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Chapter 13
Holographic Memory: A Novel Model
of Information Processing by Neuronal
Microcircuits
Alexey Redozubov
Abstract In the proposed model, each cortical minicolumn possesses a complete
copy of the memory characteristic of the entire cortical zone to which it belongs.
Hence, the cortex has holographic properties, where each fragment of an infor-
mation carrier contains not just a part of the information but a complete copy.
It is argued that each minicolumn encodes the new information using its own
interpretation. Such transcoding is equivalent to considering the source information
in a particular context. The model suggests that the cortex zone is a space of possible
contexts for interpretation. The presence of a full copy of the memory at each
minicolumn allows to determine which context is most suitable for interpreting
the current information. Possible biological mechanisms are discussed that could
implement the model components, including information processing algorithms that
enable high computing power.
Keywords Holographic memory • Microcircuits • Information waves • Hip-
pocampus • Meaning of information • Membrane receptors • Cluster of recep-
tors • Cerebral cortex • Dendrites • Combination of neurotransmitters
13.1 The Propagation of Information Waves
13.1.1 Waves at Cellular Automaton
Acellularautomaton(VonNeumannandBurks1966)isadiscretemodel,which
describes the regular lattice of cells, the possible states of the cells and the rules
of changes between those states. Each cell can be in a finite number of states, for
example, 0 or 1. For each cell, we define an area that contains its neighbors. The
current state of the cell and the states of its neighbors determine the next state of the
A. Redozubov (!)
St. Petersburg, Russia
e-mail: galdrd@gmail.com
©SpringerInternationalPublishingSwitzerland2017
I. Opris, M.F. Casanova (eds.), The Physics of the Mind and Brain Disorders,
Springer Series in Cognitive and Neural Systems 11,
https://doi.org/10.1007/978-3-319-29674-6_13
271
272 A. Redozubov
Fig. 13.1 Patterns of propagation. (a)thepatternoftheinitialactivity.Onlytheactiveelements
are shown. Elements are depicted tightly without a gap. Each pixel of the image corresponds to a
single element. (b) the tracking field of an element and active elements within. (c) the first step of
the simulation. The wave activity (gray) in front of the initial activity (red). (d)thesecondstepof
the simulation. The wave front propagation. Elements in the state of relaxation are painted in blue
cell. The most famous example of cellular automata is the “Life” game (Gardner
1970). Potentially, during the selection of a next state, cells can consider not only
neighboring states and the transition rules, but their previous state changes too. In
this case, we consider cellular automaton with memory.
Let us consider cellular automata with memory. Let’s place its elements
(automata cells) on a regular grid. For each element, we define its neighborhood
that is the tracking zone of this element. Suppose that a compact pattern of activity
appeared somehow on the automaton plane (Fig. 13.1a). The compactness of a
pattern means here that all active elements fall in space within the size of tracking
zone.
13 Holographic Memory: A Novel Model of Information Processing... 273
Fig. 13.2 (a)aseriesofinitialcyclesthatpropagatethewaveactivitypattern.White dots are the
active elements forming the wave front. Blue dots are the elements in the state of relaxation against
the spreading signal. (b) wave propagation on already trained automaton
Now we count how many active elements fall in the tracking field of each
elements (Fig. 13.1b). Let’s define some small probability pin (roughly 3 % for the
provided model). For each element in the quiet state, to count the number of active
elements within the tracking field that exceeded a certain threshold, we perform the
following procedure. Let’s force an element to switch into an active state randomly,
with the probability pin.Accordingly,anelementremainsinaninactivestatewith
probability 1 – pin.Forthatelement,let’srememberitschoiceandactiveelements
in its tracking field. As the result of this procedure, a randomly generated pattern of
activity forms around the pattern of initial activity (Fig. 13.1c). For reasons that will
soon become clear let’s define this emerged activity as wave-like. On the second
step of the simulation, the elements located on the perimeter of the wave activity
zone, will “observe” significant activity in their tracking fields. For those ones with
the activity exceeded the threshold we repeat the previously described activation
procedure. The elements activated on the previous step, using the parameter p, we
transit to the state of relaxation. We deactivate them and block for a certain amount
of time Trelax their ability to be activated by the pattern that caused their activity
before (Fig. 13.1d).
By repeating the simulation steps, we get activity propagating across the
automaton with a certain unique randomly generated pattern (Fig. 13.2a).
By changing the initial pattern, we scatter the wave front with its randomly
generated internal pattern. Wherein the machine elements to be remembered what
patterns have already ran through them. Due to this memory can be made so that
the repetition of the initial pattern will be repeated, and the wave pattern. Now let
us introduce the rule of the wave excitation. Since each element has a high level
of activity around it, we need to check whether there is a pattern of activity in his
274 A. Redozubov
memory. If there is a pattern, then the element being excited or not will depend
on the choices made in the beginning. The resulting logic of the automaton can
be described as follows: if an element encounters an unknown signal, it either
triggers or not on a random basis, and it stores the signal and the choice it has
made; if the signal is known, it repeats its initial choice. The set of triggered
elements generates the wave front, diverging from the pattern of the initial compact
activity. The relaxation ensures unidirectional wave propagation from the places
where activity occurred in the directions where it did not happen yet. This way
we defined, constructed and have got an automaton that memorized a unique wave
pattern, unambiguously corresponding to the original activity pattern. Repetition
of the initial activity will not require elements to randomly determine their states.
