• Dynamics that add new Nodes or Links to a hypergraph, or remove existing ones.
13.3 Atoms: Their Types and Weights
This section reviews a variety of CogPrime
Atom types and gives simple examples of each of them. The Atom types considered are drawn
from those currently in use in the OpenCog system. This does not represent a complete list of
Atom types referred to in the text of this book, nor a complete list of those used in OpenCog
currently (though it does cover a substantial majority of those used in OpenCog currently,
omitting only some with specialized importance or intended only for temporary use).
The partial nature of the list given here reflects a more general point: The specific collection
of Atom types in an OpenCog system is bound to change as the system is developed and experiment
with. CogPrime specifies a certain collection of representational approaches and cognitive
algorithms for acting on them; any of these approaches and algorithms may be implemented
with a variety of sets of Atom types. The specific set of Atom types in the OpenCog system
currently does not necessarily have a profound and lasting significance – the list might look a
bit different five years from time of writing, based on various detailed changes.
The treatment here is informal and intended to get across the general idea of what each
Atom type does. A longer and more formal treatment of the Atom types is given in Part II,
beginning in Chapter 20.
13.3.1 Some Basic Atom Types
We begin with ConceptNode – and note that a ConceptNode does not necessarily refer to a
whole concept, but may refer to part of a concept – it is essentially a "basic semantic node"
whose meaning comes from its links to other Atoms. It would be more accurately, but less
tersely, named "concept or concept fragment or element node." A simple example would be a
ConceptNode grouping nodes that are somehow related, e.g.
ConceptNode: C
InheritanceLink (ObjectNode: BW) C
InheritanceLink (ObjectNode: BP) C
InheritanceLink (ObjectNode: BN) C
ReferenceLink BW (PhraseNode "Ben’s watch")
ReferenceLink BP (PhraseNode "Ben’s passport")
ReferenceLink BN (PhraseNode "Ben’s necklace")
248 13 Local, Global and Glocal Knowledge Representation
indicates the simple and uninteresting ConceptNode grouping three objects owned by Ben
(note that the above-given Atoms don’t indicate the ownership relationship, they just link the
three objects with textual descriptions). In this example, the ConceptNode links transparently
to physical objects and English descriptions, but in general this won’t be the case – most
ConceptNodes will look to the human eye like groupings of links of various types, that link to
other nodes consisting of groupings of links of various types, etc.
There are Atoms referring to basic, useful mathematical objects, e.g. NumberNodes like
NumberNode #4
NumberNode #3.44
The numerical value of a NumberNode is explicitly referenced within the Atom.
A core distinction is made between ordered links and unordered links; these are handled
differently in the Atomspace software. A basic unordered link is the SetLink, which groups its
arguments into a set. For instance, the ConceptNode C defined by
ConceptNode C
MemberLink A C
MemberLink B C
is equivalent to
SetLink A B
On the other hand, ListLinks are like SetLinks but ordered, and they play a fundamental role
due to their relationship to predicates. Most predicates are assumed to take ordered arguments,
so we may say e.g.
EvaluationLink
PredicateNode eat
ListLink
ConceptNode cat
ConceptNode mouse
to indicate that cats eat mice.
Note that by an expression like
ConceptNode cat
is meant
ConceptNode C
ReferenceLink W C
WordNode W #cat
since it’s WordNodes rather than ConceptNodes that refer to words. (And note that the strength
of the ReferenceLink would not be 1 in this case, because the word "cat" has multiple senses.)
However, there is no harm nor formal incorrectness in the "ConceptNode cat" usage, since "cat"
is just as valid a name for a ConceptNode as, say, "C."
We’ve already introduced above the MemberLink, which is a link joining a member to the
set that contains it. Notable is that the truth value of a MemberLink is fuzzy rather than
probabilistic, and that PLN is able to inter-operate fuzzy and probabilistic values.
SubsetLinks also exist, with the obvious meaning, e.g.
ConceptNode cat
ConceptNode animal
SubsetLink cat animal
13.3 Atoms: Their Types and Weights 249
Note that SubsetLink refers to a purely extensional subset relationship, and that InheritanceLInk
should be used for the generic "intensional + extensional" analogue of this – more
on this below. SubsetLink could more consistently (with other link types) be named ExtensionalInheritanceLink,
but SubsetLink is used because it’s shorter and more intuitive.
There are links representing Boolean operations AND, OR and NOT. For instance, we may
say
ImplicationLink
ANDLink
ConceptNode young
ConceptNode beautiful
ConceptNode attractive
or, using links and VariableNodes instead of ConceptNodes,
AverageLink $X
ImplicationLink
ANDLink
EvaluationLink young $X
EvaluationLink beautiful $X
EvaluationLink attractive $X
NOTLink is a unary link, so e.g. we might say
AverageLink $X
ImplicationLink
ANDLink
EvaluationLink young $X
EvaluationLink beautiful $X
EvaluationLink
NOT
EvaluationLink poor $X
EvaluationLink attractive $X
ContextLink allows explicit contextualization of knowledge, which is used in PLN, e.g.
ContextLink
ConceptNode golf
InheritanceLink
ObjectNode BenGoertzel
ConceptNode incompetent
says that Ben Goertzel is incompetent in the context of golf.
13.3.2 Variable Atoms
We have already introduced VariableNodes above; it’s also possible to specify the type of a
VariableNode via linking it to a VariableTypeNode via a TypedVariableLink, e.g.
VariableTypeLink
VariableNode $X
VariableTypeNode ConceptNode
which specifies that the variable $X should be filled with a ConceptNode.
Variables are handled via quantifiers; the default quantifier being the AverageLink, so that
the default interpretation of
250 13 Local, Global and Glocal Knowledge Representation
ImplicationLink
InheritanceLink $X animal
EvaluationLink
PredicateNode: eat
ListLink
\$X
ConceptNode: food
is
AverageLink $X
ImplicationLink
InheritanceLink $X animal
EvaluationLink
PredicateNode: eat
ListLink
\$X
ConceptNode: food
The AverageLink invokes an estimation of the average TruthValue of the embedded expression
(in this case an ImplicationLink) over all possible values of the variable $X. If there are type
restrictions regarding the variable $X, these are taken into account in conducting the averaging.
For AllLink and Exist s-Link may be used in the same places as AverageLink, with uncertain
truth value semantics defined in PLN theory using third-order probabilities. There is also a
ScholemLink used to indicate variable dependencies for existentially quantified variables, used
in cases of multiply nested existential quantifiers.
EvaluationLink and MemberLink have overlapping semantics, allowing expression of the
same conceptual/logical relationships in terms of predicates or sets, i.e.
EvaluationLink
PredicateNode: eat
ListLink
$X
ConceptNode: food
has the same semantics as
MemberLink
ListLink
$X
ConceptNode: food
ConceptNode: EatingEvents
The relation between the predicate "eat" and the concept "EatingEvents" is formally given by
ExtensionalEquivalenceLink
ConceptNode: EatingEvents
SatisfyingSetLink
PredicateNode: eat
In other words, we say that "EatingEvents" is the SatisfyingSet of the predicate "eat": it is the
set of entities that satisfy the predicate "eat". Note that the truth values of MemberLink and
EvaluationLink are fuzzy rather than probabilistic.
13.3 Atoms: Their Types and Weights 251
13.3.3 Logical Links
There is a host of link types embodying logical relationships as defined in the PLN logic system,
e.g.
• InheritanceLink
• SubsetLink (aka ExtensionalInheritanceLink)
• Intensional InheritanceLink
which embody different sorts of inheritance, e.g.
SubsetLink salmon fish
IntensionalInheritanceLink whale fish
InheritanceLink fish animal
and then
• SimilarityLink
• ExtensionalSimilarityLink
• IntensionalSimilarityLink
which are symmetrical versions, e.g.
SimilaritytLink shark barracuda
IntensionalSimilarityLink shark dolphin
ExtensionalSimiliarityLink American obese\_person
There are also higher-order versions of these links, both asymmetric
• ImplicationLink
• ExtensionalImplicationLink
• IntensionalImplicationLink
and symmetric
• EquivalenceLink
• ExtensionalEquivalenceLink
• IntensionalEquivalenceLink
These are used between predicates and links, e.g.
ImplicationLink
EvaluationLink
eat
ListLink
$X
dirt
EvaluationLink
feel
ListLInk
$X
sick
or
252 13 Local, Global and Glocal Knowledge Representation
ImplicationLink
EvaluationLink
eat
ListLink
$X
dirt
InheritanceLink $X sick
or
ForAllLink $X, $Y, $Z
ExtensionalEquivalenceLink
EquivalenceLink
$Z
EvaluationLink
+
ListLink
$X
$Y
EquivalenceLink
$Z
EvaluationLink
+
ListLink
$Y
$X
Note, the latter is given as an extensional equivalence because it’s a pure mathematical equivalence.
This is not the only case of pure extensional equivalence, but it’s an important one.
13.3.4 Temporal Links
There are also temporal versions of these links, such as
• PredictiveImplicationLink
• PredictiveAttractionLink
• SequentialANDLink
• SimultaneousANDLink
which combine logical relation between the argument with temporal relation between their
arguments. For instance, we might say
PredictiveImplicationLink
PredicateNode: JumpOffCliff
PredicateNode: Dead
or including arguments,
PredictiveImplicationLink
EvaluationLink JumpOffCliff $X
EvaluationLink Dead $X
The former version, without variable arguments given, shows the possibility of using higherorder
logical links to join predicates without any explicit variables. Via using this format exclusively,
one could avoid VariableAtoms entirely, using only higher-order functions in the manner
13.3 Atoms: Their Types and Weights 253
of pure functional programming formalisms like combinatory logic. However, this purely functional
style has not proved convenient, so the Atomspace in practice combines functional-style
representation with variable-based representation.
Temporal links often come with specific temporal quantification, e.g.
PredictiveImplicationLink <5 seconds>
EvaluationLink JumpOffCliff $X
EvaluationLink Dead $X
indicating that the conclusion will generally follow the premise within 5 seconds. There is a
system for managing fuzzy time intervals and their interrelationships, based on a fuzzy version
of Allen Interval Algebra.
