The power of pattern recognition: Unsupervised neural networks may solve the paradox
of complex calculations in low-IQ savants
Emily Morson
Some low-IQ savants can give the day of the week corresponding to decades’ worth of
dates, but cannot state the number of dates in a week or solve a simple addition or
subtraction problem. This divergence seems paradoxical because we divide the world into
conscious, complex, “high-level” cognitive processes and unconscious, simple, “lowlevel” perceptual-motor ones. Yet savant abilities fit neither category: savants’ abilities,
though not fully conscious, involve more than rote memory. Indeed, savants eventually
come to resemble healthy experts, and may even become creative. Unsupervised neural
network models may illustrate how savants learn: through unconscious, yet very highlevel, pattern recognition. Savants seek out domains that have meaningful structural
regularities, e.g. calendars, math, or music, and spend a great deal of time and attention
on such domains. They may implicitly learn these regularities through a sort of pattern
recognition. This theory implies that pattern recognition is more than just a low-level
perceptual process, and more importantly, that complex cognitive processes can be
unconscious.
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Savant syndrome has long puzzled researchers because it involves “islands of
genius” that contrast with overall disability. Some savants even reach levels of
performance that would be astonishing in people without disabilities.
The causes are similarly baffling: the particular disabilities associated with savant
syndrome vary, ranging from autism to mental retardation to a missing corpus callosum;
so too do the areas of talent savants possess. Most savants are born with the syndrome,
although others have acquired it through epilepsy (Tammet, 2006) or fronto-temporal
dementia (Treffert, 2009). It can also be temporarily induced through transcranial
magnetic stimulation (Young, Ridding, & Morrell, 2004). Because savant syndrome can
be acquired, some researchers believe savant capabilities are latent in all people, but
cannot normally be accessed (Snyder & Mitchell, 1999; Treffert, 2009).
Intriguingly, savant talents occur only in certain specific areas. These include
music (perfect pitch, musical memory, or playing multiple instruments); art (drawing or
sculpting); calendar calculating; lightning mental calculation and prime factorization;
precise measurement without instruments; precise timekeeping without a clock;
navigation; and fast language learning (Treffert, 2009). Hyperlexia, or early mechanical
language learning without equally advanced comprehension, may also be a form of
savant syndrome. Regardless of the special skills, savants nearly always have prodigious
memory (Treffert, 2009). In fact, for a few, the memory is the talent.
Savants differ in the level of their talents, from a minor knack to excellence given
the level of disability to levels of performance that would astonish even in people without
disabilities. They also vary widely in their IQ: most are intellectually disabled, while a
few may be intellectually gifted (e.g., Tammet, 2006; Tammet, 2009). It is the low-IQ
savants who best illustrate the paradoxes of savant syndrome. They may also provide the
clearest examples of the very basic processes that must underlie savant abilities.
Studying higher-IQ savants can confuse the issue of which abilities are essential to savant
talents because these individuals have more capabilities that, while not essential to the
talents, could potentially interact with them (Howe & Smith, 1988).
The case of L.E., a calendar calculating savant (Iavarone et al., 2007), provides a
particularly clear illustration of what capabilities may and may not be involved in savant
syndrome. Eighteen years old when first evaluated, he presented as autistic, with rigid
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and obsessive behavior. He had a full scale IQ of 45 (with a verbal IQ of 58 and a
nonverbal IQ of less than 45). L.E. demonstrated excellent calendar calculation abilities.
Asked to give the day of the week for past and future dates, he responded within one and
three seconds, answering 69.2% of past and 48.3% of future dates correctly (compared to
a chance level of 14.3%). Most of his errors were only one day off. And, although leap
years are harder for healthy people to calculate, L.E. did just as well on leap years as
other dates.
