the power of pattern recognition, a proof of concept: unsupervised neural networks may solve the...

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, “low-level”

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 high-level,

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.

1Emily MorsonSavant Pattern Recognition Proof of Concept

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 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 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.

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 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.

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;

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 real-world

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—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.

Some researchers believe that long hours of practice

alone can explain how savants develop expertise. However,

this theory does not solve the information-processing

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). 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, 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 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 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).

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 high-level 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

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 more than

just a low-level, perceptual process and more importantly,

that complex cognitive processes can be unconscious.

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