SequentialANDLink is similar to PredictiveImplicationLink but its truth value is calculated
differently. The truth value of
SequentialANDLink <5 seconds>
EvaluationLink JumpOffCliff $X
EvaluationLink Dead $X
indicates the likelihood of the sequence of events occurring in that order, with gap lying within
the specified time interval. The truth value of the PredictiveImplicationLink version indicates
the likelihood of the second event, conditional on the occurrence of the first event (within the
given time interval restriction).
There are also links representing basic temporal relationships, such as BeforeLink and AfterLink.
These are used to refer to specific events, e.g. if X refers to the event of Ben waking
up on July 15 2012, and Y refers to the event of Ben getting out of bed on July 15 2012, then
one might have
AfterLink X Y
And there are TimeNodes (representing time-stamps such as temporal moments or intervals)
and AtTimeLinks, so we may e.g. say
AtTimeLink
X
TimeNode: 8:24AM Eastern Standard Time, July 15 2012 AD
13.3.5 Associative Links
There are links representing associative, attentional relationships,
• HebbianLink
• AsymmetricHebbianLink
• InverseHebbianLink
• SymmetricInverseHebbianLink
These connote associations between their arguments, i.e. they connote that the entities represented
by the two argument occurred in the same situation or context, for instance
HebbianLink happy smiling
AsymmetricHebbianLink dead rotten
InverseHebbianLink dead breathing
254 13 Local, Global and Glocal Knowledge Representation
The asymmetric HebbianLink indicates that when the first argument is present in a situation,
the second is also often present. The symmetric (default) version indicates that this relationship
holds in both directions. The inverse versions indicate the negative relationship: e.g. when one
argument is present in a situation, the other argument is often not present.
13.3.6 Procedure Nodes
There are nodes representing various sorts of procedures; these are kinds of ProcedureNode,
e.g.
• SchemaNode, indicating any procedure
• GroundedSchemaNode, indicating any procedure associated in the system with a Combo
program or C++ function allowing the procedure to be executed
• PredicateNode, indicating any predicate that associates a list of arguments with an output
truth value
• GroundedPredicateNode, indicating a predicate associated in the system with a Combo
program or C++ function allowing the predicate’s truth value to be evaluated on a given
specific list of arguments
ExecutionLinks and EvaluationLinks record the activity of SchemaNodes and PredicateNodes.
We have seen many examples of EvaluationLinks in the above. Example ExecutionLinks
would be:
ExecutionLink step\_forward
ExecutionLink step\_forward 5
ExecutionLink
+
ListLink
NumberNode: 2
NumberNode: 3
The first example indicates that the schema "step forward" has been executed. The second
example indicates that it has been executed with an argument of "5" (meaning, perhaps, that 5
steps forward have been attempted). The last example indicates that the "+" schema has been
executed on the argument list (2,3), presumably resulting in an output of 5.
The output of a schema execution may be indicated using an ExecutionOutputLink, e.g.
ExecutionOutputLink
+
ListLink
NumberNode: 2
NumberNode: 3
refers to the value "5" (as a NumberNode).
13.3.7 Links for Special External Data Types
Finally, there are also Atom types referring to specific types of data important to using OpenCog
in specific contexts.
13.3 Atoms: Their Types and Weights 255
For instance, there are Atom types referring to general natural language data types, such as
• WordNode
• SentenceNode
• WordInstanceNode
• DocumentNode
plus more specific ones referring to relationships that are part of link-grammar parses of sentences
• FeatureNode
• FeatureLink
• LinkGrammarRelationshipNode
• LinkGrammarDisjunctNode
or RelEx semantic interpretations of sentences
• DefinedLinguisticConceptNode
• DefinedLinguisticRelationshipNode
• PrepositionalRelationshipNode
There are also Atom types corresponding to entities important for embodying OpenCog in
a virtual world, e.g.
• ObjectNode
• AvatarNode
• HumanoidNode
• UnknownObjectNode
• AccessoryNode
13.3.8 Truth Values and Attention Values
CogPrime Atoms (Nodes and Links) are quantified with truth values that, in their simplest
form, have two components, one representing probability (strength) and the other representing
weight of evidence; and also with attention values that have two components, short-term and
long-term importance, representing the estimated value of the Atom on immediate and longterm
time-scales.
In practice many Atoms are labeled with CompositeTruthValues rather than elementary ones.
A composite truth value contains many component truth values, representing truth values of
the Atom in different contexts and according to different estimators.
It is important to note that the CogPrime declarative knowledge representation is neither
a neural net nor a semantic net, though it does have some commonalities with each of these
traditional representations. It is not a neural net because it has no activation values, and involves
no attempts at low-level brain modeling. However, attention values are very loosely analogous
to time-averages of neural net activations. On the other hand, it is not a semantic net because
of the broad scope of the Atoms in the network: for example, Atoms may represent percepts,
procedures, or parts of concepts. Most CogPrime Atoms have no corresponding English label.
However, most CogPrime
Atoms do have probabilistic truth values, allowing logical semantics.
256 13 Local, Global and Glocal Knowledge Representation
13.4 Knowledge Representation via Attractor Neural Networks
Now we turn to global, implicit knowledge representation – beginning with formal neural net
models, briefly discussing the brain, and then turning back to CogPrime. Firstly, this section
reviews some relevant material from the literature regarding the representation of knowledge
using attractor neural nets. It is a mix of well-established fact with more speculative material.
13.4.1 The Hopfield neural net model
Hopfield networks [Hop82] are attractor neural networks often used as associative memories. A
Hopfield network with N neurons can be trained to store a set of bipolar patterns P , where
each pattern p has N bipolar (±1) values. A Hopfield net typically has symmetric weights with
no self-connections. The weight of the connection between neurons i and j is denoted by w ij .
In order to apply a Hopfield network to a given input pattern p, its activation state is set to
the input pattern, and neurons are updated asynchronously, in random order, until the network
converges to the closest fixed point. An often-used activation function for a neuron is:
∑
y i = sign(p i w ij y j )
Training a Hopfield network, therefore, involves finding a set of weights w ij that stores the
training patterns as attractors of its network dynamics, allowing future recall of these patterns
from possibly noisy inputs.
Originally, Hopfield used a Hebbian rule to determine weights:
w ij =
j≠i
P∑
p i p j
p=1
Typically, Hopfield networks are fully connected. Experimental evidence, however, suggests
that the majority of the connections can be removed without significantly impacting the network’s
capacity or dynamics. Our experimental work uses sparse Hopfield networks.
13.4.1.1 Palimpsest Hopfield nets with a modified learning rule
In [SV99] a new learning rule is presented, which both increases the Hopfield network capacity
and turns it into a “palimpsest”, i.e., a network that can continuously learn new patterns, while
forgetting old ones in an orderly fashion.
Using this new training rule, weights are initially set to zero, and updated for each new
pattern p to be learned according to:
13.4 Knowledge Representation via Attractor Neural Networks 257
N∑
h ij = w ik p k
k=1,k≠i,j
∆w ij = 1 n (p ip j − h ij p j − h ji p i )
13.4.2 Knowledge Representation via Cell Assemblies
Hopfield nets and their ilk play a dual role: as computational algorithms, and as conceptual
models of brain function. In CogPrime they are used as inspiration for slightly different, artificial
economics based computational algorithms; but their hypothesized relevance to brain function
is nevertheless of interest in a CogPrime context, as it gives some hints about the potential
connection between low-level neural net mechanics and higher-level cognitive dynamics.
Hopfield nets lead naturally to a hypothesis about neural knowledge representation, which
holds that a distinct mental concept is represented in the brain as either:
1. a set of “cell assemblies”, where each assembly is a network of neurons that are interlinked
in such a way as to fire in a (perhaps nonlinearly) synchronized manner
2. a distinct temporal activation pattern, which may occur in any one (or more) of a particular
set of cell assemblies
For instance, this hypothesis is perfectly coherent if one interprets a “mental concept” as a
SMEPH (defined in Chapter 14) ConceptNode, i.e. a fuzzy set of perceptual stimuli to which
the organism systematically reacts in different ways. Also, although we will focus mainly on
declarative knowledge here, we note that the same basic representational ideas can be applied
to procedural and episodic knowledge: these may be hypothesized to correspond to temporal
activation patterns as characterized above.
In the biology literature, perhaps the best-articulated modern theories championing the cell
assembly view are those of Gunther Palm [Pal82, HAG07] and Susan Greenfield [SF05, CSG07].
Palm focuses on the dynamics of the formation and interaction assemblies of cortical columns.
Greenfield argues that each concept has a core cell assembly, and that when the concept rises
to the focus of attention, it recruits a number of other neurons beyond its core characteristic
assembly into a “transient ensemble.” 1
It’s worth noting that there may be multiple redundant assemblies representing the same
concept – and potentially recruiting similar transient assemblies when highly activated. The
importance of repeated, slightly varied copies of the same subnetwork has been emphasized by
Edelman [Ede93] among other neural theorists.
1 The larger an ensemble is, she suggests, the more vivid it is as a conscious experience; an hypothesis that
accords well with the hypothesis made in [Goe06b] that a more informationally intense pattern corresponds to
a more intensely conscious quale – but we don’t need to digress extensively onto matters of consciousness for
the present purposes.
258 13 Local, Global and Glocal Knowledge Representation
13.5 Neural Foundations of Learning
Now we move from knowledge representation to learning – which is after all nothing but the
adaptation of represented knowledge based on stimulus, reinforcement and spontaneous activity.
While our focus in this chapter is on representation, it’s not possible for us to make our points
about glocal knowledge representation in neural net type systems without discussing some
aspects of learning in these systems.
13.5.1 Hebbian Learning
The most common and plausible assumption about learning in the brain is that synaptic connections
between neurons are adapted via some variant of Hebbian learning. The original Hebbian
learning rule, proposed by Donald Hebb in his 1949 book [Heb49], was roughly
1. The weight of the synapse x → y increases if x and y fire at roughly the same time
2. The weight of the synapse x → y decreases if x fires at a certain time but y does not
Over the years since Hebb’s original proposal, many neurobiologists have sought evidence that
the brain actually uses such a method. One of the things they have found, so far, is a lot of
evidence for the following learning rule [DC02, LS05]:
1. The weight of the synapse x → y increases if x fires shortly before y does
2. The weight of the synapse x → y decreases if x fires shortly after y does
The new thing here, not foreseen by Donald Hebb, is the “postsynaptic depression” involved in
rule component 2.
