Image Transformations in a Cognitive System
Tunnel transition and combining ensembles
Ekaterina D. Kazimirova
Abstract — The nature of creativity and its hidden
mechanisms are areas that researchers have only recently
begun to approach. In this paper, within the symbol-image
cognitive architecture paradigm, we consider some operations
on graphs that can be compared to the process of image
synthesis and transformation in a cognitive system. We address
such phenomena as the combination of neural ensembles and
tunnel (sub-barrier) transition in a cognitive system. We also
consider degree of fusibility of a cognitive system that
characterizes its creative ability.
Keywords: graph, symbol, attribute, cognitive architecture,
In the era of the rapidly developing ecosystem of living
things (the Internet of Things) and human-friendly
anthropomorphic robots , the issues related to
developing artificial intelligence systems that are not only
rational, but also creative, take on a special significance.
The ability of cognitive systems to generate new thoughts
and new images will turn machine into man's equal partner
in addressing important issues of the 21st century, in solving
its challenges, such as overcoming disease and resolving
complicated economic problems.
In this paper, we discuss some of the mechanisms that
could be employed in artificial cognitive systems to
generate new information. Such ability is treated as a
synonym for creativity.
The paper is organized as follows. A description of the
model is provided in Section II. An example of the model’s
application is provided in Section III. The summary and
conclusions are in Section IV.
II. DESCRIPTION OF THE MODEL
We consider the following organization of a cognitive
system. Each image encoded in the system is represented by
its attributes and the corresponding symbol. The attributes
are linked together by the image’s symbol , . The main
role of symbolization is compressing information, but we
believe it is equally important that it prevents images with
the same attributes from being mixed together. This idea
was briefly described in .
For the sake of brevity, we consider a two-layer system
(graph), where the first layer encodes image attributes and
the second layer encodes image symbols.
A. Basic Relationships
In our model, the following relationships are formed
between a symbol and its attributes. When two or more
attributes are activated, the symbol is also activated.
Conversely, when a symbol is activated, the attributes of its
image are also activated.
Figure 1. The basic model represented by a two-layer graph. The markers
“А” and “В” correspond to symbols, 1, 2, 3, 4, 5 correspond to their
In Figure 1, the basic two-layer model is presented. The
symbol "A" is activated when there are signals from
particular attributes (nodes 1, 2, or 3) in different
combinations, (provided that more than one node is
involved). The symbol "B" is activated when there are
signals from nodes 3, 4, or 5 in different combinations (also
provided that more than one attribute is involved). When the
symbol "A" is activated, this leads to the activation of an
image consisting of a set of attributes (1, 2, 3). Activation of
the symbol "B" leads to the activation of an image consisting
of a different set of attributes (3, 4, 5).
Let us consider the following example. The relations
between attributes and symbols in our model of a cognitive
system work similarly to children’s riddles. Something that
is round, striped, and sweet (nodes: attributes) is a
watermelon (node: symbol); something that is striped and
orange, with sharp claws and teeth, is a tiger.
Concerning the problem of the possibility of images
being mixed together, note that a cat and a dog have many
attributes in common. According to our model, it is symbols
that enable the cognitive system to tell them apart.
Let us illustrate the “more than one attribute” rule.
Given the attributes “striped” and “round”, we can guess
“watermelon” and given the attributes “striped” and “with
sharp teeth”, we can guess “tiger”. However, given only one
attribute (e.g., “striped”), we cannot guess what the object
is. And conversely, specifying a symbol (e.g., watermelon),
brings its attributes to mind (“striped”, “round”, “sweet”,
“with seeds”, etc.).
In a real-world system, the number of layers is obviously
much greater. For example, there is the integrative symbol
“carnivores” (Lat. Carnivora) above the symbols “cat” and
B. Attribute and Attention
We assume that a cognitive process starts when one of
the cognitive system’s elements appears in the field of
attention. The development of a thought involves revealing
connections between that element and its neighbors, as well
as forming its new relationships and connections with other
elements of the cognitive system.
Figure 2. Activation of two symbols by one attribute.
According to our concept, prolonged activation of one
attribute (for a time interval t > tatt) increases its influence.