L.E.’s weaknesses, as striking as his strengths, preclude many of the obvious
explanations for his talent. Although savants are supposed to have superb memory, L.E.
scored below the fifth percentile on several memory tests, including tests of verbal,
logical, and visual memory, and a verbal span test. Even more surprisingly, when asked
about calendar facts, he answered only one question correctly. A sample incorrect
answer was that there were 30 days in a week; he must have confused a week with a
month. Such an error may have occurred because of his poor executive attention skills
(demonstrated by an inability to perform the standard tests, the trail-making test and the
Wisconsin Card Sorting Test). Although L.E.’s calendar calculations would seem to
involve arithmetic calculations, his mental and written calculation were severely
impaired, with 0 out of 55 mental and 1 out of 55 written problems correct. Nor could he
rely on strong visual-spatial abilities to make up for his other deficits, because he scored
below the fifth percentile on visuo-spatial tests, which included two tests of copying a
design. He also performed at chance level on Raven’s Progressive Matrices, the usual
test of visual-spatial reasoning. L.E.’s visual deficits are especially surprising because
savants of various ability levels appear to use some sort of visualization to do calculations
(Tammet, 2009; Spitz, 1995; Howe & Smith, 1988).
L.E. surely cannot calculate calendar dates the way a neurotypical person would.
First, his calculation abilities are not verbally accessible, as he cannot correctly answer a
simple addition problem. (Many other calendar calculators also fail to correctly solve
simple addition and subtraction problems; Spitz, 1995; Hermelin & O’Connor, 1989).
Neither can he access his calendar knowledge, as indicated by his incorrect answers about
simple calendar facts. L.E.’s calculation process might not even be conscious, as he
could not explain his methods when asked. Indeed, savants consistently cannot explain
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how they perform their calculations, instead giving explanations like “I just do it” or “it’s
in my head” (Spitz, 1995).
The unconscious nature of savant algorithms poses a difficult question: can
unconscious computations accomplish as complex a task as calendar calculation? Many
people may intuit that they cannot. We accept that, without our awareness, our visual
system composes a scene from edges and patches of intensity, and our motor system
performs complicated adjustments to keep us upright and balanced. On a more complex
level, we accept that some very low-level learning can happen unconsciously: classical
conditioning, or the gradual improvement of the muscles in learning to swing a baseball
bat. But these are basic tasks that animals can also do. Many people probably share the
intuition that an animal could not do calendar calculations, because there is something
fundamentally “cognitive” about them that only a fully conscious organism, such as a
human being, can solve.
An intriguing study suggests this intuition may be faulty. Researchers who studied
the famous calendar-calculating twins taught a bright graduate student, Benjamin
Langdon, a series of algorithms for calendar calculation. He got quite good at doing the
calculations, but despite extensive practice, it took him a long time to match the twins’
speed. Suddenly, he discovered that he could match their speed. He also discovered that
he had absorbed the table of calculations so effectively that he no longer had to
consciously perform the operations at all. They had become automatized, allowing him
to calculate as swiftly as a savant. When asked to explain how he was performing the
calculations, Langdon become annoyed (Spitz 1995). However, Benjamin Langdon
differs from true savant calendar calculators like L.E. in several respects, most notably
his much higher IQ; thus, one cannot know for sure whether his case applies to savants.
Thus, it seems natural to conclude, as early researchers did, that savants do not
perform calculations at all. Rather than engaging in intelligent behavior, one might
assume, they operate on pure rote memory. This approach seems tempting because
savants often have excellent memory. Furthermore, savants in general and calendar
calculators in particular often have digit spans (a measure of verbal working memory)
much higher than expected, given their IQ (Spitz, 1995).
However, the rote memory theory fails both empirically and conceptually.
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First, experimental results suggest that calendar calculations involve more than
rote memory. By its very nature, rote memory operates without regard to the content it
carries; thus, if savants use rote memory alone, they should recall both calendar-related
and general facts equally well. In fact, calendar calculators recall more calendar-related
items than do controls matched for age, verbal IQ, and diagnosis, but the same is not true
for more general material (Mottron et al, 2009). In this respect, calculators resemble
neurotypical chess experts, who have better memory for chess positions than novices,
despite equivalent digit spans (Chase & Simon, 1973).