Now, the simple rule stated above does not sum up all the research recently done on Hebbiantype
learning mechanisms in the brain. The real biological story underlying these approximate
rules is quite complex, involving many particulars to do with various neurotransmitters. Illunderstood
details aside, however, there is an increasing body of evidence that not only does
this sort of learning occur in the brain, but it leads to distributed experience-based neural
modification: that is, one instance synaptic modification causes another instance of synaptic
modification, which causes another, and so forth 2 [Bi01].
13.5.2 Virtual Synapses and Hebbian Learning Between Assemblies
Hebbian learning is conventionally formulated in terms of individual neurons, but, it can be
extended naturally to assemblies via defining “virtual synapses” between assemblies.
Since assemblies are sets of neurons, one can view a synapse as linking two assemblies
if it links two neurons, each of which is in one of the assemblies. One can then view
two assemblies as being linked by a bundle of synapses. We can define the weight of the
synaptic bundle from assembly A1 to assembly A2 as the number w so that (the change
2 This has been observed in “model systems” consisting of neurons extracted from a brain and hooked together
in a laboratory setting and monitored; measurement of such dynamics in vivo is obviously more difficult.
13.5 Neural Foundations of Learning 259
in the mean activation of A2 that occurs at time t+epsilon) is on average closest to w ×
(the amount of energy flowing through the bundle from A1 to A2 at time t). So when A1 sends
an amount x of energy along the synaptic bundle pointing from A1 to A2, then A2’s mean
activation is on average incremented/decremented by an amount w × x.
In a similar way, one can define the weight of a bundle of synapses between a certain static
or temporal activation-pattern P1 in assembly A1, and another static or temporal activationpattern
P2 in assembly A2. Namely, this may be defined as the number w so that (the amount
of energy flowing through the bundle from A1 to A2 at time t)×w best approximates (the
probability that P2 is present in A2 at time t+epsilon), when averaged over all times t during
which P1 is present in A1.
It is not hard to see that Hebbian learning on real synapses between neurons implies Hebbian
learning on these virtual synapses between cell assemblies and activation-patterns.
These ideas may be developed further to build a connection between neural knowledge representation
and probabilistic logical knowledge representation such as is used in CogPrime’s
Probabilistic Logic Networks formalism; this connection will be pursued at the end of Chapter
34, once more relevant background has been presented.
13.5.3 Neural Darwinism
A notion quite similar to Hebbian learning between assemblies has been pursued by Nobelist
Gerald Edelman in his theory of neuronal group selection, or “Neural Darwinism.” Edelman won
a Nobel Prize for his work in immunology, which, like most modern immunology, was based on
C. MacFarlane Burnet’s theory of “clonal selection” [Bur62], which states that antibody types
in the mammalian immune system evolve by a form of natural selection. From his point of view,
it was only natural to transfer the evolutionary idea from one mammalian body system (the
immune system) to another (the brain).
The starting point of Neural Darwinism is the observation that neuronal dynamics may be
analyzed in terms of the behavior of neuronal groups. The strongest evidence in favor of this
conjecture is physiological: many of the neurons of the neocortex are organized in clusters, each
one containing say 10,000 to 50,000 neurons each. Once one has committed oneself to looking at
such groups, the next step is to ask how these groups are organized, which leads to Edelman’s
concept of “maps.”
A “map,” in Edelman’s terminology, is a connected set of groups with the property that when
one of the inter-group connections in the map is active, others will often tend to be active as
well. Maps are not fixed over the life of an organism. They may be formed and destroyed in
a very simple way: the connection between two neuronal groups may be “strengthened” by increasing
the weights of the neurons connecting the one group with the other, and “weakened” by
decreasing the weights of the neurons connecting the two groups. If we replace “map” with “cell
assembly” we arrive at a concept very similar to the one described in the previous subsection.
Edelman then makes the following hypothesis: the large-scale dynamics of the brain is dominated
by the natural selection of maps. Those maps which are active when good results are
obtained are strengthened, those maps which are active when bad results are obtained are
weakened. And maps are continually mutated by the natural chaos of neural dynamics, thus
providing new fodder for the selection process. By use of computer simulations, Edelman and his
colleagues have shown that formal neural networks obeying this rule can carry out fairly compli-
260 13 Local, Global and Glocal Knowledge Representation
cated acts of perception. In general-evolution language, what is posited here is that organisms
like humans contain chemical signals that signify organism-level success of various types, and
that these signals serve as a “fitness function” correlating with evolutionary fitness of neuronal
maps.
In Neural Darwinism and his other related books and papers, Edelman goes far beyond this
crude sketch and presents neuronal group selection as a collection of precise biological hypotheses,
and presents evidence in favor of a number of these hypotheses. However, we consider that
the basic concept of neuronal group selection is largely independent of the biological particularities
in terms of which Edelman has phrased it. We suspect that the mutation and selection of
“transformations” or “maps” is a necessary component of the dynamics of any intelligent system.
As we will see later on (e.g. in Chapter 42 of Part 2, this business of maps is extremely
important to CogPrime. CogPrime does not have simulated biological neurons and synapses,
but it does have Nodes and Links that in some contexts play loosely similar roles. We sometimes
think of CogPrime Nodes and Links as being very roughly analogous to Edelman’s neuronal
clusters, and emergent intercluster links. And we have maps among CogPrime Nodes and Links,
just as Edelman has maps among his neuronal clusters. Maps are not the sole bearers of meaning
in CogPrime, but they are significant ones.
There is a very natural connection between Edelman-style brain evolution and the ideas
about cognitive evolution presented in Chapter 3. Edelman proposes a fairly clear mechanism
via which patterns that survive a while in the brain are differentially likely to survive a long
time: this is basic Hebbian learning, which in Edelman’s picture plays a role between neuronal
groups. And, less directly, Edelman’s perspective also provides a mechanism by which intense
patterns will be differentially selected in the brain: because on the level of neural maps, pattern
intensity corresponds to the combination of compactness and functionality. Among a number
of roughly equally useful maps serving the same function, the more compact one will be more
likely to survive over time, because it is less likely to be disrupted by other brain processes
(such as other neural maps seeking to absorb its component neuronal groups into themselves).
Edelman’s neuroscience remains speculative, since so much remains unknown about human
neural structure and dynamics; but it does provide a tentative and plausible connection between
evolutionary neurodynamics and the more abstract sort of evolution that patternist philosophy
posits to occur in the realm of mind-patterns.
13.6 Glocal Memory
A glocal memory is one that transcends the global/local dichotomy and incorporates both
aspects in a tightly interconnected way. Here we make the glocal memory concept more precise,
and describe its incarnation in the context of attractor neural nets (which is similar to its
incarnation in CogPrime, to be elaborated in later chapters). Though our main interest here is
in glocality in CogPrime, we also suggest that glocality may be a critical property to consider
when analyzing human, animal and AI memory more broadly.
The notion of glocal memory has implicitly occurred in a number of prior brain theories
(without use of the neologism “glocal”), e.g. [Cal96] and [Goe01], but it has not previously been
explicitly developed. However the concept has risen to the fore in our recent AI work and so
we have chosen to flesh it out more fully in [HG08], [GPI + 10] and the present section.
13.6 Glocal Memory 261
Glocal memory overcomes the dichotomy between localized memory (in which each memory
item is stored in a single location within an overall memory structure) and distributed memory
(in which a memory item is stored as an aspect of a multi-component memory system, in such
a way that the same set of multiple components stores a large number of memories). In a glocal
memory system, most memory items are stored both locally and globally, with the property
that eliciting either one of the two records of an item tends to also elicit the other one.
Glocal memory applies to multiple forms of memory; however we will focus largely on perceptual
and declarative memory in our detailed analyses here, so as to conserve space and maintain
simplicity of discussion.
The central idea of glocal memory is that (perceptual, declarative, episodic, procedural,
etc.) items may be stored in memory in the form of paired structures that are called (key,
map) pairs. Of course the idea of a “pair” is abstract, and such pairs may manifest themselves
quite differently in different sorts of memory systems (e.g. brains versus non-neuromorphic AI
systems). The key is a localized version of the item, and records some significant aspects of
the items in a simple and crisp way. The map is a dispersed, distributed version of the item,
which represents the item as a (to some extent, dynamically shifting) combination of fragments
of other items. The map includes the key as a subset; activation of the key generally (but not
necessarily always) causes activation of the map; and changes in the memory item will generally
involve complexly coordinated changes on the key and map level both.
Memory is one area where animal brain architecture differs radically from the von Neumann
architecture underlying nearly all contemporary general-purpose computers. Von Neumann
computers separate memory from processing, whereas in the human brain there is no such
distinction. In fact, it’s arguable that in most cases the brain contains no memory apart from
processing: human memories are generally constructed in the course of remembering [Ros88],
which gives human memory a strong capability for “filling in gaps” of remembered experience
and knowledge; and also causes problems with inaccurate remembering in many contexts
[BF71, RM95] We believe the constructive aspect of memory is largely associated with its
glocality.
The remainder of this section presents a fuller formalization of the glocal memory concept,
which is then taken up further in three later chapters:
• Chapter ?? discusses the potential implementation of glocal memory in the human brain
• Chapter ?? discusses the implementation of glocal memory in attractor neural net systems
• Chapter 23 presents Glocal Economic Attention Networks (ECANs), rough analogues of
glocal Hopfield nets that play a central role in CogPrime.
Our hypothesis of the potential general importance of glocality as a property of memory
systems (beyond just the CogPrime architecture) – remains somewhat speculative. The presence
of glocality in human and animal memory is strongly suggested but not firmly demonstrated by
available neuroscience data; and the general value of glocality in the context of artificial brains
and minds is also not yet demonstrated as the whole field of artificial brain and mind building
remains in its infancy. However, the utility of glocal memory for CogPrime is not tied to this
more general, speculative theme – glocality may be useful in CogPrime even if we’re wrong that
it plays a significant role in the brain and in intelligent systems more broadly.
262 13 Local, Global and Glocal Knowledge Representation
13.6.1 A Semi-Formal Model of Glocal Memory
To explain the notion of glocal memory more precisely, we will introduce a simple semi-formal
model of a system S that uses a memory to record information relevant to the actions it
carries out. The overall concept of glocal memory should not be considered as restricted to
this particular model. This model is not intended for maximal generality, but is intended to
encompass a variety of current AI system designs and formal neurological models.
