## 1. A Description of Neural Networks



A neural network consists of large number of units joined together in
a pattern of connections. Units in a net are usually segregated into
three classes: input units, which receive information to be processed,
output units where the results of the processing are found, and units
in between called hidden units. If a neural net were to model the
whole human nervous system, the input units would be analogous to the
sensory neurons, the output units to the motor neurons, and the hidden
units to all other neurons. 



Here is a simple illustration of a simple neural net:



![a diagram of three columns with the first having seven circles, the second having four circles, and the third having three circles. Each circle in the first column is connected to each circle in the second by a line. Each circle in the second column is connected to each circle in the third column by a line.](net.svg)


Each input unit has an activation value that represents some feature
external to the net. An input unit sends its activation value to each
of the hidden units to which it is connected. Each of these hidden
units calculates its own activation value depending on the activation
values it receives from the input units. This signal is then passed on
to output units or to another layer of hidden units. Those hidden
units compute their activation values in the same way, and send them
along to their neighbors. Eventually the signal at the input units
propagates all the way through the net to determine the activation
values at all the output units.



The pattern of activation set up by a net is determined by the
weights, or strength of connections between the units. Weights may be
either positive or negative. A negative weight represents the
inhibition of the receiving unit by the activity of a sending unit.
The activation value for each receiving unit is calculated according a
simple activation function. Activation functions vary in detail, but
they all conform to the same basic plan. The function sums together
the contributions of all sending units, where the contribution of a
unit is defined as the weight of the connection between the sending
and receiving units times the sending unit's activation value.
This sum is usually modified further, for example, by adjusting the
activation sum to a value between 0 and 1 and/or by setting the
activation to zero unless a threshold level for the sum is reached.
Connectionists presume that cognitive functioning can be explained by
collections of units that operate in this way. Since it is assumed
that all the units calculate pretty much the same simple activation
function, human intellectual accomplishments must depend primarily on
the settings of the weights between the units.



The kind of net illustrated above is called a feed forward net.
Activation flows directly from inputs to hidden units and then on to
the output units. More realistic models of the brain would include
many layers of hidden units, and recurrent connections that send
signals back from higher to lower levels. Such recurrence is necessary
in order to explain such cognitive features as short-term memory. In a
feed forward net, repeated presentations of the same input produce the
same output every time, but even the simplest organisms habituate to
(or learn to ignore) repeated presentation of the same stimulus.
Connectionists tend to avoid recurrent connections because little is
understood about the general problem of training recurrent nets.
However Elman (1991) and others have made some progress with simple
recurrent nets, where the recurrence is tightly constrained.


## 2. Neural Network Learning and Backpropagation



Finding the right set of weights to accomplish a given task is the
central goal in connectionist research. Luckily, learning algorithms
have been devised that can calculate the right weights for carrying
out many tasks (see Hinton 1992 for an accessible review). These fall
into two broad categories: supervised and unsupervised learning.
Hebbian learning is the best known unsupervised form. As each input is
presented to the net, weights between nodes that are active together
are increased, while those weights connecting nodes that are not
active together are decreased. This form of training is especially
useful for building nets that can classify the input into useful
categories. The most widely used supervised algorithm is called
backpropagation. To use this method, one needs a training set
consisting of many examples of inputs and their desired outputs for a
given task. This external set of examples "supervises" the
training process. If, for example, the task is to distinguish male
from female faces, the training set might contain pictures of faces
together with an indication of the sex of the person depicted in each
one. A net that can learn this task might have two output units
(indicating the categories male and female) and many input units, one
devoted to the brightness of each pixel (tiny area) in the picture.
The weights of the net to be trained are initially set to random
values, and then members of the training set are repeatedly exposed to
the net. The values for the input of a member are placed on the input
units and the output of the net is compared with the desired output
for this member. Then all the weights in the net are adjusted slightly
in the direction that would bring the net's output values closer
to the values for the desired output. For example, when male's
face is presented to the input units the weights are adjusted so that
the value of the male output unit is increased and the value of the
female output unit is decreased. After many repetitions of this
process the net may learn to produce the desired output for each input
in the training set. If the training goes well, the net may also have
learned to generalize to the desired behavior for inputs and outputs
that were not in the training set. For example, it may do a good job
of distinguishing males from females in pictures that were never
presented to it before.