Furthermore, if savants relied purely on rote memory, their error patterns would
be random. However, L.E.’s errors followed consistent patterns. His incorrect answers
were usually 1 day before or after the correct date. His error rate increased with the
temporal remoteness of the year from the present date, both for past and future dates.
Remoteness also affected his response time for past dates (Iavarone et al, 2007). Rote
memory would not be affected in such a systematic way.
If savants only used rote memory, they could not be primed. Calendar priming
works by presenting another date with some sort of relationship to the target, such as a
date in a corresponding month. Studies demonstrate this sort of priming in savants
(Hermelin & O’Connor, 1986; O’Connor, Cowan & Samella, 2000). In these studies, six
out of eight savants were faster when primed with dates in corresponding months. There
is a calendrical pattern that repeats every 28 years. Four of the eight savants were faster
for future dates 28 years from the present than for closer years, even if they did not
articulate the rule. Thus, rote memory alone cannot explain calendar calculators’
performance.
The rote memory theory also has conceptual problems. For rote memory to
retrieve information, it must have been stored. How does the information get into the
savant’s brain in the first place? If it is simply passively absorbed from the environment
without any further processing or storage in some sort of conceptual structure, then
savants could only answer problems they had been exposed to before. This clearly
cannot be the case. Savants, particularly calendar calculators, develop their abilities
untaught (Mottron et al, 2009; Spitz, 2005; Howe & Smith, 1988); even if they were
taught, they could not have been presented with every possible problem. While many
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savants have studied perpetual calendars (Spitz, 1995; Howe & Smith, 1988), calendrical
structure must still be abstracted from it to answer the specific questions posed by the
experimenter. If savants do not have prior exposure to every problem, they must
somehow absorb meaningful structure from their environments—an intelligent process.
Thus, the paradox of accurate, complex calculations in a person with low IQ and
few explicit learning resources remains. Low IQ savants are not taught a set of rules, nor
do they seem able to consciously generate them. Yet they somehow can perform
complex computations to solve problems they have never seen before. How can this
occur?
We propose the following account to explain this mystery: the domains in which
savants excel have strong, meaningful statistical regularities. Savants are drawn to things
with structure from early childhood, leading them to pay attention to one or more of these
domains. Pattern recognition allows them to absorb meaningful patterns in these
domains without conscious reflection. If this process works like statistical learning in
self-teaching connectionist computer models of learning (“neural nets”), then savants will
form strong associations between related units, such as a day and a date. These
associations are bidirectional: a day can call up a date, and vice versa. By these means,
savants can function like experts without going through the typical intermediate stage of
conscious, effortful computation.
The role of the domains: Meaningful statistical regularities
Although it may not be obvious at first glance, music, art, calendars, prime
factorization, and languages all have structure. That is, they have certain basic units that
are combined in regular, predictable ways to generate larger structures (Mottron, Dawson
& Soulieres, 2009). For instance, letters, the basic unit in written language, are combined
in regular ways to produce words. Words, in turn, are arranged according to various
grammatical rules to produce sentences. There is a hierarchy of levels, where items are
more similar to others within the same level than to others across levels. More
importantly, the structures in savant-friendly domains are non-arbitrary. For instance, the
order “article-noun-verb” does not happen at random; it denotes that a specified noun is
carrying out the verb.
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The regularities in math, music, and calendar calculations are easiest to recognize.
Integers are the basic unit in mental calculation, and the various mathematical operations
can be thought of as rules for combining and rearranging numbers to get new ones. The
basic unit in music is notes, and indeed, musical savants have perfect pitch, the ability to
name a note played on any instrument (Synder & Mitchell, 1999). Notes are arranged
into musical phrases. Musical phrases follow structures based on major and minor keys
and types of chords. With calendars, the basic units are dates and days of the week.