In this model, we will consider S’s memory subsystem as a set of objects we’ll call “tokens,”
embedded in some metric space. The metric in the space, which we will call the “basic distance”
of the memory, generally will not be defined in terms of the semantics of the items stored in the
memory; though it may come to shape these dynamics through the specific architecture and
evolution of the memory. Note that these tokens are not intended as generally being mapped
one-to-one onto meaningful items stored in the memory. The “tokens” are the raw materials
that the memory arranges in various patterns in order to store items.
We assume that each token, at each point in time, may meaningfully be assigned a certain
quantitative “activation level.” Also, tokens may have other numerical or discrete quantities
associated with them, depending on the particular memory architecture. Finally, tokens may
relate other tokens, so that optionally a token may come equipped with an (ordered or unordered)
list of other tokens.
To understand the meaning of the activation levels, one should think about S’s memory
subsystem as being coupled with an action-selection subsystem, that dynamically chooses the
actions to be taken by the overall system in which the two subsystems are embedded. Each
combination of actions, in each particular type of context, will generally be associated with the
activation of certain tokens in memory.
Then, as analysts of the system S, we may associate each token T with an “activation vector”
v(T, t), whose value for each discrete time t consists of the activation of the token T at time t.
So, the 50 ′ th entry of the vector corresponds to the activation of the token at the 50 ′ th time
step.
“Items stored in memory” over a certain period of time, may then be defined as clusters in
the set of activation vectors associated with memory during that period of time. Note that the
system S itself may explicitly recognize and remember patterns regarding what items are stored
in its memory – but, from an external analyst’s perspective, the set of items in S’s memory is
not restricted to the ones that S has explicitly recognized as memory items.
The “localization” of a memory item may be defined as the degree to which the various tokens
involved in the item are close to each other according to the metric in the memory metric-space.
This degree may be formalized in various ways, but choosing a particular quantitative measure
is not important here. A highly localized item may be called “local” and a not-very-localized
item may be called “global.”
We may define the “activation distance” of two tokens as the distance between their activation
vectors. We may then say that a memory is “well aligned” to the extent that there is a correlation
between the activation distance of tokens, and the basic distance of the memory metric-space.
Given the above set-up, the basic notion of glocal memory can be enounced fairly simply. A
glocal memory is one:
• that is reasonably well-aligned (i.e. the correlation between activation and basic distance is
significantly greater than random)
13.6 Glocal Memory 263
• in which most memory items come in pairs, consisting of one local item and one global
item, so that activation of the local item (the “key”) frequently leads in the near future to
activation of the global item (the “map”)
Obviously, in the scope of all possible memory structures constructible within the above
formalism, glocal memories are going to be very rare and special. But, we suggest that they are
important, because they are generally going to be the most effective way for intelligent systems
to structure their memories.
Note also that many memories without glocal structure may be “well-aligned” in the above
sense.
An example of a predominantly local memory structure, in which nearly all significant memory
items are local according to the above definition, is the Cyc logical reasoning engine [LG90].
To cast the Cyc knowledge base in the present formal model, the tokens are logical predicates.
Cyc does not have an in-built notion of activation, but one may conceive the activation of a
logical formula in Cyc as the degree to which the formula is used in reasoning or query processing
during a certain interval in time. And one may define a basic metric for Cyc by associating
a predicate with its extension (the set of satisfying inputs), and defining the similarity of two
predicates as the symmetric distance of their extensions. Cyc is reasonably well-aligned, but
according to the dynamics of its querying and reasoning engines, it is basically a local memory
structure without significant global memory structure.
On the other hand, an example of a predominantly global memory structure, in which nearly
all significant memory items are global according to the above definition, is the Hopfield associative
memory network [Ami89]. Here memories are stored in the pattern of weights associated
with synapses within a network of formal neurons, and each memory in general involves a large
number of the neurons in the network. To cast the Hopfield net in the present formal model, the
tokens are neurons and synapses; the activations are neural net activations; the basic distance
between two neurons A and B may be defined as the percentage of the time that stimulating
one of the neurons leads to the other one firing; and to calculate a basic distance involving a
synapse, one may associate the synapse with its source and target neurons. With these definitions,
a Hopfield network is a well-aligned memory, and (by intentional construction) a markedly
global one. Local memory items will be very rare in a Hopfield net.
While predominantly local and predominantly global memories may have great value for particular
applications, our suggestion is that they also have inherent limitations. If so, this means
that the most useful memories for general intelligence are going to be those that involve both
local and global memory items in central roles. However, this is a more general and less risky
claim than the assertion that glocal memory structure as defined above is important. Because,
“glocal” as defined above doesn’t just mean “neither predominantly global nor predominantly
local.” Rather, it refers to a specific pattern of coordination between local and global memory
items – what we have called the “keys and maps” pattern.
13.6.2 Glocal Memory in the Brain
Science’s understanding of human brain dynamics is still very primitive, one manifestation of
which is the fact that we really don’t understand how the brain represents knowledge, except
in some very simple respects. So anything anyone says about knowledge representation in the
brain, at this stage, has to be considered highly speculative. Existing neuroscience knowledge
264 13 Local, Global and Glocal Knowledge Representation
does imply constraints on how knowledge representation in the brain may work, but these are
relatively loose constraints. These constraints do imply that, for instance, the brain is neither a
relational database (in which information is stored in a wholly localized manner) nor a collection
of “grandmother neurons” that respond individually to high-level percepts or concepts; nor a
simple Hopfield type neural net (in which all memories are attractors globally distributed across
the whole network). But they don’t tell us nearly enough to, for instance, create a formal neural
net model that can confidently be said to represent knowledge in the manner of the human brain.
As a first example of the current state of knowledge, we’ll discuss here a series of papers
regarding the neural representation of visual stimuli [QaGKKF05, QKKF08], which deal with
the fascinating discovery of a subset of neurons in the medial temporal lobe (MTL) that are
selectively activated by strikingly different pictures of given individuals, landmarks or objects,
and in some cases even by letter strings. For instance, in their 2005 paper titled ”Invariant visual
representation by single neurons in the human brain”, it is noted that
in one case, a unit responded only to three completely different images of the ex-president Bill Clinton.
Another unit (from a different patient) responded only to images of The Beatles, another one to cartoons
from The Simpson’s television series and another one to pictures of the basketball player Michael Jordan.
Their 2008 follow-up paper backed away from the more extreme interpretation in the title as
well as the conclusion, with the title “Sparse but not ‘Grandmother-cell’ coding in the medial
temporal lobe.” As the authors emphasize there,
Given the very sparse and abstract representation of visual information by these neurons, they could in
principle be considered as ‘grandmother cells’. However, we give several arguments that make such an
extreme interpretation unlikely.
. . .
MTL neurons are situated at the juncture of transformation of percepts into constructs that can be
consciously recollected. These cells respond to percepts rather than to the detailed information falling
on the retina. Thus, their activity reflects the full transformation that visual information undergoes
through the ventral pathway. A crucial aspect of this transformation is the complementary development
of both selectivity and invariance. The evidence presented here, obtained from recordings of single-neuron
activity in humans, suggests that a subset of MTL neurons possesses a striking invariant representation
for consciously perceived objects, responding to abstract concepts rather than more basic metric details.
This representation is sparse, in the sense that responsive neurons fire only to very few stimuli (and are
mostly silent except for their preferred stimuli), but it is far from a Grandmother-cell representation.
The fact that the MTL represents conscious abstract information in such a sparse and invariant way is
consistent with its prominent role in the consolidation of long-term semantic memories.
It’s interesting to note how inadequate the [QKKF08] data really is for exploring the notion
of glocal memory in the brain. Suppose it’s the case that individual visual memories correspond
to keys consisting of small neuronal subnetworks, and maps consisting of larger neuronal
subnetworks. Then it would be not at all surprising if neurons in the “key” network corresponding
to a visual concept like “Bill Clinton’s face” would be found to respond differentially
to the presentation of appropriate images. Yet, it would also be wrong to overinterpret such
data as implying that the key network somehow comprises the “representation” of Bill Clinton’s
face in the individual’s brain. In fact this key network would comprise only one aspect of said
representation.
In the glocal memory hypothesis, a visual memory like “Bill Clinton’s face” would be hypothesized
to correspond to an attractor spanning a significant subnetwork of the individual’s brain
13.6 Glocal Memory 265
– but this subnetwork still might occupy only a small fraction of the neurons in the brain (say,
1/100 or less), since there are very many neurons available. This attractor would constitute the
map. But then, there would be a much smaller number of neurons serving as key to unlock
this map: i.e. if a few of these key neurons were stimulated, then the overall attractor pattern
in the map as a whole would unfold and come to play a significant role in the overall brain
activity landscape. In prior publications [Goe97] the primary author explored this hypothesis
in more detail in terms of the known architecture of the cortex and the mathematics of complex
dynamical attractors.
So, one possible interpretation of the [QKKF08] data is that the MTL neurons they’re
measuring are part of key networks that correspond to broader map networks recording percepts.
The map networks might then extend more broadly throughout the brain, beyond the MTL
and into other perceptual and cognitive areas of cortex. Furthermore, in this case, if some MTL
key neurons were removed, the maps might well regenerate the missing keys (as would happen
e.g. in the glocal Hopfield model to be discussed in the following section).
Related and interesting evidence for glocal memory in the brain comes from a recent study of
semantic memory, illustrated in Figure ?? [PNR07]. Their research probed the architecture of
semantic memory via comparing patients suffering from semantic dementia (SD) with patients
suffering from three other neuropathologies, and found reasonably convincing evidence for what
they call a “distributed-plus-hub” view of memory.
The SD patients they studied displayed highly distinctive symptomology; for instance, their
vocabularies and knowledge of the properties of everyday objects were strongly impaired,
whereas their memories of recent events and other cognitive capacities remain perfectly intact.
These patients also showed highly distinctive patterns of brain damage: focal brain lesions
in their anterior temporal lobes (ATL), unlike the other patients who had either less severe or
more widely distributed damage in their ATLs. This led [PNR07] to conclude that the ATL
(being adjacent to the amygdala and limbic systems that process reward and emotion; and the
anterior parts of the medial temporal lobe memory system, which processes episodic memory)
is a “hub” for amodal semantic memory, drawing general semantic information from episodic
memories based on emotional salience.
