate the sweet jelly.
What ate the jelly?
The ants were in the kitchen.Where were the ants?
The ants in the kitchen ate the sweet jelly.Have you read this sentence before?
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Comparison
semantic nets vs. treelets
each primitive element is represented once, by asingle node
primitive elements are represented multiple times,seperately for each proposition
avoids damagedgrandmothernodeproblem
no creation of new nodes or pointers needed
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Comparison
temporalsynchronynetworks vs. treelets
treelets can represent a genuine hierarchicalstructure
just a single level of binding
store a large number of facts without interference
temporal synchrony
short term memorytreelets long term memory
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Comparison
alternative connectionist nets vs. treelets
all propositions are stored in a single overlapping,
superpositional substrateeach proposition is stored in a separate treelet
avoid catastrophic interference
treelets require an external system forgeneralization, extra mechanism
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Limits of treelets
computers do not represent information thisway
search through hierarchical structure is quite slow
serial search one by one
But treelets can be searched in parallel
external signal calling for matching treeletstreelets need to be more active than the standardpassive computer memory
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Examples
NETL Fahlmann 1979
interested parties bid parallel for an offer
central executive collects information ofbidders
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Further limits
treelets are just proposals aboutrepresentational formats
virtually unconstrained in what they can express
easy to abuse the system, fail to use nodes in a
consistent way
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Open questions
What sorts of mechanisms can manipulatetreelets?
How should the supervisory machinery looklike?
What do you think about this suggetion?Is it explicit enough?