Training nets to model aspects of human intelligence is a fine art.
Success with backpropagation and other connectionist learning methods
may depend on quite subtle adjustment of the algorithm and the
training set. Training typically involves hundreds of thousands of
rounds of weight adjustment. Given the limitations of computers in the
past, training a net to perform an interesting task took days or even
weeks. More recently, the use of massively parallel dedicated
processors (GPUs) has helped relieve these heavy computational
burdens. But even here, some limitations to connectionist theories of
learning will remain to be faced. Humans (and many less intelligent
animals) display an ability to learn from single examples; for
example, a child shown a novel two-wheeled vehicle and given the name
"Segway", knows right away what a Segway is (Lake, Zaremba
et al. 2015). Connectionist learning techniques such as
backpropagation are far from explaining this kind of "one
shot" learning.


## 3. Samples of What Neural Networks Can Do



Connectionists have made significant progress in demonstrating the
power of neural networks to master cognitive tasks. Here are three
well-known experiments that have encouraged connectionists to believe
that neural networks are good models of human intelligence. One of the
most attractive of these efforts is Sejnowski and Rosenberg's
1987 work on a net that can read English text called NETtalk. The
training set for NETtalk was a large data base consisting of English
text coupled with its corresponding phonetic output, written in a code
suitable for use with a speech synthesizer. Tapes of NETtalk's
performance at different stages of its training are very interesting
listening. At first the output is random noise. Later, the net sounds
like it is babbling, and later still as though it is speaking English
double-talk (speech that is formed of sounds that resemble English
words). At the end of training, NETtalk does a fairly good job of
pronouncing the text given to it. Furthermore, this ability
generalizes fairly well to text that was not presented in the training
set.



Another influential early connectionist model was a net trained by
Rumelhart and McClelland (1986) to predict the past tense of English
verbs. The task is interesting because although most of the verbs in
English (the regular verbs) form the past tense by adding the suffix
"-ed", many of the most frequently verbs are irregular
("is" / "was", "come" /
"came", "go" / "went"). The net
was first trained on a set containing a large number of irregular
verbs, and later on a set of 460 verbs containing mostly regulars. The
net learned the past tenses of the 460 verbs in about 200 rounds of
training, and it generalized fairly well to verbs not in the training
set. It even showed a good appreciation of "regularities"
to be found among the irregular verbs ("send" /
"sent", "build" / "built";
"blow" / "blew", "fly" /
"flew"). During learning, as the system was exposed to the
training set containing more regular verbs, it had a tendency to
overregularize, i.e., to combine both irregular and regular forms:
("break" / "broked", instead of
"break" / "broke"). This was corrected with
more training. It is interesting to note that children are known to
exhibit the same tendency to overregularize during language learning.
However, there is hot debate over whether Rumelhart and
McClelland's is a good model of how humans actually learn and
process verb endings. For example, Pinker and Prince (1988) point out
that the model does a poor job of generalizing to some novel regular
verbs. They believe that this is a sign of a basic failing in
connectionist models. Nets may be good at making associations and
matching patterns, but they have fundamental limitations in mastering
general rules such as the formation of the regular past tense. These
complaints raise an important issue for connectionist modelers, namely
whether nets can generalize properly to master cognitive tasks
involving rules. Despite Pinker and Prince's objections, many
connectionists believe that generalization of the right kind is still
possible (Niklasson & van Gelder 1994).