So, in this view, the memory of something like a “banana” would contain a distributed aspect,
spanning multiple brain systems, and also a localized aspect, centralized in the ATL.
The distributed aspect would likely contain information on various particular aspects of bananas,
including their sights, smells, and touches, the emotions they evoke, and the goals and
motivations they relate to. The distributed and localized aspects would influence one another
dynamically, but, the data [PNR07] gathered do not address dynamics and they don’t venture
hypotheses in this direction.
There is a relationship between the “distributed-plus-hub” view and [Dam00] better-known
notion of a “convergence zone”, defined roughly as a location where the brain binds features together.
A convergence zone, in [Dam00] perspective, is not a “store” of information but an agent
capable of decoding a signal (and of reconstructing information). He also uses the metaphor
that convergence zones behave like indexes drawing information from other areas of the brain –
but they are dynamic rather than static indices, containing the instructions needed to recognize
and combine the features constituting the memory of something. The mechanism involved in
the distributed-plus-hub model is similar to a convergence zone, but with the important difference
that hubs are less local: [PNR07] semantic hub may be thought of a kind of “cluster of
convergence zones” consisting of a network of convergence zones for various semantic memories.
266 13 Local, Global and Glocal Knowledge Representation
Fig. 13.1: A Simplified Look at Feedback-Control in Uncertain Inference
What is missing in [PNR07] and [Dam00] perspective is a vision of distributed memories
as attractors. The idea of localized memories serving as indices into distributed knowledge
stores is important, but is only half the picture of glocal memory: the creative, constructive,
dynamical-attractor aspect of the distributed representation is the other half. The closest thing
to a clear depiction of this aspect of glocal memory that seems to exist in the neuroscience
literature is a portion of William Calvin’s theory of the “cerebral code” [Cal96]. Calvin proposes
a set of quite specific mechanisms by which knowledge may be represented in the brain
using complexly-structured strange attractors, and by which these strange attractors may be
propagated throughout the brain. Figure 13.2 shows one aspect of his theory: how a distributed
attractor may propagate from one part of the brain to another in pieces, with one portion of
the attractor getting propagated first, and then seeding the formation in the destination brain
region of a close approximation of the whole attractor.
Calvin’s theory may be considered a genuinely glocal theory of memory. However, it also
makes a large number of other specific commitments that are not part of the notion of glocality,
such as his proposal of hexagonal meta-columns in the cortex, and his commitment to
evolutionary learning as the primary driver of neural knowledge creation. We find these other
13.6 Glocal Memory 267
Fig. 13.2: Calvin’s Model of Distributed Attractors in the Brain
hypotheses interesting and highly promising, yet feel it is also important to separate out the
notion of glocal memory for separate consideration.
Regarding specifics, our suggestion is that Calvin’s approach may overemphasize the distributed
aspect of memory, not giving sufficient due to the relatively localized aspect as accounted
for in the [QKKF08] results discussed above. In Calvin’s glocal approach, global memories
are attractors and local memories are parts of attractors. We suggest a possible alternative,
in which global memories are attractors and local memories are particular neuronal subnetworks
such as the specialized ones identified by [QKKF08]. However, this alternative does not seem
contradictory to Calvin’s overall conceptual approach, even though it is different from the particular
proposals made in [Cal96].
The above paragraphs are far from a complete survey of the relevant neuroscience literature;
there are literally dozens of studies one could survey pointing toward the glocality of various
sorts of human memory. Yet experimental neuroscience tools are still relatively primitive, and
every one of these studies could be interpreted in various other ways. In the next couple decades,
as neuroscience tools improve in accuracy, our understanding of the role of glocality in human
memory will doubtless improve tremendously.
268 13 Local, Global and Glocal Knowledge Representation
13.6.3 Glocal Hopfield Networks
The ideas in the previous section suggest that, if one wishes to construct an AGI, it is worth
seriously considering using a memory with some sort of glocal structure. One research direction
that follows naturally from this notion is “glocal neural networks.” In order to explore the nature
of glocal neural networks in a relatively simple and tractable setting, we have formalized and
implemented simple examples of “glocal Hopfield networks”: palimpsest Hopfield nets with the
addition of neurons representing localized memories. While these specific networks are not used
in CogPrime, they are quite similar to the ECAN networks that are used in CogPrime and
described in Chapter 23 of Part 2.
Essentially, we augment the standard Hopfield net architecture by adding a set of “key
neurons.” These are a small percentage of the neurons in the network, and are intended to be
roughly equinumerous to the number of memories the network is supposed to store. When the
Hopfield net converges to an attractor A, then new links are created between the neurons that
are active in A, and one of the key neurons. Which key neuron is chosen? The one that, when
it is stimulated, gives rise to an attractor pattern maximally similar to A.
The ultimate result of this is that, in addition to the distributed memory of attractors in the
Hopfield net, one has a set of key neurons that in effect index the attractors. Each attractor
corresponds to a single key neuron. In the glocal memory model, the key neurons are the keys
and the Hopfield net attractors are the maps.
This algorithm has been tested in sparse Hopfield nets, using both standard Hopfield net
learning rules and Storkey’s modified palimpsest learning rule [SV99], which provides greater
memory capacity in a continuous learning context. The use of key neurons turns out to slightly
increase Hopfield net memory capacity, but this isn’t the main point. The main point is that
one now has a local representation of each global memory, so that if one wants to create a
link between the memory and something else, it’s extremely easy to do so – one just needs
to link to the corresponding key neuron. Or, rather, one of the corresponding key neurons:
depending on how many key neurons are allocated, one might end up with a number of key
neurons corresponding to each memory, not just one.
In order to transform a palimpsest Hopfield net into a glocal Hopfield net, the following steps
are taken:
1. Add a fixed number of “key neurons” to the network (removing other random neurons to
keep the total number of neurons constant)
2. When the network reaches an attractor, create links from the elements in the attractor to
one of the key neurons
3. The key neuron chosen for the previous step is the one that most closely matches the current
attractor (which may be determined in several ways, to be discussed below)
4. To avoid the increase of the number of links in the network, when new links are created in
Step 2, other key-neuron links are then deleted (several approaches may be taken here, but
the simplest is to remove the key-neuron links with the lowest-absolute-value weights)
In the simple implementation of the above steps that we implemented, and described in
[GPI + 10], Step 3 is carried out simply by comparing the weights of a key neuron’s links to the
nodes in an attractor. A more sophisticated approach would be to select the key neuron with
the highest activation during the transient interval immediately prior to convergence to the
attractor.
13.6 Glocal Memory 269
The result of these modifications to the ordinary Hopfield net, is a Hopfield net that continually
maintains a set of key neurons, each of which individually represents a certain attractor
of the net.
Note that these key neurons – in spite of being “symbolic” in nature – are learned rather
than preprogrammed, and are every bit as adaptive as the attractors they correspond to. Furthermore,
if a key neuron is removed, the glocal Hopfield net algorithm will eventually learn it
back, so the robustness properties of Hopfield nets are retained.
The results of experimenting with glocal Hopfield nets of this nature are summarized in
[GPI + 10]. We studied Hopfield nets with connectivity around .1, and in this context we found
that glocality
• slightly increased memory capacity
• massively increased the rate of convergence to the attractor, i.e. the speed of recall
However, probably the most important consequence of glocality is a more qualitative one: it
makes it far easier to link the Hopfield net into a larger system, as would occur if the Hopfield net
were embedded in an integrative AGI architecture. Because a neuron external to the Hopfield
net may now link to a memory in the Hopfield net by linking to the corresponding key neuron.
13.6.4 Neural-Symbolic Glocality in CogPrime
In CogPrime, we have explicitly sought to span the symbolic/emergentist pseudo-dichotomy,
via creating an integrative knowledge representation that combines logic-based aspects with
neural-net-like aspects. As reviewed in Chapter 6 above, these function not in the manner of
multimodular systems, but rather via using (probabilistic) truth values and (attractor neural
net like) attention values as weights on nodes and links of the same (hyper) graph. The nodes
and links in this hypergraph are typed, like a standard semantic network approach for knowledge
representation, so they’re able to handle all sorts of knowledge, from the most concrete
perception and actuation related knowledge to the most abstract relationships. But they’re also
weighted with values similar to neural net weights, and pass around quantities (importance
values, discussed in Chapter 23 of Part 2) similar to neural net activations, allowing emergent
attractor/assembly based knowledge representation similar to attractor neural nets.
The concept of glocality lies at the heart of this combination, in a way that spans the pseudodichotomy:
• Local knowledge is represented in abstract logical relationships stored in explicit logical
form, and also in Hebbian-type associations between nodes and links.
• Global knowledge is represented in large-scale patterns of node and link weights, which
lead to large-scale patterns of network activity, which often take the form of attractors
qualitatively similar to Hopfield net attractors. These attractors are called maps.
The result of all this is that a concept like “cat” might be represented as a combination of:
• A small number of logical relationships and strong associations, that constitute the “key”
subnetwork for the “cat” concept.
• A large network of weak associations, binding together various nodes and links of various
types and various levels of abstraction, representing the “cat map”.
270 13 Local, Global and Glocal Knowledge Representation
The activation of the key will generally cause the activation of the map, and the activation of
a significant percentage of the map will cause the activation of the rest of the map, including the
key. Furthermore, if the key were for some reason forgotten, then after a significant amount of
effort, the system would likely to be able to reconstitute it (perhaps with various small changes)
from the information in the map. We conjecture that this particular kind of glocal memory will
turn out to be very powerful for AGI, due to its ability to combine the strengths of formal
logical inference with those of self-organizing attractor neural networks.
As a simple example, consider the representation of a “tower”, in the context of an artificial
agent that has built towers of blocks, and seen pictures of many other kinds of towers, and seen
some tall building that it knows are somewhat like towers but perhaps not exactly towers. If
this agent is reasonably conceptually advanced (say, at Piagetan the concrete operational level)
then its mind will contain some declarative relationships partially characterizing the concept of
“tower,” as well as its sensory and episodic examples, and its procedural knowledge about how
to build towers.
The key of the “tower” concept in the agent’s mind may consist of internal images and
episodes regarding the towers it knows best, the essential operations it knows are useful for
building towers (piling blocks atop blocks atop blocks...), and the core declarative relations
summarizing “towerness” – and the whole “tower” map then consists of a much larger number
of images, episodes, procedures and declarative relationships connected to “tower” and other
related entities. If any portion of the map is removed – even if the key is removed – then the
rest of the map can be approximately reconstituted, after some work. Some cognitive operations
are best done on the localized representation – e.g. logical reasoning. Other operations, such as
attention allocation and guidance of inference control, are best done using the globalized map
representation.