The elements “recognize” pattern they encountered before and propagate it further,
thus, in the end, propagation of a wave happens with the same pattern as initially
(Fig. 13.2b).When a different compact activity pattern appears, the automaton will
generate the propagation front wave of activity exactly the same way. However,
importantly, the new wave pattern will be unique and different from the previous
wave pattern. Any compact combination of active elements will generate a unique
wave pattern. For each emitting pattern, the propagating wave, firstly, will have
auniquepatterndifferentfromallotherwavepatternsand,secondly,thispattern
would always be the same for the same initial activity. It means that, if we define
a glossary where each item is encoded by a compact pattern, then we will be able
to transmit the information about activity of that item (i.e. its encoding pattern)
across the plate of a cellular automaton. Indeed, as each initial pattern creates a
unique wave pattern, it is possible to judge what notion the wave propagates in any
arbitrary location of a cellular automaton plate. The Fig. 13.3 shows how patterns of
wavefronts differ in the same location of a cellular automaton plate for two different
initial patterns.
13.1.2 Properties of Information Waves
If a signal is encoded by a rather small percentage of activity across elements,
then several waves can propagate through the automaton simultaneously without
losing their individuality and not interfering with each other. During simultaneous
spreading of several waves, the wavefronts of these waves can pass through each
other keeping their pattern intact.
Abinaryvectorcandescribetheactivityoftheautomatonineacharea.The
crossing of signals forms a binary vector as the logical sum of each signal’s
binary vectors. It is equivalent to a Bloom filter (Bloom 1970). Accordingly, the
false positive rate can be calculated the way it is for the Bloom filter. It is worth
mentioning that the signals encoded by such an automaton gain a property of duality
that corresponds to the wave-particle duality. Same as quantum-scale objects may
be partly described in terms not only of particles, but also of waves, an informational
signal in the simulation described acts as a pattern that triggers a wave, and a wave
13 Holographic Memory: A Novel Model of Information Processing... 275
Fig. 13.3 The wave patterns from different initial patterns emerging at the same position of the
cellular automaton
itself. In each phase of its propagation this wave forms a pattern which in turn
propagates the wave further. The Huygens-Fresnel principle is applicable to the
spreading of an information wave where each point reached by the wavefront could
be considered as an independent source of emission of a spherical wave.
Let us pick an item known to the automaton. That item would match a wave with
a unique pattern. If a fragment of this pattern is reproduced anywhere in the plane of
the automaton, then this area will spread a wave reproducing the same unique pattern
on all the way through its repetition. For example, if a specific pattern is created in
the automaton in the area encircled by the line 1 (Fig. 13.4a), then the wave front
will create a unique pattern for this wave reaching the area 2 (Fig. 13.4b). If a new
wave is being emitted from the area 2 (Fig. 13.4c)bythepatternthatwasapartof
the original wave then wave front reaching the area 1 re-creates the original pattern
there (Fig. 13.4d).
This way the full connectivity of the automaton plate is achieved. Potentially,
any area can store in memory any wave information and play it back later, all areas
on the automaton plate reached by the corresponding wave, will have access to this
information. The cellular automaton described here was modeled on a computer and
showed stable operation over a wide range of parameters (Redozubov, Programs.
[Online] http://www.aboutbrain.ru/programs/).
276 A. Redozubov
Fig. 13.4 Apatternemitsawavefromthearea1and,reachingthearea2,createsauniquepattern
there (topfigures). A new wave is being emitted from the area 2 by the pattern that was a part of
the original wave. The wave front reaching the area 1 re-creates the original pattern there (bottom
figures)
13.1.3 Brain Cortex Patterns
What structures in the cortex can act as elements of a cellular automaton? Such a
structure should meet the following requirements:
• The structure can have at least two different states;
• There should be the capacity to transmit information about the state to the
neighbors;
•Thereshouldbeamechanismtoallowthestructureundertheinfluenceofthe
pattern of neighbors to change its status;
13 Holographic Memory: A Novel Model of Information Processing... 277
• There should be a mechanism to selectively respond to different surrounding
patterns;
•Transferofinformationshouldbefastenoughtomatchtherhythmsofthebrain;
• Since it is assumed that the pattern-wave mechanism should involve for every
time transfer a large number of elements, the energy cost of each item should be
minimal.
Thin branches of the dendritic trees are the most suitable candidate for these
functions. According to neuron doctrine, the branches of the dendritic tree contribute
to the functions performed by the neurons to which they belong. However, they can
also have individual properties and act in some situations as autonomous elements.
It has been shown that dendrites have cable properties (Wilfrid 1959). A branch of
a dendrite can be compared with a cable, which has an internal resistance, leakage
resistance and capacity of the surface. Although dendrite resistance very large and
significant leakage, nevertheless currents that arise from excitatory postsynaptic
potentials can have a significant impact on the overall state of the neuron. It can
be assumed that the role of these currents is especially high at short distances, for
example, within single dendritic branches of the tree.
A detailed mechanism of how the dendritic sections can act as carriers of
information waves is described in (Redozubov 2016).
It can be assumed that the spread of dendritic activity patterns is accompanied by
the appearance of spontaneous activity in certain neurons. This spontaneous activity
can be interpreted as the calculation by local neuronal groups of the hash functions
from the dendritic signals. Such spontaneous activity of neurons is very similar to
the “neural avalanches” observed in the monkey cortex (Petermanna et al. 2009).
In the described model, all information arriving at any area of the cortex can
be read by analyzing the state of any of it small fragments. This view on cortical
processing suggests the possibility of brain-machine interfaces based on cortical
microcircuits (Lebedev and Opris 2015).
13.2 Holography Memory
13.2.1 Patterns Interference in a Cellular Automaton
As described above, the cellular automaton wave activity, while spreading, creates
auniquepatternontheautomatonplate.Auniquefeatureofourautomatonisthat
reproducing a fragment of this wave anywhere in the automaton will cause the wave
propagation from this point with exactly the same pattern as the original wave had.
This means that the information encoded by a wave can be stored anywhere on the
automaton plate by memorizing the pattern that occurs at that location when the
information wave passes through. The elements of the described automaton have
memory. The memory of an element is its ability to store certain patterns of activity
278 A. Redozubov
within its field tracking area and then respond with its own activity whenever any of
the stored patterns reappears.