Elman's 1991 work on nets that can appreciate grammatical
structure has important implications for the debate about whether
neural networks can learn to master rules. Elman trained a simple
recurrent network to predict the next word in a large corpus of
English sentences. The sentences were formed from a simple vocabulary
of 23 words using a subset of English grammar. The grammar, though
simple, posed a hard test for linguistic awareness. It allowed
unlimited formation of relative clauses while demanding agreement
between the head noun and the verb. So for example, in the
sentence



> 
> 
> Any **man** that chases dogs that chase cats ...
> run**s**.
> 
> 
> 



the singular "**man**" must agree with the
verb "run**s**" despite the intervening
plural nouns ("dogs", "cats") which might
cause the selection of "run". One of the important
features of Elman's model is the use of recurrent connections.
The values at the hidden units are saved in a set of so called context
units, to be sent back to the input level for the next round of
processing. This looping back from hidden to input layers provides the
net with a rudimentary form of memory of the sequence of words in the
input sentence. Elman's nets displayed an appreciation of the
grammatical structure of sentences that were not in the training set.
The net's command of syntax was measured in the following way.
Predicting the next word in an English sentence is, of course, an
impossible task. However, these nets succeeded, at least by the
following measure. At a given point in an input sentence, the output
units for words that are grammatical continuations of the sentence at
that point should be active and output units for all other words
should be inactive. After intensive training, Elman was able to
produce nets that displayed perfect performance on this measure
including sentences not in the training set. The work of Christiansen
and Chater (1999a) and Morris, Cottrell, and Elman (2000) extends this
research to more complex grammars. For a broader view of progress in
connectionist natural language processing see summaries by
Christiansen and Chater (1999b), and Rohde and Plaut (2003).



Although this performance is impressive, there is still a long way to
go in training nets that can process a language like English.
Furthermore, doubts have been raised about the significance of
Elman's results. For example, Marcus (1998, 2001) argues that
Elman's nets are not able to generalize this performance to
sentences formed from a novel vocabulary. This, he claims, is a sign
that connectionist models merely associate instances, and are unable
to truly master abstract rules. On the other hand, Phillips (2002)
argues that classical architectures are no better off in this respect.
The purported inability of connectionist models to generalize
performance in this way has become an important theme in the
systematicity debate. (See Section 7 below.)



A somewhat different concern about the adequacy of connectionist
language processing focuses on tasks that mimic infant learning of
simple artificial grammars. Data on reaction time confirms that
infants can learn to distinguish well-formed from ill-formed sentences
in a novel language created by experimenters. Shultz and Bale (2001)
report success in training neural nets on the same task. Vilcu and
Hadley (2005) object that this work fails to demonstrate true
acquisition of the grammar, but see Shultz and Bale (2006) for a
detailed reply.


## 4. Strengths and Weaknesses of Neural Network Models



Philosophers are interested in neural networks because they may
provide a new framework for understanding the nature of the mind and
its relation to the brain (Rumelhart & McClelland 1986: Chapter
1). Connectionist models seem particularly well matched to what we
know about neurology. The brain is indeed a neural net, formed from
massively many units (neurons) and their connections (synapses).
Furthermore, several properties of neural network models suggest that
connectionism may offer an especially faithful picture of the nature
of cognitive processing. Neural networks exhibit robust flexibility in
the face of the challenges posed by the real world. Noisy input or
destruction of units causes graceful degradation of function. The
net's response is still appropriate, though somewhat less
accurate. In contrast, noise and loss of circuitry in classical
computers typically result in catastrophic failure. Neural networks
are also particularly well adapted for problems that require the
resolution of many conflicting constraints in parallel. There is ample
evidence from research in artificial intelligence that cognitive tasks
such as object recognition, planning, and even coordinated motion
present problems of this kind. Although classical systems are capable
of multiple constraint satisfaction, connectionists argue that neural
network models provide much more natural mechanisms for dealing with
such problems.



Over the centuries, philosophers have struggled to understand how our
concepts are defined. It is now widely acknowledged that trying to
characterize ordinary notions with necessary and sufficient conditions
is doomed to failure. Exceptions to almost any proposed definition are
always waiting in the wings. For example, one might propose that a
tiger is a large black and orange feline. But then what about albino
tigers? Philosophers and cognitive psychologists have argued that
categories are delimited in more flexible ways, for example via a
notion of family resemblance or similarity to a prototype.
Connectionist models seem especially well suited to accommodating
graded notions of category membership of this kind. Nets can learn to
appreciate subtle statistical patterns that would be very hard to
express as hard and fast rules. Connectionism promises to explain
flexibility and insight found in human intelligence using methods that
cannot be easily expressed in the form of exception free principles
(Horgan & Tienson 1989, 1990), thus avoiding the brittleness that
arises from standard forms of symbolic representation.