Chapter 14
Representing Implicit Knowledge via Hypergraphs
14.1 Introduction
Explicit knowledge is easy to write about and talk about; implicit knowledge is equally important,
but tends to get less attention in discussions of AI and psychology, simply because we don’t
have as good a vocabulary for describing it, nor as good a collection of methods for measuring
it. One way to deal with this problem is to describe implicit knowledge using language and
methods typically reserved for explicit knowledge. This might seem intrinsically non-workable,
but we argue that it actually makes a lot of sense. The same sort of networks that a system like
CogPrime uses to represent knowledge explicitly, can also be used to represent the emergent
knowledge that implicitly exists in an intelligent system’s complex structures and dynamics.
We’ve noted that CogPrime uses an explicit representation of knowledge in terms of weighted
labeled hypergraphs; and also uses other more neural net like mechanisms (e.g. the economic
attention allocation network subsystem) to represent knowledge globally and implicitly. Cog-
Prime combines these two sorts of representation according to the principle we have called
glocality. In this chapter we pursue glocality a bit further – describing a means by which even
implicitly represented knowledge can be modeled using weighted labeled hypergraphs similar to
the ones used explicitly in CogPrime. This is conceptually important, in terms of making clear
the fundamental similarities and differences between implicit and explicit knowledge representation;
and it is also pragmatically meaningful due to its relevance to the CogPrime methods
described in Chapter 42 of Part 2 that transform implicit into explicit knowledge.
To avoid confusion with CogPrime’s explicit knowledge representation, we will refer to the
hypergraphs in this chapter as composed of Vertices and Edges rather than Nodes and Links. In
prior publications we have referred to "derived" or "emergent" hypergraphs of the sort described
here using the acronym SMEPH, which stands for Self-Modifying, Evolving Probabilistic Hypergraphs.
14.2 Key Vertex and Edge Types
We begin by introducing a particular collection of Vertex and Edge types, to be used in modeling
the internal structures of intelligent systems.
The key SMEPH Vertex types are
271
272 14 Representing Implicit Knowledge via Hypergraphs
• ConceptVertex, representing a set, for instance, an idea or a set of percepts
• SchemaVertex, representing a procedure for doing something (perhaps something in the
physical world, or perhaps an abstract mental action).
The key SMEPH Edge types, using language drawn from Probabilistic Logic Networks (PLN)
and elaborated in Chapter 34 below, are as follows:
• ExtensionalInheritanceEdge (ExtInhEdge for short: an edge which, linking one Vertex or
Edge to another, indicates that the former is a special case of the latter)
• ExtensionalSimilarityEdge (ExtSim: which indicates that one Vertex or Edge is similar to
another)
• ExecutionEdge (a ternary edge, which joins S,B,C when S is a SchemaVertex and the result
from applying S to B is C).
So, in a SMEPH system, one is often looking at hypergraphs whose Vertices represent ideas or
procedures, and whose Edges represent relationships of specialization, similarity or transformation
among ideas and/or procedures.
The semantics of the SMEPH edge types is given by PLN, but is simple and commonsensical.
ExtInh and ExtSim Edges come with probabilistic weights indicating the extent of
the relationship they denote (e.g. the ExtSimEdge joining the cat ConceptVertex to the dog
ConceptVertex gets a higher probability weight than the one joining the cat ConceptVertex
to the washing-machine ConceptVertex). The mathematics of transformations involving these
probabilistic weights becomes quite involved - particularly when one introduces SchemaVertices
corresponding to abstract mathematical operations, a step that enables SMEPH hypergraphs
to have the complete mathematical power of standard logical formalisms like predicate calculus,
but with the added advantage of a natural representation of uncertainty in terms of
probabilities, as well as a natural representation of networks and webs of complex knowledge.
14.3 Derived Hypergraphs
We now describe how SMEPH hypergraphs may be used to model and describe intelligent
systems. One can (in principle) draw a SMEPH hypergraph corresponding to any individual
intelligent system, with Vertices and Edges for the concepts and processes in that system’s
mind. This is called the derived hypergraph of that system.
14.3.1 SMEPH Vertices
A ConceptVertex in the derived hypergraph of a system corresponds to a structural pattern
that persists over time in that system; whereas a SchemaVertex corresponds to a multi-timepoint
dynamical pattern that recurs in that system’s dynamics. If one accepts the patternist
definition of a mind as the set of patterns in an intelligent system, then it follows that the
derived hypergraph of an intelligent system captures a significant fraction of the mind of that
system.
To phrase it a little differently, we may say that a ConceptVertex, in SMEPH, refers to the
habitual pattern of activity observed in a system when some condition is met (this condition
14.3 Derived Hypergraphs 273
corresponding to the presence of a certain pattern). The condition may refer to something in
the world external to the system, or to something internal. For instance, the condition may be
observing a cat. In this case, the corresponding Concept vertex in the mind of Ben Goertzel
is the pattern of activity observed in Ben Goertzel’s brain when his eyes are open and he’s
looking in the direction of a cat. The notion of pattern of activity can be made rigorous using
mathematical pattern theory, as is described in The Hidden Pattern [Goe06a].
Note that logical predicates, on the SMEPH level, appear as particular kinds of Concepts,
where the condition involves a predicate and an argument. For instance, suppose one wants to
know what happens inside Ben’s mind when he eats cheese. Then there is a Concept corresponding
to the condition of cheese-eating activity. But there may also be a Concept corresponding
to eating activity in general. If the Concept denoting the activity of eating X is generally easily
computable from the Concepts for X and eating individually, then the eating Concept is
effectively acting as a predicate.
A SMEPH SchemaVertex, on the other hand, is like a Concept that’s defined in a timedependent
way. One type of Schema refers to a habitual dynamical pattern of activity occurring
before and/or during some condition is met. For instance, the condition might be saying the
word Hello. In that case the corresponding SchemaVertex in the mind of Ben Goertzel is the
pattern of activity that generally occurs before he says Hello.
Another type of Schema refers to a habitual dynamical pattern of activity occurring after
some condition X is met. For instance, in the case of the Schema for adding two numbers, the
precondition X consists of the two numbers and the concept of addition. The Schema is then
what happens when the mind thinks of adding and thinks of two numbers.
Finally, there are Schema that refer to habitual dynamical activity patterns occurring after
some condition X is met and before some condition Y is met. In this case the Schema is viewed
as transforming X into Y. For instance, if X is the condition of meeting someone who is not a
friend, and Y is the condition of being friends with that person, then the habitually intervening
activities constitute the Schema for making friends.
14.3.2 SMEPH Edges
SMEPH edge types fall into two categories: functional and logical. Functional edges connect
Schema vertices to their input and outputs; logical edges refer mainly to conditional probabilities,
and in general are to be interpreted according to the semantics of Probabilistic Logic
Networks.
Let us begin with logical edges. The simplest case is the Subset edge, which denotes a
straightforward, extensional conditional probability. For instance, it may happen that whenever
the Concept for cat is present in a system, the Concept for animal is as well. Then we would
say
Subset cat animal
(Here we assume a notation where “R A B” denotes an Edge of type R between Vertices A and
B.)
On the other hand, it may be that 50% of the time that cat is present in the system, cute is
present as well: then we would say
Subset cat cute <.5>
274 14 Representing Implicit Knowledge via Hypergraphs
where the <.5> denotes the probability, which is a component of the Truth Value associated
with the edge.
Next, the most basic functional edge is the Execution edge, which is ternary and denotes a
relation between a Schema, its input and its output, e.g.
Execution father_of Ben_Goertzel Ted_Goertzel
for a schema father_of that outputs the father of its argument.
The ExecutionOutput (ExOut) edge denotes the output of a Schema in an implicit way, e.g.
ExOut say_hello
refers to a particular act of saying hello, whereas
ExOut add_numbers {3, 4)
refers to the Concept corresponding to 7. Note that this latter example involves a set of three
entities: sets are also part of the basic SMEPH knowledge representation. A set may be thought
of as a hypergraph edge that points to all its members.
In this manner we may define a set of edges and vertices modeling the habitual activity
patterns of a system when in different situations. This is called the derived hypergraph of the
system. Note that this hypergraph can in principle be constructed no matter what happens
inside the system: whether it’s a human brain, a formal neural network, Cyc, OCP, a quantum
computer, etc. Of course, constructing the hypergraph in practice is quite a different story: for
instance, we currently have no accurate way of measuring the habitual activity patterns inside
the human brain. fMRI and PET and other neuroimaging technologies give only a crude view,
though they are continually improving.
Pattern theory enters more deeply here when one thoroughly fleshes out the Inheritance
concept. Philosophers of logic have extensively debated the relationship between extensional
inheritance (inheritance between sets based on their members) and intensional inheritance (inheritance
between entity-types based on their properties). A variety of formal mechanisms have
been proposed to capture this conceptual distinction; see (Wang, 2006, 1995 TODO make ref)
for a review along with a novel approach utilizing uncertain term logic. Pattern theory provides
a novel approach to defining intension: one may associate with each ConceptVertex in a system’s
derived hypergraph the set of patterns associated with the structural pattern underlying that
ConceptVertex. Then, one can define the strength of the IntensionalInheritanceEdge between
two ConceptVertices A and B as the percentage of A’s pattern-set that is also contained in B’s
pattern-set. According to this approach, for instance, one could have
IntInhEdge whale fish <0.6>
ExtInhEdge whale fish <0.0>
since the fish and whale sets have common properties but no common members.
14.4 Implications of Patternist Philosophy for Derived Hypergraphs
of Intelligent Systems
Patternist philosophy rears its head here and makes some definite hypotheses about the structure
of derived hypergraphs. It suggests that derived hypergraphs should have a dual network
14.4 Implications of Patternist Philosophy for Derived Hypergraphs of Intelligent Systems 275
structure, and that in highly intelligent systems they should have subgraphs that constitute
models of the whole hypergraph (these are self systems). SMEPH does not add anything to
the patternist view on a philosophical level, but it gives a concrete instantiation to some of the
general ideas of patternism. In this section we’ll articulate some "SMEPH principles", constituting
important ideas from patternist philosophy as they manifest themselves in the SMEPH
context.