The memory of elements can be used as a universal cellular automaton storage
device that implements an associative array. The associative array is a storage of
“key-value” pairs. To be able to manipulate the stored data, an associative array
must support the following operations: to add a pair, to search for pairs (by key
or data), and to remove the pair. For closer analogies to the cortex, let us turn
from the flat cellular automata to the 3D by replacing the flat tracking field with
volumetric. Let’s place the elements in the nodes of a regular lattice. We assume
that the automaton thickness is substantially smaller than its surface. Let’s allocate
for observations a cylindrical volume with dimensions comparable to the tracking
field of the automaton elements (Fig. 13.5a). We call this the unit volume size,
meaning that this is the minimum space that would guarantee a wave propagation,
if a fragment of this wave is reproduced inside this volume.
Suppose that two information waves were sequentially emitted. The first wave
carries a value that we want to store. The second wave is a unique key that will serve
Fig. 13.5 (a) a spatial cellular automaton and the marked cylindrical fragment of a size compara-
ble to the size of the tracking field of an element. (b)thetraceoftheinformationwave,carrying
the value that will be remembered. (c) the trace of two waves. Elements that encode value are in
yellow.Elementsthatencodekeyarepaintedblack
13 Holographic Memory: A Novel Model of Information Processing... 279
as the identifier for the information stored. Each wave will propagate its pattern over
the entire automaton space, that is, each area will contain two patterns formed by
the first and the second waves, respectively. In the observed fragment, the first wave
will leave a trace, as shown in the figure (Fig. 13.5b). The second wave will leave its
trace in the same place. Let’s mark elements of each waves with a different color,
while some elements can receive two colors at once (Fig. 13.5c).
Now let’s consider memorizations. For this purpose all yellow elements remem-
ber the pattern of the black elements. As a result of this kind of “interference”,
this area will memorize a “key-value” pair. Since we have chosen the volume
comparable to the tracking area, the pattern enclosed therein can propagate its own
wave if necessary. That is, if we subsequently reproduce the wave encoding key (the
black wave), then the yellow items activate, because the pattern of black elements is
the signal that causes their activity. As a result, a pattern encoding the value for the
corresponding key arises in this volume. This pattern emits a wave that will spread
the information retrieved from the memory space along the automaton. Actually, the
described above is the implementation of store-and-search the information by a key.
If all keys are unique, the key propagation will cause a unique responding
information wave corresponding to the paired value for that key. If the values are
also unique, it is possible to do a reverse search of a key by its value. To store a
single information element (a “key-value” pair), memorizing in a unit volume is
enough. However, nothing prevents to store information “redundantly” distributed
across the automaton. This means that the information is stored not in one place,
but in the entire volume of a cellular automaton. Both local and distributed memory,
as shown below, are extremely important for the implementation of information
processes.
Interference of two waves of information and distributed storage makes the
described mechanism extremely similar to optical holography (Gabor 1948). The
main property of optical holograms is that each section of a hologram contains all
the information about the entire light beam. The same property is incorporated in
our memory model.
13.2.2 Special Dendrites Points
The pyramidal and stellate neurons constitute the main percentage of cortical
neurons (Braitenberg and Schuz 1998). The axons of these neurons are characterized
by highly branching collaterals. Most of the synaptic axon contacts falls on the
volume of a size comparable to the size of the dendritic tree. This axon geometry
ensures that the axon signal becomes available in almost all dendritic branches,
located in a neighborhood (radius of the order of 50–70 microns) of the neuron.
The availability of a signal means that any dendritic branch in a proximity of a
neuron has a segment close to the axon of this neuron. Accordingly, in a moment of
activity of the neuron, when each synapse of its axon releases neurotransmitters, a
portion of these neurotransmitters can reach the dendritic branch due to spillover.
280 A. Redozubov
The synapses surrounding a dendritic branch, both its own and external, are the
sources of the extrasynaptical neurotransmitters for this branch.
In reference (Redozubov 2016)itisshownthatwithaprobabilitycloseto1on
any dendrite segment for each selected surround neurons signal will be a place in
which will meet a minimum 5 of active axons of neurons. This place on the dendrite
can be considered as the favorite in relation to the selected signal. To recall exactly
which axons (synapses) had been active, it will subsequently with high accuracy
detect repetition of the same signal.
13.2.3 Coding Signal in Selected Place by a Combination
of Neurotransmitters
For the majority of synapses, at the time the activity is allocated a “basic”
neurotransmitter, and in addition to one or more of the neuropeptide (Lundberg
1996;Bondyetal.1989). The presence a large number of neurotransmitters and
neuromodulators let us suggests, that the primary function of such a manifold –
is the creation in time of synchronous neuronal activity in each point in space a
unique combination of neurotransmitters and modulators. It can be assumed that the
additional substances in synaptic vesicles distributed throughout the synapses so as
to provide at each location a maximum space diversity among neighbors. If so, the
detection of a particular combination of synaptic activity reduced to determining
that the corresponding synapses unique set of emitted substances.
Thus, if in a location selected against a specific dendrite signal to place the
detector, sensitive to the combination of substances, characteristic of this signal,
the operation of the detector is very likely to represent the repetition of the original
signal.
13.2.4 Receptors Neurons as Storage Elements
In addition to direct transfer mechanisms, there exist indirect mechanisms, which
is activity-related metabotropic receptors. These receptors are not ion channels
and, therefore, do not participate directly in the polarization or depolarization. The
metabotropic receptors act indirectly by modifying the activity of ion channels,
ion transporters and receptor proteins. Impact on the neuron’s membrane potential
metabotropic receptors is exerted through G-proteins (Dunlap et al. 1987).