As a result, that attribute, even if it is alone, can activate the
associated symbols. In Figure 2, the attribute “3” is
activated by attention and, in turn, activates the symbols
“A” and “B”.
For example, thinking about speed, we can recall a car, a
cheetah, and an airplane.
Below we look at the ways in which a system based on
these rules can generate new information by transforming
images – that is, creating new images out of existing ones.
C. Combining ensembles
Thus, the symbols associated with a certain attribute can
be activated by activating the attribute for a time interval t >
tatt. These symbols, in turn, activate the rest of their
attributes. As a result, a new ensemble combining the
elements of two images (symbols and attributes) is formed.
Figure 3. The activation of symbols A and B leads to the activation of all
their attributes. This gives rise to an ensemble ("A + B").
In Figure 3, the attribute “3” is enhanced by attention or
emotion, i.e., it receives additional activation from “neurons”
(represented by nodes in our model) that are external relative
to the ensembles A and B. Due to enduring activation, it
activates both neuron-symbols “A” and “B” simultaneously.
These two images, i.e., symbols "A" and "B" plus all their
attributes, are temporarily united into an ensemble. Starting
from that moment, the attributes of image “B” also belong to
the symbol “A”, and vice versa (for a certain time interval).
This mechanism could serve as the basis for metaphorical
thinking (feature transfer). We briefly described this problem
in . Issues related to the integration of information in the
cognitive system are also discussed in .
Let us consider the following example of metaphorical
thinking. In , the general metaphor “argument is war” is
presented. G. Lakoff and M. Johnsen write, “We see the
person we are arguing with as an opponent. We attack his
positions and we defend our own. We gain and lose ground.
We plan and use strategies. If we find a position
indefensible, we can abandon it and take a new line of
attack.” What they describe in this passage is attribute
transfer between the concepts “war” and “argument”.
It is important to realize that the transfer process starts
after the common attribute of two concepts is found. In the
case of the metaphor “argument is war”, the term
“confrontation” represents the common attribute, while the
transfer process follows the mechanism described above.
G. Lakoff and M. Johnsen write, “The most important
claim we have made so far is that metaphor is not just a
matter of language, that is, of mere words. We shall argue
that, on the contrary, human thought processes are largely
D. Tunnel transition
Under certain conditions, the activation of attributes can
lead to transitions on the same (attribute) level (activation of
attributes through attributes) rather than the activation of
symbols. Suppose that there is a neurotransmitter acting at
the network’s attribute level, dynamically strengthening the
connections and thus facilitating the transition from one
attribute to another. Under such conditions, attributes
(neuron attributes) can activate each other without the
activation of symbols (see Figure 4). We called this effect
“tunnel (sub-barrier) transition”. In this case, the activation
wave can “dive” under an adjacent symbol and activate one
of the more remote symbols rather than the nearest one.
This process could be controlled by presence or absence
of a neurotransmitter. Favorable conditions for such a
process could also be created by the "constitutional"
characteristics of the cognitive system, e.g., relatively weak
connections between the attribute and symbolic levels
(attribute-symbol), or, on the contrary, by the relatively
strong connections at the attribute level (attribute-attribute).
Figure 4. Flow within the cognitive system.
We would like to emphasize that Hebb's rule  describes
the strengthening of connections between closely spaced
(directly contacting) neurons. In contrast, the tunnel
transition corresponds to the formation of connections
between non-neighboring neurons that are not directly
E. Fusibility of thinking
Within our model, the presence of a “neurotransmitter” in
a subnet containing attributes and/or the cognitive system’s
constitutional features make this system more "fusible", i.e.,
more fluid (akin to molten metal). It would be interesting to
study the "coefficient of fusibility” (Kfus) of a cognitive
system defined as the ratio of the connection strength at the
attribute level to the strength of attribute-symbol
symbatrfus WWK /
Note that mental disorders can be associated with
different types of associative thinking impairment. For
example, the so-called acceleration of thinking (racing
thoughts) is characterized by an excessive emergence of
associations. As a result, thinking becomes superficial, with
attention being switched too easily.
Let us examine how the character of thinking depends
on Kfus. The creative process involves working with
associations as the mechanism of new image production.