The logical edges in a SMEPH hypergraph are weighted with probabilities, as in the simple
example given above. The functional edges may be probabilistically weighted as well, since some
Schema may give certain results only some of the time. These probabilities are critical in terms
of SMEPH’s model of system dynamics; they underly one of our SMEPH principles,
Principle of Implicit Probabilistic Inference: In an intelligent system, the temporal
evolution of the probabilities on the edges in the system’s derived hypergraph should approximately
obey the rules of probability theory.
The basic idea is that, even if a system - through its underlying dynamics - has no explicit
connection to probability theory, it still must behave roughly as if it does, if it is going to be
intelligent. The roughly part is important here; it’s well known that humans are not terribly
accurate in explicitly carrying out formal probabilistic inferences. And yet, in practical contexts
where they have experience, humans can make quite accurate judgments; which is all that’s
required by the above principle, since it’s the contexts where experience has occurred that will
make up a system’s derived hypergraph.
Our next SMEPH principle is evolutionary, and states
Principle of Implicit Evolution: In an intelligent system, new Schema and Concepts will
continually be created, and the Schema and Concepts that are more useful for achieving system
goals (as demonstrated via probabilistic implication of goal achievement) will tend to survive
longer.
Note that this principle can be fulfilled in many different ways. The important thing is that
system goals are allowed to serve as a selective force.
Another SMEPH dynamical principle pertains to a shorter time-scale than evolution, and
states
Principle of Attention Allocation: In an intelligent system, Schema and Concepts that
are more useful for attaining short-term goals will tend to consume more of the system’s energy.
(The balance of attention oriented toward goals pertaining to different time scales will vary from
system to system.)
Next, there is the
Principle of Autopoesis: In an intelligent system, if one removes some part of the system
and then allows the system’s natural dynamics to keep going, a decent approximation to that
removed part will often be spontaneously reconstituted.
And there is the
276 14 Representing Implicit Knowledge via Hypergraphs
Cognitive Equation Principle: In an intelligent system, many abstract patterns that are
present in the system at a certain time as patterns among other Schema and Concepts, will at
a near-future time be present in the system as patterns among elementary system components.
The Cognitive Equation Principle, briefly discussed in Chapter 3, basically means that Concepts
and Schema emergent in the system are recognized by the system and then embodied
as elementary items in the system so that patterns among them in their emergent form become,
with the passage of time, patterns among them in their directly-system-embodied form.
This is a natural consequence of the way intelligent systems continually recognize patterns in
themselves.
Note that derived hypergraphs may be constructed corresponding to any complex system
which demonstrates a variety of internal dynamical patterns depending on its situation. However,
if a system is not intelligent, then according to the patternist philosophy evolution of its
derived hypergraph can’t necessarily be expected to follow the above principles.
14.4.1 SMEPH Principles in CogPrime
We now more explicitly elaborate the application of these ideas in the CogPrime context. As
noted above, in addition to explicit knowledge representation in terms of Nodes and Links,
CogPrime also incorporates implicit knowledge representation in the form of what are called
Maps: collections of Nodes and Links that tend to be utilized together within cognitive processes.
These Maps constitute a CogPrime system’s derived hypergraph, which will not be identical
to the hypergraph it uses for explicit knowledge representation. However, an interesting
feedback loop arises here, in that the intelligence’s self-study will generally lead it to recognize
large portions of its derived hypergraph as patterns in itself, and then embody these patterns
within its concretely implemented knowledge hypergraph. This relates to the Cognitive Equation
Principle defined above 3, in which an intelligent system continually recognizes patterns in
itself and embodies these patterns in its own basic structure (so that new patterns may more
easily emerge from them).
Often it happens that a particular CogPrime node will serve as the center of a map, so that
e.g. the Concept Link denoting cat will consist of a number of nodes and links roughly centered
around a ConceptNode that is linked to the WordNode cat. But this is not guaranteed and
some CogPrime maps are more diffuse than this with no particular center.
Somewhat similarly, the key SMEPH dynamics are represented explicitly in CogPrime: probabilistic
reasoning is carried out via explicit application of PLN on the CogPrime hypergraph,
evolutionary learning is carried out via application of the MOSES optimization algorithm, and
attention allocation is carried out via a combination of inference and evolutionary pattern mining.
But the SMEPH dynamics also occur implicitly in CogPrime: emergent maps are reasoned
on probabilistically as an indirect consequence of node-and-link level PLN activity; maps evolve
as a consequence of the coordinated whole of CogPrime dynamics; and attention shifts between
maps according to complex emergent dynamics.
To see the need for maps, consider that even a Node that has a particular meaning attached
to it - like the Iraq Node, say - doesn’t contain much of the meaning of Iraq in it. The meaning
of Iraq lies in the Links attached to this Node, and the Links attached to their Nodes - and
the other Nodes and Links not explicitly represented in the system, which will be created by
14.4 Implications of Patternist Philosophy for Derived Hypergraphs of Intelligent Systems 277
CogPrime’s cognitive algorithms based on the explicitly existent Nodes and Links related to
the Iraq Node.
This halo of Atoms related to the Iraq node is called the Iraq map. In general, some maps
will center around a particular Atom, like this Iraq map, others may not have any particular
identifiable center. CogPrime’s cognitive processes act directly on the level of Nodes and Links,
but they must be analyzed in terms of their impact on maps as well. In SMEPH terms, Cog-
Prime maps may be said to correspond to SMEPH ConceptNodes, and for instance bundles of
Links between the Nodes belonging to a map may correspond to a SMEPH Link between two
ConceptNodes.

Chapter 15
Emergent Networks of Intelligence
15.1 Introduction
When one is involved with engineering an AGI system, one thinks a lot about the aspects of
the system one is explicitly building – what are the parts, how they fit together, how to test
they’re properly working, and so forth. And yet, these explicitly engineered aspects are only a
fraction of what’s important in an AGI system. At least as critical are the emergent aspects –
the patterns that emerge once the system is up and running, interacting with the world and
other agents, growing and developing and learning and self-modifying. SMEPH is one toolkit
for describing some of these emergent patterns, but it’s only a start.
In line with these general observations, most of this book will focus on the structures and
processes that we have built, or intend to build, into the CogPrime system. But in a sense, these
structures and processes are not the crux of CogPrime’s intended intelligence. The purpose
of these pre-programmed structures and processes is to give rise to emergent structures and
processes, in the course of CogPrime’s interaction with the world and the other minds within
it. We will return to this theme of emergence at several points in later chapters, e.g. in the
discussion of map formation in Chapter 42 of Part 2.
Given the important of emergent structures – and specifically emergent network structures –
for intelligence, it’s fortunate the scientific community has already generated a lot of knowledge
about complex networks: both networks of physical or software elements, and networks of
organization emergent from complex systems. As most of this knowledge has originated in
fields other than AGI, or in pure mathematics, it tends to require some reinterpretation or
tweaking to achieve maximal applicability in the AGI context; but we believe this effort will
become increasingly worthwhile as the AGI field progresses, because network theory is likely
to be very useful for describing the contents and interactions of AGI systems as they develop
increasing intelligence.
In this brief chapter we specifically focus on the emergence of certain large-scale network
structures in a CogPrime knowledge store, presenting heuristic arguments as to why these
structures can be expected to arise. We also comment on the way in which these emergent
structures are expected to guide cognitive processes, and give rise to emergent cognitive processes.
The following chapter expands on this theme in a particular direction, exploring the
possible emergence of structures characterizing inter-cognitive reflection.
279
280 15 Emergent Networks of Intelligence
15.2 Small World Networks
One simple but potentially useful observation about CogPrime Atomspaces is that they are
generally going to be small world networks [Buc03], rather than random graphs. A small world
network is a graph in which the connectivities of the various nodes display a power law behavior
– so that, loosely speaking, there are a few nodes with very many links, then more nodes with a
modest number of links ... and finally, a huge number of nodes with very few links. This kind of
network occurs in many natural and human systems, including citations among papers, financial
arrangements among banks, links between Web pages and the spread of diseases among people
or animals. In a weighted network like an Atomspace, "small-world-ness" must be defined in a
manner taking the weights into account, and there are several obvious ways to do this. Figure
15.1 depicts a small but prototypical small-worlds network, with a few "hub" nodes possessing
far more neighbors than the others, and then some secondary hubs, etc.
An excellent reference on network theory in general, including but not limited to small world
networks, is Peter Csermely’s Weak Links [Cse06]. Many of the ideas in that work have apparent
OpenCog applications, which are not elaborated here.
Fig. 15.1: A typical, though small-sized, small-worlds network.
One process via which small world networks commonly form is "preferential attachment"
[Bar02]. This occurs in essence when "the rich get richer" – i.e. when nodes in the network
grow new links, in a manner that causes them to preferentially grow links to nodes that already
have more links. It is not hard to see that CogPrime’s ECAN dynamics will naturally lead to
15.3 Dual Network Structure 281
preferential attachment, because Atoms with more links will tend to get more STI, and thus
will tend to get selected by more cognitive processes, which will cause them to grow more
links. For this reason, in most circumstances, a CogPrime system in which most link-building
cognitive processes rely heavily on ECAN to guide their activities will tend to contain a smallworld-network
Atomspace. This is not rigorously guaranteed to be the case for any possible
combination of environment and goals, but it is commonsensically likely to nearly always be
the case.
One consequence of the small worlds structure of the Atomspace is that, in exploring other
properties of the Atom network, it is particularly important to look at the hub nodes. For
instance, if one is studying whether hierarchical and heterarchical subnetworks of the Atomspace
exist, and whether they are well-aligned with each other, it is important to look at hierarchical
and heterarchical connections between hub nodes in particular (and secondary hubs, etc.). A
pattern of hierarchical or dual network connection that only held up among the more sparsely
connected nodes in a small-world network would be a strange thing, and perhaps not that
cognitively useful.
15.3 Dual Network Structure
One of the key theoretical notions in patternist philosophy is that complex cognitive systems
evolve internal dual network structures, comprising superposed, harmonized hierarchical and
heterarchical networks. Now we explore some of the specific CogPrime structures and dynamics
militating in favor of the emergence of dual networks.