Neighbor receptors can be connected, creating dimers. Dimers, in turn, unite to
form clusters of receptors. The receptors cluster suitable for such role are neighbors
synapses specific combination activity detectors. However, in order to use these
receptors as universal memory elements, there must be mechanisms transform those
13 Holographic Memory: A Novel Model of Information Processing... 281
receptors from sensitive state to insensitive state and back. Such mechanisms are
detailed in (Radchenko 2007).
Therefore, there is a possibility to describe a hypothetical mechanism of memo-
rizing that’s based on patterns interference Assume in a local capacity of the crust
we have two patterns of activity which sequentially replace by each other The first
pattern describes an information, a second is an id. The both patterns consist of
the great amounts of active dendritic elements. After performing hashing for the
first pattern we’ve got a pattern of spikes synchronous activity of neurons. Active
elements by the second pattern indicate dendritic segments, which have to memorize
apatternofneuronsactivity.Oneachsegment,thathastomemorizeanimageof
volume activity, will found a favorites location relative to the signal. In favorite’s
location either through a random combinatorics already exists a ready cluster of
receptors corresponding to the chemical composition by spillovers, or perhaps, such
aclustercanbedynamicallygenerated.Thecluster’sreceptorsarechangingtheir
conformation that brings the cluster into the sensitive state.
In this way, a pair of identifier pattern and its informational description in form of
“hash” is memorized. Swapping of the information description and identifier, will
result in memorization of the information description pattern in conjunction with
the identifier “hash code”.
Passage of such processes throughout the cortex will result in a “holographic”
memory, where the same information is stored in each element.
It turns out that the clusters are receptive, sensitive to certain surround signals,
potentially, may be memory elements that form a memory trace called engrams.
Memory, created in such a way is time-dependent. The conformation of the receptor
has hysteresis properties (Radchenko 2007). This means that receptors can stay
in sensitive mode until external stimulus returns them to their original state. Such
exposure may be, for example, a strong change in membrane potential. In this state,
the memory status is short-term. That is the latest recording readily available for
the memories, but the availability is reduced over time as going receptors reset.
Engrams can be stored for long time. Adhesion and polymerization processes can
fix receptor conformational changes. This is transforming memory into a state of
sustainable storage. This memory can be stored until the end of life.
In a spatial structure that interlaces axons and dendrites, and which employs the
principle of “favorite locations”, the memory elements could include various types
of receptors. This means that, most likely, the majority of membrane receptors
are associated with any working memory systems. Furthermore, glial cells of the
cortex have the same sets of receptors as neurons (Halassa et al. 2007), and thus
can participate in mechanisms of memory. Astrocytes are able to both enhance
the reaction of the synapse due to release of the corresponding mediator, and to
weaken it by its absorption or release of the neurotransmitter binding proteins. In
addition, astrocytes are capable of releasing signaling molecules that regulate the
release of the neurotransmitter axon. Concept signaling between neurons that takes
into account the effect of astrocytes, is called tripartite synapse (Fields and Stevens-
Graham 2002). It is possible that the tripartite synapse is the main element that
implements the mechanisms of mutual work of the various memory systems.
282 A. Redozubov
13.2.5 The Hippocampus Role. IDs for Information
In 1953, bilateral hippocampus resection was made as anti-epilepsy therapy for
patient that is known as H.M. (Henry Molaison) (Scoviille and Milner 1957). As
aresult,H.M.hadlostabilitytomemorizeanything.Herememberedallthatwere
happened to him before the operation. However, new memories became completely
lost on his attention switch. H.M. case is unique. In other cases of hippocampus
resection, without full both sided destruction memory corruption were not so well
presented of were not existed at all (Scoviille and Milner 1957). Full hippocampus
resection makes forming new memories impossible. Hippocampus dysfunction may
lead to Korsakov syndrome, which appears as impossibility to fix current events
while old memory is safe.
The widely known hippocampus role is holding current memories and reor-
ganization later within cortex space of this memories. In the describing model
hippocampus have different role. It is memories unique keys creation. The keys
created by the hippocampus are distributed to the corresponding cortex zones
through projection system. Interference of hippocampus identifiers and information
descriptions creates the memory. Thus, memory forms “in its own place” and does
not move between the hippocampus and cortex. Such representation agrees with the
experimental data quite well. Hippocampus removal makes new memories forma-
tion impossible because of memories keys lack. Old memories stays untouched as
they are independent of hippocampus. Their identifiers may be extracted and used
without hippocampus action.
But the main arguments in favor of described hippocampus role connected with
functions found in hippocampus and have no direct relationship with memory
mechanism. In 1971 John O’Keefe discovered place cells in hippocampus (O’Keefe
and Dostrovsky 1971). These cells act as inner navigation system. If a rat is placed
in long hall, then it is possible to determine rat particular place from particular
cells activity. What is more that cells activity is independent of way rat is come
in particular place.
Hippocampal formation contains neurons that encode spatial location using grid-
like coordinates (Hafting et al. 2005). In 2011, it was revealed that there are cells in
hippocampus that code time intervals in the same way. Their activity forms rhythmic
patterns even if there is nothing happening around (MacDonald et al. 2011).
Storing data in form of key-value pairs creates associative array. In an associative
array, key has two functions. It is unique identifier, which lets differ one key-value
pair from another. In other side key may hold information that can make search
simpler. As example, PC file system may be considered as associative array. Value
is information in the file; key is information about file. Information about the file
is the path that defines storage place, name of the file, date of creation. For photos
additional information – geotags, place where picture was taken, may exists. For
music files there are album name and performer name. All this data about files
forms complex keys that is identifies file uniquely but at the same time lets perform
13 Holographic Memory: A Novel Model of Information Processing... 283
searching by any key field or its combination. The more key details, the more
flexible search ability is.
As brain implements the same informational tasks as computer systems, it is
reasonable to make an assumption that storing data in key-value pairs by a brain
will lead to creation of the keys which will be more convenient for searching.