Despite these intriguing features, there are some weaknesses in
connectionist models that bear mentioning. First, most neural network
research abstracts away from many interesting and possibly important
features of the brain. For example, connectionists usually do not
attempt to explicitly model the variety of different kinds of brain
neurons, nor the effects of neurotransmitters and hormones.
Furthermore, it is far from clear that the brain contains the kind of
reverse connections that would be needed if the brain were to learn by
a process like backpropagation, and the immense number of repetitions
needed for such training methods seems far from realistic. Attention
to these matters will probably be necessary if convincing
connectionist models of human cognitive processing are to be
constructed. A more serious objection must also be met. It is widely
felt, especially among classicists, that neural networks are not
particularly good at the kind of rule based processing that is thought
to undergird language, reasoning, and higher forms of thought. (For a
well known critique of this kind see Pinker and Prince 1988.) We will
discuss the matter further when we turn to
 the systematicity debate.



There has been a cottage industry in developing more
biologically-plausible algorithms for error-driven training that can
be shown to approximate the results of backpropagation without its
implausible features. Prominent examples include
O'Reilly's Generalized Error Recirculation algorithm
(O'Reilly 1996), using randomized error signals rather than
error signals individually computed for each neuron (Lillicrap,
Cownden, Tweed, & Akerman 2016), and modifying weights using
spike-timing dependent plasticity--the latter of which has been a
favorite of prominent figures in deep learning research (Bengio et al.
2017). (For more on deep learning see
 section 11
 below.) 


## 5. The Shape of the Controversy between Connectionists and Classicists



The last forty years have been dominated by the classical view that
(at least higher) human cognition is analogous to symbolic computation
in digital computers. On the classical account, information is
represented by strings of symbols, just as we represent data in
computer memory or on pieces of paper. The connectionist claims, on
the other hand, that information is stored non-symbolically in the
weights, or connection strengths, between the units of a neural net.
The classicist believes that cognition resembles digital processing,
where strings are produced in sequence according to the instructions
of a (symbolic) program. The connectionist views mental processing as
the dynamic and graded evolution of activity in a neural net, each
unit's activation depending on the connection strengths and
activity of its neighbors.



On the face of it, these views seem very different. However many
connectionists do not view their work as a challenge to classicism and
some overtly support the classical picture. So-called implementational
connectionists seek an accommodation between the two paradigms. They
hold that the brain's net implements a symbolic processor. True,
the mind is a neural net; but it is also a symbolic processor at a
higher and more abstract level of description. So the role for
connectionist research according to the implementationalist is to
discover how the machinery needed for symbolic processing can be
forged from neural network materials, so that classical processing can
be reduced to the neural network account.



However, many connectionists resist the implementational point of
view. Such radical connectionists claim that symbolic processing was a
bad guess about how the mind works. They complain that classical
theory does a poor job of explaining graceful degradation of function,
holistic representation of data, spontaneous generalization,
appreciation of context, and many other features of human intelligence
which are captured in their models. The failure of classical
programming to match the flexibility and efficiency of human cognition
is by their lights a symptom of the need for a new paradigm in
cognitive science. So radical connectionists would eliminate symbolic
processing from cognitive science forever.



The controversy between radical and implementational connectionists is
complicated by the invention of what are called hybrid connectionist
architectures. Here elements of classical symbolic processing are
included in neural nets (Wermter & Sun 2000). For example,
Miikkulainen (1993) champions a complex collection of neural net
modules that share data coded in activation patterns. Since one of the
modules acts as a memory, the system taken as a whole resembles a
classical processor with separate mechanisms for storing and operating
on digital "words". Smolensky (1990) is famous for
inventing so called tensor product methods for simulating the process
of variable binding, where symbolic information is stored at and
retrieved from known "locations". More recently, Eliasmith
(2013) has proposed complex and massive architectures that use what
are called semantic pointers, which exhibit features of classical
variable binding. Once hybrid architectures such as these are on the
table, it becomes more difficult to classify a given connectionist
model as radical or merely implementational. This opens the
interesting prospect that whether symbolic processing is actually
present in the human brain may turn out to be a matter of degree.



