structured representations

8/2/2019 Structured Representations

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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


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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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



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Marcus Rebuttal:

Inablity to generalize

No unique encoding of each recursivestructure



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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



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Marcus Rebuttal:

Catastrophic interference

Overgeneralization



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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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Temporal

Synchrony

Structured

Space

Semantic

Networks

old

proposals


Recursion


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

buyer

buyee

blicket

Vendor

I

Martin


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buyer

buyee

blicket

Vendor

I

Martin


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buyer

buyee

blicket

Vendor

I

Martin


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solving problems of new connections temporal synchrony

buyer

buyee

blicket

Vendor

I

Martin

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

buyer

buyee

blicket

Vendor

I

Martin

Employee


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temporal synchrony with oscillationfrequenciesrecursion

buyer

buyee

blicket

Vendor

I

Martin

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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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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structuredspace III

the semantic treesfor each proposition

internal representationof the trees


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structuredspace IV


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structuredspace Problems

Marcus Rebuttal:

each node in the hidden layer must be able to

represent too many distinctable values


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ComparisonTreelets

New

proposal

old

proposals


Recursion


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?

structured representations

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