15.3.1 Hierarchical Networks
The hierarchical nature of human linguistic concepts is well known, and is illustrated in Figure
15.2 for the commonsense knowledge domain (using a graph drawn from WordNet, a huge concept
hierarchy covering 50K+ English-language concepts), and in Figure 15.4 for a specialized
knowledge subdomain, genetics. Due to this fact, a certain amount of hierarchy can be expected
to emerge in the Atomspace of any linguistically savvy CogPrime, simply due to its modeling
of the linguistic concepts that it hears and reads.
Hierarchy also exists in the natural world apart from language, which is the reason that many
sensorimotor-knowledge-focused AGI systems (e.g. DeSTIN and HTM, mentioned in Chapter
4 above) feature hierarchical structures. In these cases the hierarchies are normally spatiotemporal
in nature - with lower layers containing elements responding to more localized aspects
of the perceptual field, and smaller, more localized groups of actuators. This kind of hierarchy
certainly could emerge in an AGI system, but in CogPrime we have opted for a different route.
If a CogPrime system is hybridized with a hierarchical sensorimotor network like one of those
mentioned above, then the Atoms linked to the nodes in the hierarchical sensorimotor network
will naturally possess hierarchical conceptual relationships, and will thus naturally grow hierarchical
links between them (e.g. InheritanceLinks and IntensionalInheritanceLinks via PLN,
AsymmetricHebbianLinks via ECAN).
282 15 Emergent Networks of Intelligence
Fig. 15.2: A typical, though small, subnetwork of WordNet’s hierarchical network.
Once elements of hierarchical structure exist via the hierarchical structure of language and
physical reality, then a richer and broader hierarchy can be expected to accumulate on top
of it, because importance spreading and inference control will implicitly and automatically be
guided by the existing hierarchy. That is, in the language of Chaotic Logic [Goe94] and patternist
theory, hierarchical structure is an "autopoietic attractor" – once it’s there it will tend to enrich
itself and maintain itself. AsymmetricHebbianLinks arranged in a hierarchy will tend to cause
importance to spread up or down the hierarchy, which will lead other cognitive processes to look
for patterns between Atoms and their hierarchical parents or children, thus potentially building
more hierarchical links. Chains of InheritanceLinks pointing up and down the hierarchy will lead
PLN to search for more hierarchical links – e.g. most simply, A → B → C where C is above
B is above A in the hierarchy, will naturally lead inference to check the viability of A → C
by deduction. There is also the possibility to introduce a special DefaultInheritanceLink, as
discussed in Chapter 34 of Part 2, but this isn’t actually necessary to obtain the inferential
maintenance of a robust hierarchical network.
15.3.2 Associative, Heterarchical Networks
Heterarchy is in essence a simpler structure than hierarchy: it simply refers to a network in
which nodes are linked to other nodes with which they share important relationships. That is,
there should be a tendency that if two nodes are often important in the same contexts or for
15.3 Dual Network Structure 283
Fig. 15.3: A typical, though small, subnetwork of the Gene Ontology’s hierarchical network.
the same purposes, they should be linked together. Portrayals of typical heterarchical linkage
patterns among natural language concepts are given in Figures 15.5 and 15.6. Just for fun,
Figure 15.7 shows one person’s attempt to draw a heterarchical graph of the main concepts
in one of Douglas Hofstadter’s books. Naturally, real concept heterarchies are far more large,
complex and tangled than even this one.
In CogPrime, ECAN enforces heterarchy via building SymmetricHebbianLinks, and PLN
by building SimilarityLinks, IntensionalSimilarityLinks and ExtensionalSimilarityLinks. Furthermore,
these various link types reinforce each other. PLN control is guided by importance
spreading, which follows Hebbian links, so that a heterarchical Hebbian network tends to cause
PLN to explore the formation of links following the same paths as the heterarchical Hebbian-
Links. And importance can spread along logical links as well as explicit Hebbian links, so that
the existence of a heterarchical logical network will tend to cause the formation of additional
heterarchical Hebbian links. Heterarchy reinforces itself in "autopoietic attractor" style even
more simply and directly than heterarchy.
284 15 Emergent Networks of Intelligence
Fig. 15.4: Small-scale portrayal of a portion of the spatiotemporal hierarchy in Jeff Hawkins’
Hierarchical Temporal Memory architecture.
15.3.3 Dual Networks
Finally, if both hierarchical and heterarchical structures exist in an Atomspace, then both ECAN
and PLN will naturally blend them together, because hierarchical and heterarchical links will
feed into their link-creation processes and naturally be combined together to form new links.
This will tend to produce a structure called a dual network, in which a hierarchy exists, along
with a rich network of heterarchical links joining nodes in the hierarchy, with a particular density
of links between nodes on the same hierarchical level. The dual network structure will emerge
without any explicit engineering oriented toward it, simply via the existence of hierarchical
and heterarchical networks, and the propensity of ECAN and PLN to be guided by both the
hierarchical and heterarchical networks. The existence of a natural dual network structure in
both linguistic and sensorimotor data will help the formation process along, and then creative
cognition will enrich the dual network yet further than is directly necessitated by the external
world.
15.3 Dual Network Structure 285
Fig. 15.5: Portions of a conceptual heterarchy centered on specific concepts.
Fig. 15.6: A portion of a conceptual heterarchy, showing the "dangling links" leading this portion
to the rest of the heterarchy.
A rigorous mathematical analysis of the formation of hierarchical, heterarchical and dual
networks in CogPrime systems has not yet been undertaken, and would certainly be an interesting
enterprise. Similar to the theory of small world networks, there is ample ground here
for both theorem-proving and heuristic experimentation. However, the qualitative points made
here are sufficiently well-grounded in intuition and experience to be of some use guiding our
286 15 Emergent Networks of Intelligence
Fig. 15.7: A fanciful evocation of part of a reader’s conceptual heterarchy related to Douglas
Hofstadter’s writings.
ongoing work. One of the nice things about emergent network structures is that they are relatively
straightforward to observe in an evolving, learning AGI system, via visualization and
inspection of structures such at the Atomspace.
Section V
A Path to Human-Level AGI

Chapter 16
AGI Preschool
Co-authored with Stephan Vladimir Bugaj
16.1 Introduction
In conversations with government funding sources or narrow AI researchers about AGI work, one
of the topics that comes up most often is that of “evaluation and metrics” – i.e., AGI intelligence
testing. We actually prefer to separate this into two topics: environments and methods for careful
qualitative evaluation of AGI systems, versus metrics for precise measurement of AGI systems.
The difficulty of formulating bulletproof metrics for partial progress toward advanced AGI
has become evident throughout the field, and in Chapter 8 we have elaborated one plausible
explanation for this phenomenon, the "trickiness" of cognitive synergy. [LWML09], summarizing
a workshop on “Evaluation and Metrics for Human-Level AI” held in 2008, discusses some of
the general difficulties involved in this type of assessment, and some requirements that any
viable approach must fulfill. On the other hand, the lack of appropriate methods for careful
qualitative evaluation of AGI systems has been much less discussed, but we consider it actually
a more important issue – as well as an easier (though not easy) one to solve.
We haven’t actually found the lack of quantitative intelligence metrics to be a major obstacle
in our practical AGI work so far. Our OpenCogPrime implementation lags far behind the
CogPrime design as articulated in Part 2 of this book, and according to the theory underlying
CogPrime, the more interesting behaviors and dynamics of the system will occur only when all
the parts of the system have been engineered to a reasonable level of completion and integrated
together. So, the lack of a great set of metrics for evaluating the intelligence of our partiallybuilt
system hasn’t impaired too much. Testing the intelligence of the current OpenCogPrime
system is a bit like testing the flight capability of a partly-built airplane that only has stubs
for wings, lacks tail-fins, has a much less efficient engine than the one that’s been designed for
use in the first "real" version of the airplane, etc. There may be something to be learned from
such preliminary tests, but making them highly rigorous isn’t a great use of effort, compared
to working on finishing implementing the design according to the underlying theory.
On the other hand, the problem of what environments and methods to use to qualitatively
evaluate and study AGI progress, has been considerably more vexing to us in practice, as
we’ve proceeded in our work on implementing and testing OpenCogPrime and developing the
CogPrime theory. When developing a complex system, it’s nearly always valuable to see what
this system does in some fairly rich, complex situations, in order to gain a better intuitive
understanding of the parts and how they work together. In the context of human-level AGI, the
theoretically best way to do this would be to embody one’s AGI system in a humanlike body
289
290 16 AGI Preschool
and set it loose in the everyday human world; but of course, this isn’t feasible given the current
state of development of robotics technology. So one must seek approximations. Toward this end
we have embodied OpenCogPrime in non-player characters in video game style virtual worlds,
and carried out preliminary experiments embodying OpenCogPrime in humanoid robots. These
are reasonably good options but they have limitations and lead to subtle choices: what kind of
game characters and game worlds, what kind of robot environments, etc.?
One conclusion we have come to, based largely on the considerations in Chapter 11 on
development and Chapter 9 on the importance of environment, is that it may make sense to
embed early-stage proto-AGI and AGI systems in environments reminiscent of those used for
teaching young human children. In this chapter we will explore this approach in some detail:
emulation, in either physical reality or an multiuser online virtual world, of an environment
similar to preschools used in early human childhood education. Complete specification of an
“AGI Preschool” would require much more than a brief chapter; our goal here is to sketch the
idea in broad outline, and give a few examples of the types of opportunities such an environment
would afford for instruction, spontaneous learning and formal and informal evaluation of certain
sorts of early-stage AGI systems.
The material in this chapter will pop up fairly often later in the book. The AGI Preschool
context will serve, throughout the following chapters, as a source of concrete examples of the
various algorithms and structures. But it’s not proposed merely as an expository tool; we are
making the very serious proposal that sending AGI systems to a virtual or robotic preschool is
an excellent way – perhaps the best way – to foster the development of human-level human-like
AGI.
16.1.1 Contrast to Standard AI Evaluation Methodologies
The reader steeped in the current AI literature may wonder why it’s necessary to introduce a
new methodology and environment for evaluating AGI systems. There are already very many
different ways of evaluating AI systems out there ... do we really need another?
Certainly, the AI field has inspired many competitions, each of which tests some particular
type or aspect of intelligent behavior. Examples include robot competitions, tournaments of
computer chess, poker, backgammon and so forth at computer olympiads, trading-agent competition,