The disagreement concerning the degree to which human cognition
involves symbolic processing is naturally embroiled with the
innateness debate--whether higher level abilities such as
language and reasoning are part of the human genetic endowment, or
whether they are learned. The success of connectionist models at
learning tasks starting from randomly chosen weights gives heart to
empiricists, who would think that the infant brain is able to
construct intelligence from perceptual input using a simple learning
mechanism (Elman et al. 1996). On the other hand, nativists in the
rationalist tradition argue that at least for grammar-based language,
the poverty of perceptual stimulus (Chomsky 1965: 58) entails the
existence of a genetically determined mechanism tailored to learning
grammar. However, the alignment between connectionism and non-nativism
is not so clear-cut. There is no reason that connectionist models
cannot be interpreted from a nativist point of view, where the ongoing
"learning" represents the process of evolutionary
refinement from generation to generation of a species. The idea that
the human brain has domain specific knowledge that is genetically
determined can be accommodated in the connectionist paradigm by
biasing the initial weights of the models to make that knowledge easy
or trivial to learn. Connectionist research makes best contact with
the innateness debate by providing a new strategy for disarming
poverty of stimulus arguments. Nativists argue that association of
ideas, the mechanism for learning proposed by the traditional
empiricist, is too slender a reed to support the development of higher
level cognitive abilities. They suppose that innate mechanisms are
essential for learning (for example) a grammar of English from a
child's linguistic input, because the statistical regularities
available to "mere association" massively underdetermine
that grammar. Connectionism could support an empiricism here by
providing a proof-of-concept that such structured knowledge can be
learned from inputs available to humans using only learning mechanisms
found in non-classical architectures. Of course it is too soon to tell
whether this promise can be realized. 


## 6. Connectionist Representation



Connectionist models provide a new paradigm for understanding how
information might be represented in the brain. A seductive but naive
idea is that single neurons (or tiny neural bundles) might be devoted
to the representation of each thing the brain needs to record. For
example, we may imagine that there is a grandmother neuron that fires
when we think about our grandmother. However, such local
representation is not likely. There is good evidence that our
grandmother thought involves complex patterns of activity distributed
across relatively large parts of cortex.



It is interesting to note that distributed, rather than local
representations on the hidden units are the natural products of
connectionist training methods. The activation patterns that appear on
the hidden units while NETtalk processes text serve as an example.
Analysis reveals that the net learned to represent such categories as
consonants and vowels, not by creating one unit active for consonants
and another for vowels, but rather in developing two different
characteristic patterns of activity across all the hidden units.



Given the expectations formed from our experience with local
representation on the printed page, distributed representation seems
both novel and difficult to understand. But the technique exhibits
important advantages. For example, distributed representations,
(unlike symbols stored in separate fixed memory locations) remain
relatively well preserved when parts of the model are destroyed or
overloaded. More importantly, since representations are coded in
patterns rather than firings of individual units, relationships
between representations are coded in the similarities and differences
between these patterns. So the internal properties of the
representation carry information on what it is about (Clark 1993: 19).
In contrast, local representation is conventional. No intrinsic
properties of the representation (a unit's firing) determine its
relationships to the other symbols. This self-reporting feature of
distributed representations promises to resolve a philosophical
conundrum about meaning. In a symbolic representational scheme, all
representations are composed out of symbolic atoms (like words in a
language). Meanings of complex symbol strings may be defined by the
way they are built up out of their constituents, but what fixes the
meanings of the atoms?



Connectionist representational schemes provide an end run around the
puzzle by simply dispensing with atoms. Every distributed
representation is a pattern of activity across all the units, so there
is no principled way to distinguish between simple and complex
representations. To be sure, representations are composed out of the
activities of the individual units. But none of these
"atoms" codes for any symbol. The representations are
sub-symbolic in the sense that analysis into their components leaves
the symbolic level behind.