For human memories it is reasonable to have the following key descriptors:
•Scenedesignation;
•Positioninspacedesignation
• Time designation
•Numberofconceptsthatisrelatedtowhatishappening.Somethinglikearticle
keywords which describes article content.
It looks like the hippocampus not just works with the scene, position in space
and time, but uses it for composing complex informational keys for the memories.
At least this explains why such different functions came together in one place that
is responsible for memory formation.
Time encoding is of special interest. Human memory let remember not only
static images, but a sequence of scenes with their chronology. So, memory coding
system must contain such ability. It was shown that the hippocampus has time cells
that creates rhythmic patterns (MacDonald et al. 2011). Patterns cyclicity suggests
that hippocampus may use the same principles for creation identifiers time fields as
humans do for time measuring.
13.3 Algorithmic Model Based on the Meaning
of Information
13.3.1 Cryptography and Meaning
Consider an example from the field of cryptography. Suppose that we have a stream
of encrypted messages. The encryption algorithm is based on substituting characters
of the original message with another according to rules, which are defined by
encrypting mechanism and key. With something like that has dealt Alan Turing,
hacking the code of the German “Enigma”. Suppose that there is a finite set of keys
and that we know the algorithm of the encrypting mechanism. Then, to decrypt the
current message you need to iterate over all the keys, decode messages and try to
find meaningful among them.
To determine the meaning of the message, it is necessary to have a dictionary
with words that may appear in the message. As soon as the message will take the
form in which the message words coincide with the words from the dictionary,
it will be possible to say that we found the right key and decrypted received
message. If we want to speed up key search, then we will have to parallelize the
decoding process. Ideally, you can take as much parallel processors as number of
284 A. Redozubov
different keys. Allocate keys on the processors and run on each transformation
reverse conversion with his key. Then check the result for the meaning. In one
passage of the calculations, we will be able to check all the possible hypotheses
about the key used to find out which one is most suitable to decrypt the mes-
sage.
To test the meaningfulness each of the processors should have access to a
dictionary of possible words in the message. Another option – each processor must
have a copy of the dictionary and turn to it for checking. Let us consider the second
option. Now, make the task more interesting. Suppose that we know only a few
words for meaningfulness test, which constitute our dictionary. Then in the message
stream, we can find the key only to those in which there is at least one of the
known words. There may be situations when multiple keys will show words in the
decoded message, which we have in the dictionary. Then, you can either ignore such
messages as undeciphered, or select the key that gives a greater match of words in
the dictionary. When we find out the right code for these few messages, we will get
the correct spelling for the other previously unknown to us words. These words
can supplement vocabulary of the processor, which had found the right answer.
Furthermore, new words can be transferred to all other processors in addition to
their local dictionaries. As you gain experience, we will decrypt greater percentage
of messages until we get a complete dictionary and close to one hundred percent
decryption effectiveness.
The resulting cryptographic system is interesting because it allows us to intro-
duce the notion of “meaning” and give an algorithm that allows to work with it.
Sense for such system is a property of the encoded message that appears in the
selection of such a code, which creates a decoded message, interpreted on the
existing dictionary. For described cryptographic task the meaning of the encoded
message can be called the couple “key-decrypted content.” A proper understanding
of the meaning of the message – is the selection of the same code, and obtaining
the same messages that were laid by the sender. The algorithm for determining the
meaning – is to check all the possible interpretations and the selection of one that
looks the most plausible in terms of memory, which stores all previous experience
of interpretations.
13.3.2 The Meaning of Discrete Information. Frames
Interpretation of the meaning and the algorithm of its determination imposed
for cryptographic tasks can be extended to the more general case of arbitrary
information messages composed of discrete elements. We introduce the term
“concept” – c (concept). We assume that we have N available concepts. A set of
all available concepts forms a dictionary.
CDfc1!!!cNg
13 Holographic Memory: A Novel Model of Information Processing... 285
We define informati on message as s et of concept s length k
ID.i1!!!ik/;where ij2C
We assume that the message can be associated with his treatment Iint (inter-
pretation). The interpretation of messages – it is also an informational message,
consisting of concepts from set C. We introduce the rule for interpretations
producing. We believe that any interpretation is obtained by replacing each concept
of the original message with some other concept or with itself. Assume that exists a
system for performed replacements, which is generally not known to us.
Let us introduce the notion of “subject” S. We define subject’s memory as an
array of information known to him, received interpretation. Information with the
interpretation can be written as a couple
mD!I;Iint"
Then, the memory can be represented as:
MDfmijiD1!!!NMg
Determine the first stage of subject’s learning. Perform supervised learning. We
submit informational messages and their correct interpretation. Memorize all the
information received. Based on the memory, formed supervised, we can try to find
asystemincomparisonconceptsandtheirinterpretations.
Firstly, we can draw up a range of possible interpretations for each concept. To
do this, for each concept we need to collect all its interpretations that are stored
in memory. By the way, the frequency of using a particular interpretation can give
the appropriate estimate of the interpretation probability. Secondly, we can use any
reasonable method to solve the problem of clustering and divide miobjects into
classes, according to how the same concepts are interpreted in the class. We will try
to make sure that all objects within the class use the same interpretation rules for the
constituent concepts. Let us call classes resulting from a clustering – “contexts”.
The set of all contexts for the subject S forms the space of contexts fContig.For
each context i, you can specify a set of rules for interpretation of concepts
RiDn!corig;cint "jˇˇˇjD1!!!NContext o
After finishing supervised learning, we can introduce the new algorithm that
allows us to interpret new information. We distinguish memory Mint from M,
consisting solely of interpretations
Mint D˚Iint
iˇˇjD1!!!NM#
286 A. Redozubov
We introduce a measure of coheren ce of interpr etation and m emory of inte rpre-
tations. In the simplest case, this may be the number of matches interpretation and
memory elements, i.e. the number of times it occurs in such an interpretation in
interpretations memory
!.I/DX
i$1; IDIint
i
0; I¤Iint
i
Now for any new information I for each context Contjwe can get an interpre-
tation Iint
j, applying to the original data transformation rules Rj.Foreachofthe
resulting interpretations can determine its consistency with interpretations memory
!jD!!Iint
j"
The scheme for the calculations of the context is shown in Fig. 13.6a.