These are combined into weeks, months, and years. Still higher-level regularities include
similarities between months and years. For instance, the same date will occur on the
same day of the week in April and July, and also at 28-year intervals (the so-called “28
year rule”) (Snyder & Mitchell, 1999).
Artistic savants also perceive basic units arranged in regular ways. Art teachers
routinely tell students to break what they see into basic shapes, lines and curves (e.g.,
Brookes, 1996). Psychologists have also observed that real-world objects can be broken
into basic three-dimensional elements (“geons”) and two-dimensional ones arranged
according to rules of linear perspective (Mottron et al., 2009). Linear perspective is
probably one of the highest-level regularities. Lower-level ones might include the shapes
repeated in most mammals—i.e., a trunk shaped like a cylinder, capped by circular
shoulders and haunches; cylindrical legs projecting downward from the shoulders and
haunches; a tubular tail coming out behind the haunches; and a cylinder neck topped with
a more or less circular head in front of the shoulders.
In short, the structure of savant domains should allow savants to develop a lexicon
of basic units and some form of storage of the recurrent structures formed by arranging
these units (Mottron et al, 2009). Two questions remain: why do savants notice this
structure in the first place? And once they do, how do they create this lexicon and
collection of stored rules? Research on autism may answer the first question, while
neural networks capable of pattern recognition may answer the second.
The role of temperament: the search for structure
Many researchers have reported that savants spend many hours absorbed in their
domain of interest; for instance, studying calendars (Spitz, 1995; Mottron et al., 2009;
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O’Connor, Cowan & Samella, 2000). In fact, some argue that savants become calendar
calculators far more often than neurotypical people because the latter are not motivated to
spend the considerable time and focus required. Arguably, savants find activities like
calendar calculating intrinsically rewarding because they are so well-structured (Mottron
et al., 2009; Spitz, 1995).
Studies of musical savants support this hypothesis. When asked to repeat musical
passages heard in the lab, musical savants tended to impose structure on their renditions
that did not exist in the original. Savants actually produced less literal—though more
structured—renditions than comparison participants (Mottron et al., 2009).
One reason as much as 10 percent of autistics may have savant abilities is that
autistic people are drawn from an early age to absorb themselves in well-structured
domains. In fact, “restricted patterns of interest that are abnormal in intensity or focus”
are considered a symptom of autistic spectrum disorders (National Institute of
Neurological Disorders and Stroke, 2009).
It takes time and repeated exposure for learning to occur, especially for people of
low intelligence. Even learning by pattern recognition, a presumably fast and
unconscious mechanism, takes hundreds of trials in models of neural networks. Thus,
obsessive interest might be a necessary condition for the emergence of savant abilities.
One study by Uta Frith (1970) casts doubts on autistics’ (and thus, many savants’)
abilities to detect structure. When asked to reproduce structured and unstructured color
sequences, autistic subjects did not reproduce the patterns that existed. Instead, they
produced simple patterns of the same color or alternating colors. Neurotypical controls,
on the other hand, produced such patterns only when the given pattern lacked structure.
However, it is not clear how well performance on a task which may not have
interested the subjects, such as color pattern reproduction, actually compares to realworld behavior. Patterns in savant domains—the arrangement of days into weeks and
months, for instance—are highly meaningful. Color patterns like this are arbitrary, and
probably do not correspond to anything in participants’ experience.
One could interpret Frith’s data differently. Perhaps autistic subjects are sensitive
to structure—but only of certain, highly repetitive sorts. When exposed to data that is not
repetitively structured enough for them, they will impose the preferred structure on it—
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just as musical savants, asked to repeat a musical sequence, produce versions more
structured than the original. Thus, this study should not prevent us from concluding that
savants can detect, and crave, structure.