We believe that the "coefficient of fusibility" may control
the ease with which associations emerge in the cognitive
system. At low values of Kfus, the "flow" (activation of
connections) between images on the same attribute level and
the subsequent merging of different images into new ones is
hampered, and the system becomes rigid. Such a system can
only work with the images (symbols together with their
attributes) it already contains. The system can analyze them,
i.e., it knows the properties of each symbol and can attribute
it. However, such a cognitive system is virtually incapable
of synthesizing new images. As Kfus increases, it becomes
possible for new images to appear within the cognitive
system. With Kfus > Kcritical, flow across the attribute level
becomes too easy, numerous associations arise, but they are
not fixed in new images. This process represents a thinking
In psychology, our concept corresponds (to some extent)
to Raymond Cattell’s concept  of fluid and crystallized
intelligence, where crystallized intelligence is the ability to
operate with already acquired knowledge, skills and
experience, while fluid intelligence (or fluid reasoning)
corresponds to the ability to reason and solve novel
problems in new ways.
As an example, let us consider the poem “The Soft
Moscow Rain” by Osip Mandelstam, translated by Richard
It shares so stingily
its sparrow cold –
a little for us, a little for the clumps of trees,
a little for the cherries for the hawker’s stall.
And a bubbling grows in the darkness,
the light fussing of tea-leaves,
as though an ant-hill in the air
were feasting in the dark green grass;
fresh drops stirred
like grapes in the grass,
as though the hot-bed of the cold
was revealed in web-footed Moscow.
Let us consider the main symbols and their important
attributes that are mentioned in this poem.
Figure 5. Semantic connections in Mandelstam’s poem The Soft Moscow
rain. "Tunnel transitions" result in unexpected combinations of symbols.
In Figure 5, we can see that symbols that are
semantically close to the term “rain” (such as “cloud” and
“water”) do not appear in the poem. At the same time,
connections are established via attribute-attribute transitions
between semantically distant symbols, such as “rain”, “ant-
hill”, “tea leaves”, and “grapes”. The artistic value of the
poem and the fact that it is a masterpiece seems to be due to
the “tunnel effect” which reveals distant connections, thus
helping to communicate an impression of the rain.
Problems associated with understanding the mechanisms
of creativity and reproducing them form a barrier to creating
general Artificial Intelligence (AI), which has not been
overcome so far. It seems that entirely anthropomorphic AI
could only be developed if artificial intelligence systems
were able to think independently and perform creative tasks.
To achieve this, we will have to solve the problem of
generating new information in the cognitive system, which
was discussed within the framework of Dynamic Theory of
Information . In this paper, we made an attempt to show
the possible basic mechanisms of information synthesis in
the cognitive system, illustrating them with some operations
on graphs. The main concepts discussed in this paper are:
formation of ensembles that combine different
the "tunnel effect", i.e., the attribute-attribute
transition that leads to unexpected combinations of
the "degree of fusibility" of a cognitive system.
The formation of ensembles and the “tunnel effect” are
associated with the mechanism that can transform images in
the cognitive system. In the former case (the formation of
ensembles), image transformation is caused by the transfer of
attributes from one image to another. In the latter case (the
“tunnel effect”), the attributes of semantically distant
symbols are combined together. This can result not only in
the enrichment of an existing image, but also in the
generation of a new image (e.g., as in Mandelstam’s poem,
where rain is associated with an ant-hill and grapes). Both
mechanisms are characteristic of cognitive processes, not the
simple image classification provided by existing artificial
neural networks. It should be emphasized that in both of the
above cases, new information is generated. These
mechanisms could be closely connected with the intuitive
and creative thinking process.
The concept of the degree of fusibility, as well as the
coefficient of fusibility introduced in this paper, when
applied to an artificial cognitive system, could provide a way
of controlling the rigidity of artificial cognitive systems,
making them more adept at reflecting the reality or, on the
contrary, more intuitive and creative.
Implementing these mechanisms could help to achieve an
AI that can think creatively and has intuition. The next step
would be to develop these ideas further as a mathematical
The author is grateful to Olga Chernavskaya, Evgeny
Volovich and Artem Vorontsov for the fruitful discussions.
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