We intr oduce the pro bability of i nterpreta tion the information in the c ontext j.
p
jD$0; !jD0
!j=Pi!i;!
j¤0
As a result, we will get the interpretation of the information I in each of the K
possible contexts and the probability of this interpretation
!!Iint
1;p
1"!!!!Iint
K;p
K""
Fig. 13.6 (a) computational scheme of the context module. (b) computational scheme for
determining one of the meanings in the system with K contexts. (c)diagramofbasiccomputing
functions for minicolumn of cortex
13 Holographic Memory: A Novel Model of Information Processing... 287
If the probability is zero, we can state that the information is not understood
by the subject and has no meaning for him. If there is a probability different from
zero, then the corresponding interpretation form a set of possible meanings of the
information. If we decide to determine the one main information interpretation for
the subject, you can use context with the maximum probability value. As a result, the
notion of “meaning” can be described as follows. The meaning of the information
ItothesubjectSisasetofinterpretationsthatthesubjectfindsduringcontext
matching, which was built on the determination of the conformity of interpretations
that have arisen in different contexts and memory. General computational diagram
associated with the meaning determining can be represented as a set of parallel
working contextual computing modules (Fig. 13.6b). Each module performs the
interpretation of the original description by its own transformation rules. The
memory of all the modules has identical content. Comparison with memory provides
the conformity assessment of the interpretation and experience. Meaning selection
is based on the probabilities of interpretations. The procedure is repeated several
times to retrieve the set of possible interpretations.
Once the meaning of the information is defined, memory can be supplemented by
new experience. This new experience can be used for determining the interpretation
of subsequent information and to clarify the context of space and transformation
rules. Thus, you should not allocate a separate stage of primary education, but
simply accumulate experience, while improving the ability to retrieve the meaning.
Described semantic approach to data contains a few key points:
• Information descriptions to which this approach is applicable are built from
discrete (nominal) terms. This is determined by the ideology of the concepts
comparison and their interpretations in a certain context. Descriptions of different
nature, for example, quantitative indicative descriptions can be used only after
conversion of the quantitative variables to their approximate discrete representa-
tion.
•Experienceallowsyoutocreatethespaceofcontextsandinterpretationrulesin
these contexts. Accordingly, the meaning can be determined by the subject only
with a certain experience.
•Sinceexperienceofdifferentsubjectscanvaryanddifferentmeaningscanbe
obtained as a result of perception of the same information;
•Informationcanbespeciallypreparedbythesendersoastomaximizethe
probability of the specific meaning for recipient;
•Needlesstosaythattheinformationcontainsmeaningregardlessoftheperceiv-
ing subject.
288 A. Redozubov
Meaning is the result of “measurement” of the information made by the subject.
Prior to determining the meaning, for a specific subject information contains
interpretations in all contexts for which was a non-zero probability of these inter-
pretations. Each “measurement” allows you to see one of the possible meanings.
Described context meaning model, in many respects, solves the same problem
as the concept of Marvin Minsky’s frames (Minsky 1974). Common challenges,
that models are facing, will inevitably lead to similar realizations. Describing the
frames, Minsky uses the term “microworlds”, meaning by them situations in which
there is a certain consistency of definitions, rules and actions. These microworlds
can be compared with the contexts in our definition. Selection of the most successful
frame from the memory, and adaptation to the real situation, the same can be largely
matched to the procedure of determining the meaning.
When using frames to describe visual scenes frames are treated as different
“points of view”. In this case, different frames have a common terminal that allows
you to coordinate information between frames. This corresponds to the way, how
in different contexts interpretation rules may lead different initial description to the
same descriptions-interpretations.
Popular in the programming, object-oriented approach is directly related to the
theory of frames. It uses the idea of polymorphism, when the same interface when
applied to objects of different types causes different actions. It is close enough to
the idea of interpretation the information in context.
Despite the similarity of approaches associated with the need to answer the same
questions, context-semantic mechanism differs significantly from the theory of the
frames, and, as will be seen below, cannot be reduced to it.
The main value of the context-semantic approach is that it is equally well
applicable to all kinds of information faced by the brain and operates. All the zones
of the real cerebral cortex extremely similar in terms of the internal organization. It
makes one think that they all use the same principle of information processing. It
can be assumed that the semantic context approach is that general principle.
13.3.3 Semantic Information
Words t hat build s peech can be in terpreted i n differ ent ways depending on the
overall context. However, for every word is possible to make a range of values
described in other words. Consistent variation of interpretation of the words allows
to allocate the available set of contexts. Contexts can be associated with time,
number, gender, subject area, topics and so on. Determining the meaning of the
phrase – is the choice of the context and interpretation that the most plausible,
based on the experience of one who tries to understand the meaning. There may be a
situation where the same phrase in different contexts create different interpretations,
but these interpretations will be allowed on the basis of previous experience. If the
task is to determine the only meaning of this phrase, it is possible to choose the
interpretation that has higher match to memory and, respectively, the calculated
13 Holographic Memory: A Novel Model of Information Processing... 289
probability for it. If the phrase was originally formulated as ambiguous, it is
appropriate to accept each of the senses individually and establish the fact that the
author of the phrase intentionally or unintentionally managed to combine them in a
single statement.
Natural language is a powerful tool for expression and conveying meaning.