It remains unclear whether savants’ pattern recognition ability applies universally
or only to their area(s) of interest. Possibly, when savants are observed later in life, their
pattern recognition abilities have become associated with one domain at the expense of
others. They likely did not start that way: since calendars are a recent phenomenon, there
can be no calendar-processing module in the brain. Most likely, savants have an inborn
ability to detect structure and a drive to do so. Experience leads them to fixate on certain
domains (calendars, music, math, etc.) that possess such structure. With obsessive
practice, their originally undifferentiated structure-detecting systems gradually become
specialized for processing structure in these particular domains—just as the typically
developing brain gradually becomes more functionally specialized over development, or
the weights of neural network models become associated with patterns in familiar sets of
data. Since calendars, music, math, languages, art, and the rest differ in their basic units
and structure, they pose different computational requirements, so expertise in one would
not necessarily translate to expertise in others. Indeed, the Frith study discussed earlier
(1970) could be interpreted as suggesting that autistic savants, at least, might not possess
a general skill at pattern recognition. She tested autistic subjects on patterns of color
blocks, a task likely unrelated to their areas of expertise. That the subjects failed to detect
the color patterns she used suggests that their pattern-recognition abilities did not
translate to this unfamiliar task. Other researchers have also interpreted Frith’s study in
this way (Mottron et al., 2009).
On the other hand, savants have picked up additional domains of talent later in
life. For instance, mnemonist Kim Peek could also do calendar calculations, and took up
music late in life (Treffert, 2009a). Because of the conflicting evidence, it remains
unclear whether savants’ structured representations translate to other savant-friendly
domains. Researchers have not compared pattern-detection in a novel, savant-friendly
domain with pattern detection in a novel arbitrary or non-savant-friendly domain. Thus,
it has not yet been established whether, and in what way, savants’ pattern recognition
becomes specialized.
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Some researchers believe that long hours of practice alone can explain how
savants develop expertise. However, this theory does not solve the informationprocessing problem: how low-IQ people can learn and store structured information that
they cannot verbalize.
The mechanism for unconscious learning: pattern recognition
Savants must, untaught, perform a series of tasks. First, they must abstract the
basic units of their domain—letters, numbers, days and dates, notes, or geons—from raw
sensory data. Next, they must observe regularities in how these basic units are grouped
together to form higher-level units, creating a hierarchy of regularities. They must see
that members of each level of the hierarchy are more similar to each other than to
members of other levels. Finally, they must map one set of structures onto another
(Mottron et al., 2009). For example, musical savants with absolute pitch map note names
or keyboard locations with pitches and calendar calculators map days of the week with
dates. Prime factorization requires savants to map numbers with their factor composition.
Unsupervised neural network models might illustrate how these processes occur.
Like savants, such models never receive explicit feedback, either about the identity of the
correct answer or about how to modify their activation levels to obtain it. Neither are
they programmed with a set of goals or a drive to maximize benefits or minimize costs.
Instead, they are programmed with a learning algorithm that gradually changes the
structure of the network as it is exposed to more data.
Neural network models are composed of nodes arranged in layers, including an
input layer and an output layer. Data presented to the network are assigned to the input
layer. Each type of input is linked, either directly or via another layer of nodes, with a
particular output node (Grimshaw, 2001). These nodes are arranged in layers, including
an input layer and an output layer. In the output layer, each node represents a meaningful
category in the input; for example, a network trained to distinguish sonar signals from
mines versus rocks would have two output nodes, one representing mines and one
representing rocks. Information is not represented discretely, as a node per unit of
information, but as a pattern of activation across the entire network (Grimshaw, 2001).
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This is the most efficient way to represent a large amount of information in a small space.
Thus, such networks work by learning to recognize patterns in data presented to them.
Nodes are linked to each other by connections, which are assigned a mathematical
weight indicating the strength of the connection. In the network distinguishing sonar
from mines versus rocks, input nodes associated with sonar from rocks will have stronger
connections to one another and to the output node for rocks than they will with input
nodes for sonar from mines or the output node for mines. Training the network involves
teaching it how to adjust the connection weights so as to link the input nodes with the
right output node(s).
Like the more familiar supervised networks, unsupervised neural networks work
by adjusting the connection weights between the nodes of which they are composed.
Unlike in other network models, unsupervised learning works by competition. When
data is presented, only the “winning” node has its connection weights adjusted by the
learning algorithm. The “winning node” is the one most like the input—that is, the one
whose vector is closest to that of the input (Grimshaw, 2001). In other words, whichever
state of the nodes provides the best approximation of reality wins, so the network
gradually gets better at representing real patterns in the data it receives. Different inputs
produce different winners, and eventually, each node becomes associated with a
particular set of inputs.
Popular unsupervised learning networks, called Kohonen self-organizing maps
(SOM), also incorporate the idea of a “neighborhood.” Each node has a set of neighbors,
those nodes that are closest to it spatially. When a node wins a competition, not only are
its weights adjusted, but so are those of its neighbors. The amount of adjustment is
largest for neighbors closest to the winner. In the resulting network, “neighbors”
represent patterns in the input data that are somehow “close,” that is, related, to each
other (Grimshaw, 2001). Thus, meaningful regularities in the input data are converted to
topographical relationships in the network. The output is a map that not only classifies
types of input, but also records which ones are closely related to one another.
Unsupervised neural networks might provide a good model of savant processing
for several reasons. First, according to many definitions, these networks lack
consciousness; as such, they could provide an example of complex, yet unconscious,
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processing. Second, like savants, they teach themselves. Furthermore, like other neural
networks, unsupervised neural networks are supremely good at pattern recognition.
Neural networks have been used for face recognition, speech recognition, alphabetic
character recognition (Neural Network Solutions, 2009), distinguishing sonar from rocks
versus mines, and even predicting patterns in stock market prices (Bermudez, 2005).
Such pattern recognition can abstract basic units and create a hierarchy of
regularities. Some neural nets can do both. For instance, McClelland and Elman’s
TRACE model of speech perception (1986) has an input layer representing acoustic
features of speech, a layer representing phonemes, and a layer representing words. The
structure of the network allows it to represent a three-level hierarchy of features,
phonemes, and words, and this arrangement has significant effects on processing. Units
tend to activate across levels and inhibit within levels (McClelland & Elman, 1986). For
example, certain features tend to activate the phoneme /t/, which tends to activate words
with the letter t present at that time point. The phoneme /t/ inhibits other phoneme units,
and the “t” words inhibit competitor words. Neural networks like TRACE show that
pattern recognition can allow a presumably unconscious machine to internalize the sort of
basic units and hierarchy of regularities that a savant would need.
Mottron, Dawson, and Soulieres (2009) believe that savants store dual-code
mappings (like the links between days and dates) as one “unit in long-term memory.”
The presentation of a cue for one (the date, for instance) automatically activates the other
(the day). Thus, savants can accurately answer such questions as: “What day of the week
is…?” “What is the square root of…?” “Can you sing a C sharp?” Crucially, the
association applies in either direction: a savant could answer “What are the months
beginning with a Friday?” and “what day of the week was the 30th of April, 1988?” with
equal facility (Mottron et al., 2009). This reversibility allows us to conclude that each
day-date pair functions as a unit. We can call this process bidirectional mapping.
Neural networks like TRACE perform bidirectional mapping. That is, nodes at
different levels are linked such that activating a node at one level activates related nodes
on other levels. The basic mechanisms are as follows: suppose TRACE is given the word
“plug.” The first phoneme could be either /p/ or /b/, because these are the voiced and
voiceless versions of the same sound. Thus, activation build up for these phonemes and
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decreases for other possible phonemes. As the /l/ and /^/ sounds come in, the system has
/pl^/ and /bl^/ active. These combinations of phonemes activate all familiar words
starting with these phonemes—e.g., “plug,” “plus,” “blush,” and “blood.” When /g/
comes in, the network finally has the necessary information to select a word. “Plug”
wins the competition at the word level and sends activation back to /p/, causing it to win
over /b/ at the phoneme level.