However, this power is achieved due to ambiguities and interpretations of proba-
bilistic nature, depending on the experience of the perceiver. When the meaning of
the phrase is rather complicated, as it happens often enough, for example, when
discussing the scientific or legal matters makes sense to switch to the use of special
terms. Transition to terminology is the choice of the interlocutors a coordinated
context in which the terms are treated equally by interlocutors. For this context to
be available to both interlocutors each of them needs some relevant experience. In
order to interpretations were similar its require a certain similarity of experience
(learning).
For the natural language, it is possible to use a measure of consistency of the
context and memory based not only on complete coincidence of descriptions, but
also on their similarity. Then becomes available a larger number of possible mean-
ings and there is a possibility of additional interpretations of phrases. For example,
so you can correctly interpret phrases containing errors or internal contradictions.
In determining the meaning is easy to take into account the overall context. For
example, if the phrase allows interpretation in different contexts, preference is given
to contexts that were active in the previous sentences and established the general
context. If the phrase allows interpretation only in the context different from the
main, it will be taken as shifting to another topic.
13.3.4 Auditory and Visual Information
Analog audio signal can be easily converted into a discrete form. First the
discretization of time when a continuous signal is replaced by measurements
performed with a sampling frequency. Then, quantization of the amplitude is done.
Wherein signal level is replaced by the number of the nearest quantization level.
The resulting recorded signal can be divided into time intervals and for each applied
windowed Fourier transform. The result is a sound encoded as a series of spectral
measurements.
Let’s define a cyclic identifier with period NTfor time intervals The first NT
intervals will then be numbered from 1 to NT.TheN
TC1interval will then be
numbered 1 again, and so on. Thus, interval numbers will be repeating every NT
intervals. Let’s assume that a Fourier transform contains NFfrequency intervals.
Then, any spectral measurement will consist of NFcomplex values. Let’s replace
every complex value with its respective amplitude and phase and apply quantization.
Number of quantization levels is NAfor amplitude and NPfor phase. Within the
range of NTtime intervals each spectral record element may be described with the
following set: (time interval code, frequency value, amplitude value, phase value).
290 A. Redozubov
Let’s introduce the set of concepts C, allowing us to describe the sound within
the period of the cyclic identifier. This set will include all the possible combinations
of type
.nT;nF;nA;nP/
Total number of such concepts will
NDNTNFNANP
The set of concepts C will then contain N elements
CDfc1!!!cNg
Any sound signal not longer than NTtime intervals can thus be recorded as the
sequence of concepts.
ID.i1!!!ik/;where ij2C
In practical applications, e.g. in speech recognition, the signal may be trans-
formed according to some set of rules, while still retaining its original meaning,
i.e. the words it represents.
The simplest signal transformations are:
•Timeshift
•Frequencyshift
•Generalvolumechange
•Timescalechange(reproductionspeedchange)
Let’s introduce the context space, covering all possible transformation combina-
tions. For each context transition rules can be defined, i.e. we can describe how each
of the source concepts will look like in the context of the appropriate transformation.
E.g. for the context, shifting the frequency one position up all the concepts will get
interpretation, shifting their frequency one position down. Pure 1 kHz tone is equal
to 900 Hz tone in the context of common frequency shift 100 Hz up. The same
applies to other transformation types. After the transition rules for different contexts
are described it becomes possible to recognize words regardless of how they are
transformed. The moment of pronunciation, loudness, voice pitch and speed will
not affect the possibility to compare current information with the memorized one.
Current sounding will be transformed to different interpretations, corresponding to
all possible contexts. In the context, corresponding to the appropriate transforma-
tion, description will result in an interpretation that could be easily recognized as
being heard earlier.
In practice, while working with complex signals, like speech, single processing
step is not sufficient. Initially, it is useful to separate simple phonemes. Contexts
13 Holographic Memory: A Novel Model of Information Processing... 291
will then contain rules for transformations of simple sounds, as shown above.
Then we can compose a description, consisting of phonemes. Here phonemes are
complex elements, identifying not only the sound form, but also it’s pitch, timing
and pronunciation speed. Information consisting of phonemes can then be further
processed on the space of own contexts and own memory. Sophisticated contexts
may be constructed, not just limited by simple transformations. The definition of
appropriate context in itself creates additional information. For example, in case of
speech different intonations and language accents are contexts. Not only intonation
and accent contexts increase the precision of speech recognition, but also give
additional information on how the phrase was told.
Similar considerations are valid for visual information (Redozubov 2016). The
visual description may correspond to a certain binary code. Different image trans-
formations are the rules for changing this code. A set of various transformations,
for example, horizontal and vertical displacements, and rotations creates a space of
visual contexts.
The basic idea of this approach lies in the fact that for the invariant representation
of an object is not necessarily to spend a lot of time for training, showing the object
from different angles. It’s much more efficient to teach the system the basic rules
of geometric transformations inherent in this world and common to all objects.
Partially the described approach is implemented in a well-proven convolutional
network (Fukushima 1980;LeCunandBengio1995).
13.4 Cortical Minicolumns
13.4.1 The Memory Capacity of One Minicolumn
The cerebral cortex is composed of minicolumns. Minicolumn is a vertically spaced
group of 80–120 neurons.
Previously it was shown the formation of a memory circuit, built on the
interference of two wave patterns. The first pattern defines the elements (dendritic
section), which should keep the memory. The second pattern defines a memory
key. Hash conversion from the second pattern creates a short key of memories
(spiking activity of neurons). In special places receptor clusters that are specific
to the combination of neurotransmitters has arisen, fixed memory. In (Redozubov
2016) show that with this approach, one mini-column of the cortex can store about
300 MB of information.
The approach based on the plasticity of synapses provides a much more modest
result as the main memory element. The minicolumn contains about 800,000
synapses. Even assuming that the synapse due to changes in the level of plasticity
encode multiple bits of information, obtained value will total only the hundreds of
kilobytes. Increasing memory capacity three orders of magnitude gives a qualitative
leap in information capabilities minicolumns. Since the nature of information stored
292 A. Redozubov
in minicolumn, is close to the semantic information, the 300 MB capacity are quite
sufficient to save, for example, all human memories that accumulate in the course
of life.