One might reply that these associations are very different from savants’
associations between days and dates or names and pitches. Although bidirectional, the
associations between the phoneme /p/ and the word “plug” are not a unit because they are
at different levels of the hierarchy, whereas days and dates are on the same level.
However, similar mechanisms work within the same level. Studies inspired by the
TRACE model show that words automatically activate other words with the same initial
phonemes and rhymes, as well as semantically related words—in other words, units can
activate other units on the same level (Desroches, Newman, & Joanisse, 2009; Tammet,
2009). So the word cat will produce low-level activation for “cat,” “catalog,” “cab,”
“cap,” “captain,” “capital,” “hat,” “mat,” etc., as well as for semantically related words
such as “meow,” “mouse,” or “purr.” Each of these words also automatically activates
“cat.” Like savants, neural network models can have representations that activate others
on the same level in the hierarchy.
During typical spoken language listening, many words are activated, and compete
for further activation as the spoken word unfolds (Desroches et al., 2009). Yet we do not
become conscious of all of these words, only the winner. A similar process may occur
with savants, explaining why they are aware of the answer but not their method of
obtaining it. Bidirectional mapping of this sort can explain the unconscious nature of
savants’ processing and also the fact that they can answer both questions about days and
questions about dates.
Neural networks may also have similar weaknesses to savants. Opponents of
connectionist models (of which unsupervised neural networks are one type) have
suggested that, while these networks successfully make associations and match patterns,
they have fundamental limitations in mastering general rules, such as the formation of the
regular past tense in English (Garson, 2007). These contentions are actually based on
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older models, such as a network of Rumelhart’s and McClelland’s that was trained to
predict the past tense of English verbs. It remains to be seen whether more advanced
connectionist models can answer questions based on “general rules” and what level of
performance they would have to achieve to satisfy the critics. Critics may or may not be
correct about the outcome of neural networks’ calculations, but are surely right about
their methods. Neural networks may well resemble low-IQ savants, who can successfully
notice calendar patterns and map days onto dates, but cannot verbalize even the most
basic general rule about calendars.
In short, neural networks share many similarities with low-IQ savants. If we can
take them as modeling the computations these savants perform, then we can conclude that
savants, too, might use sophisticated pattern-recognition and bidirectional mapping.
Whether the analogy holds has yet to be tested.
The end result: creative expertise
While the learning process probably differs greatly for savants and neurotypical
experts, the outcome seems the same. Both groups achieve extraordinary performance in
particular areas, despite having no particular advantage in other domains. Furthermore,
neither group can explain its solution methods.
Viewing savants as experts in a domain, albeit with unusual, unconscious learning
methods, allows us to explain how savants can become creative. Until recently, savants
were believed to be incapable of creativity: artists and musicians merely copied what they
heard or saw, and mnemonists repeated what they had memorized by rote. However,
Treffert (2009) observed that savants gradually progress from literal replication to
improvisation to creation. Musicians eventually compose original pieces, while artists
can draw original scenes in various styles and show them in their own art gallery.
Mnemonists can move from a literal understanding of language to fairly sophisticated
wordplay. If savants do not have structured representations, such creativity would be
impossible. But if they can recombine familiar basic elements into new patterns, they can
achieve creativity, and their originality should increase as they develop more expertise.
This relationship does, indeed, seem to occur (Treffert, 2009).
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What happens with higher intelligence?
This domain structure plus obsessive interest plus pattern recognition model of
savant skills comes from analyzing extreme cases like L.E.’s. Not all savants have the
same degree of limitations as L.E. Some can verbalize the 28 year rule, a fairly highlevel calendar regularity (O’Connor, Cowan, & Samella, 2000). Some can do basic
addition and subtraction problems, although their mathematical ability seems unrelated to
their calendar calculation ability (O’Connor, Cowan, & Samella, 2000). Some can
accurately perform calendar calculations for a greater span of years, or have a faster
response speed. And, of course, many savants have higher IQ. A theory based on cases
like L.E.’s must also explain what happens when savants have greater conscious
computation ability.
Higher-IQ savants are better able to transfer mathematical patterns in calendars to
non-calendar material. They also seem better able to verbalize calendar regularities
(O’Connor, Cowan, & Samella, 2000).
However, O’Connor, Cowan, and Samella (2000) found only weak and
inconclusive evidence that overall IQ had any relationship to any measures of calendar
calculation ability. They found only an overall relationship with accuracy. However,
they found no correlation between IQ and the range of years over which savants can
answer date questions; the speed of their calculations; the ability to benefit from priming;
or other tests of calendar knowledge. That greater intelligence did not increase the speed
of calendar calculation is interesting, given that a number of studies have found that
higher intelligence is linked to greater processing speed (Sheppard & Vernon, 2008).
Perhaps this relationship does not exist for savants because IQ tests measure highly
conscious, verbalizable mental processes, whereas savants use unconscious processes
inaccessible to verbalization.
Interestingly, one subset of the Wechsler IQ test was associated with almost every
measure of calendar calculation performance, including speed. This task, the Digit
Symbol task, requires subjects to learn an arbitrary system associating numbers with
symbols and to write as many symbols under the right numbers as possible during a
limited time. It requires visual-spatial ability, processing speed, and the ability to retain
an arbitrary list of associations. It is not yet clear which of these abilities might drive the
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Savant Pattern Recognition Proof of Concept
correlation. I propose that pattern recognition allows savants to quickly associate digits
with symbols, as it does with days and dates.
Between neurotypical people and the lowest-IQ savants lies not a sharp divide but
a continuum. The lowest-IQ savants possess the minimum requirements needed for
talent, but as more intelligence and verbal ability become available, so do more
computational techniques. Unconscious pattern recognition mechanisms may become
just one tool among many. Some savants, such as Daniel Tammet, may not use them at
all. His synesthesia allows him to associate visual features (i.e., size, color, and shape)
with meaningful properties of numbers. Performing mathematical operations involves
combining and recombining number shapes and reading off the shape of the answer
(Tammet, 2006; Tammet, 2009). He can describe his computations in detail and has even
developed a theory of how he accomplishes them (Tammet, 2009).
We focused on very low-IQ savants here because they provide the clearest
examples of the very basic processes that must underlie savant abilities. Higher-IQ
savants have other capabilities that interact with and amplify their special talents but may
not be essential to them; thus, studying them may only cause confusion (Howe & Smith,
1988).
Conclusion
Low IQ savants like L.E. can give the day of the week corresponding to decades’
worth of dates, yet cannot state the number of days in a week or solve an addition or
subtraction problem. This divergence seems paradoxical because we divide the mental
world into conscious, complex, “high-level,” cognitive processes and unconscious,
simple, “low-level,” perceptual-motor processes. But more mental processes exist than
the computations used by neurotypical people and pure rote memory. Unsupervised
neural networks, which rely on pattern recognition, may illustrate how savants process
information. Savants may also use pattern recognition, allowing them to pick up the
meaningful structural regularities in calendars, math, or music. They are drawn to such
structure and seek it out, leading them to spend the necessary time and attention to learn
the patterns in their domain. Eventually, despite this unusual learning process, savants
can function like neurotypical experts. This theory implies that pattern recognition is
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Savant Pattern Recognition Proof of Concept
more than just a low-level, perceptual process and more importantly, that complex
cognitive processes can be unconscious.
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