The book of 500 pages in the uncompressed form is about 500 KB. A one mini-
column allows to store memories library consisting of 600 volumes. Approximately
one book per month of life, or 15 pages per day. It seems that it is enough to hold
the semantic description of everything that happens to us.
Three hundred megabytes of memory minicolumns should not be compared with
the gigabyte range photographic libraries or film libraries. When the image stored in
the memory, it not stored in photographic form. It can be stored in the form of short
semantic description consisting of concepts corresponding to the image. At moment
of memories image is not reproduced, it reconstructed anew, creating the illusion of
photographic memory. This can be compared with the way the human portrait can
be restored close enough to photograph only according to his verbal description.
At the first moment the idea that only 100 minicolumns neurons can store the
memories of a lifetime seems absurd, especially for those who are accustomed to
believe that memory is distributed over the entire space of the cortex. Moreover,
the duplication on many millions of minicolumns of the same information in the
traditional approach seems pointless waste of resources. However, the meaning
approach allows us to take under such an architecture of cortex serious justification.
13.4.2 The Basic Computing Functions of Cortical
Minicolumns
The basic idea of defining the operation of a minicolumn, is quite simple
(Fig. 13.6c). Consider one operating cycle of cortex. The information which
carrying the current description, is distributed by zone of cortex consisting of
apluralityofminicolumns.Eachminicolumnseesthisinformationaspatterns
passing therethrough defined activity (presumably activity of dendritic segments).
Each minicolumn keeps the memory of transformations. Each of the minicolumn is
responsible for its own perception of the information context. Each context implies
its own, distinct from others, rules of transformation source descriptions in their
interpretation. Minicolumns memory of transformations – a mechanism for the
transformation of patterns of basic concepts, that constitute the description, in the
patterns of concepts relevant in the context of the interpretation of a particular
minicolumn.
As a result of the transformation of concepts constituting present description, in
their context-dependent interpretation in each minicolumn appears own hypothesis
of interpretation of this description. This hypothesis is a description, composed
of corresponding interpretations. Physically, it most likely, looks like accumulated
over clock cycle the activity of dendritic segments. This activity can be associated
with a binary array, composed on the basis of Bloom filter. It can be assumed
13 Holographic Memory: A Novel Model of Information Processing... 293
that there are mechanisms that allow the transformed information and the original
description co-exist without interfering with each other. It is possible that for a
separate processing correspond to different layers of the cortex. The combination of
the activity of dendritic segments leads to spike activity of minicolumns neurons.
The code compiled from the activity of neurons, can be interpreted as a hash
function of information description, corresponding to the interpretation of the
original information.
Previously, it has been shown that the combination of neuronal activity may
be the key to which the memory can be retrieved previous experience with the
same or such like him the key. Memory of each minicolumn stores all the events
previously. Previous experience, supposedly, stored as pairs “hash of information
description – the identifier” and pair “hash of identifier – information description”
Cloning the same memory on all minicolumns necessary so, that each minicolumn
could compare own interpretation of information with all previous experiences.
It can be assumed that the result of comparing the current interpretation of the
description and the memory is the calculation of the compliance functions. The
first function of compliance indicates the presence of an exact match interpretation
and some memory elements. The second function evaluates the overall similarity of
interpretation and experience stored in the memory.
Signals compliance functions potentially can be encoded changes in the mem-
brane potential of individual neurons or groups of neurons.
Matching functions allow to judge about how minicolumns context appropriate
for the interpretation of the current information, that is, how much interpretation
received in this context, in line with earlier experience. Making a comparison
between minicolumns, you can select a minicolumn-winner.
The interpretation received at a winning minicolumn is based on the concepts
common to the entire cortex. The winning treatment can be pattern-wave method
distributed throughout cortex area and memorized by all cortical minicolumns.
The above description of the interference information and the identifier will
allow to fill up the memory of each minicolumns “correct” interpretation of the
new experience. New information will be comparing with that interpretation.
Winning minicolumns elements can, depending on what is required, to reproduce
the relevant interpretation or current information or the most appropriate under the
current description memory of past experience or even any information stored in the
minicolumn. Reproduced information can spread on cortex area or can be projected
to other areas for further processing.
If the initial information allows for multiple interpretations, all of them can be
produced in succession. To do this, after the determination of the first interpretation
suppress the activity of the relevant context and repeat the context selection
procedure. So one by one, you can single out all the possible semantic interpretation
of the analyzed information.
A cortical minicolumn in our approach is a universal module that performs
and the autonomic computing, and interaction with others minicolumns. However,
different areas face different information tasks. In some tasks more important is
number of contexts and less important volume of internal memory of minicolumn.
294 A. Redozubov
In others, conversely, more important is volume of internal memory and as a
consequence an increase of internal bit hash code, i.e., the number of neurons
in the minicolumn. The optimal setting of universal computing modules for task
specific areas of the cortex can go two ways. Firstly, the number of neurons in
the minicolumn may vary for different areas of the cortex. Second, the potentially
possible to combine several vertical columns of neurons in one computation module.
The scope of axonal and dendritic trees of neurons, constituting a diameter on the
order of 150 microns, can combine multiple columns into a single computer system
without altering the above general principles of work.
In addition, it can be assumed that a full copy of the memory cannot fit into
one minicolumn and be distributed in the space of a few neighboring minicolumns.
Since dendritic tree diameter is about 300 microns, this space is potentially available
for minicolumn for operation with memory.
Acknowledgments The author expresses his deep gratitude to Ioan Opris, Dmitry Shabanov and
Mikhail Lebedev for the constructive discussion and assistance in the preparation and translation
of this article.
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