The sub-symbolic nature of distributed representation provides a novel
way to conceive of information processing in the brain. If we model
the activity of each neuron with a number, then the activity of the
whole brain can be given by a giant vector (or list) of numbers, one
for each neuron. Both the brain's input from sensory systems and
its output to individual muscle neurons can also be treated as vectors
of the same kind. So the brain amounts to a vector processor, and the
problem of psychology is transformed into questions about which
operations on vectors account for the different aspects of human
cognition.



Sub-symbolic representation has interesting implications for the
classical hypothesis that the brain must contain symbolic
representations that are similar to sentences of a language. This
idea, often referred to as the language of thought (or LOT) thesis may
be challenged by the nature of connectionist representations. It is
not easy to say exactly what the LOT thesis amounts to, but van Gelder
(1990) offers an influential and widely accepted benchmark for
determining when the brain should be said to contain sentence-like
representations. It is that when a representation is tokened one
thereby tokens the constituents of that representation. For example,
if I write "John loves Mary" I have thereby written the
sentence's constituents: "John" "loves"
and "Mary". Distributed representations for complex
expressions like "John loves Mary" can be constructed that
do not contain any explicit representation of their parts (Smolensky
1990). The information about the constituents can be extracted from
the representations, but neural network models do not need to
explicitly extract this information themselves in order to process it
correctly (Chalmers 1990). This suggests that neural network models
serve as counterexamples to the idea that the language of thought is a
prerequisite for human cognition. However, the matter is still a topic
of lively debate (Fodor 1997).



The novelty of distributed and superimposed connectionist information
storage naturally causes one to wonder about the viability of
classical notions of symbolic computation in describing the brain.
Ramsey (1997) argues that though we may attribute symbolic
representations to neural nets, those attributions do not figure in
legitimate explanations of the model's behavior. This claim is
important because the classical account of cognitive processing, (and
folk intuitions) presume that representations play an explanatory role
in understanding the mind. It has been widely thought that cognitive
science requires, by its very nature, explanations that appeal to
representations (Von Eckardt 2003). If Ramsey is right, the point may
cut in two different ways. Some may use it to argue for a new and
non-classical understanding of the mind, while others would use it to
argue that connectionism is inadequate since it cannot explain what it
must. However, Haybron (2000) argues against Ramsey that there is
ample room for representations with explanatory role in radical
connectionist architectures. Roth (2005) makes the interesting point
that contrary to first impressions, it may also make perfect sense to
explain a net's behavior by reference to a computer program,
even if there is no way to discriminate a sequence of steps of the
computation through time.



The debate concerning the presence of classical representations and a
language of thought has been clouded by lack of clarity in defining
what should count as the representational "vehicles" in
distributed neural models. Shea (2007) makes the point that the
individuation of distributed representations should be defined by the
way activation patterns on the hidden units cluster together. It is
the relationships between clustering *regions* in the space of
possible activation patterns that carry representational content, not
the activations themselves, nor the collection of units responsible
for the activation. On this understanding, prospects are improved for
locating representational content in neural nets that can be compared
in nets of different architectures, that is causally involved in
processing, and which overcomes some objections to holistic accounts
of meaning.



In a series of papers Horgan and Tienson (1989, 1990) have championed
a view called representations without rules. According to this view
classicists are right to think that human brains (and good
connectionist models of them) contain explanatorily robust
representations; but they are wrong to think that those
representations enter in to hard and fast rules like the steps of a
computer program. The idea that connectionist systems may follow
graded or approximate regularities ("soft laws" as Horgan
and Tienson call them) is intuitive and appealing. However, Aizawa
(1994) argues that given an arbitrary neural net with a representation
level description, it is always possible to outfit it with hard and
fast representation-level rules. Guarini (2001) responds that if we
pay attention to notions of rule following that are useful to
cognitive modeling, Aizawa's constructions will seem beside the
point.


## 7. The Systematicity Debate



The major points of controversy in the philosophical literature on
connectionism have to do with whether connectionists provide a viable
and novel paradigm for understanding the mind. One complaint is that
connectionist models are only good at processing associations. But
such tasks as language and reasoning cannot be accomplished by
associative methods alone and so connectionists are unlikely to match
the performance of classical models at explaining these higher-level
cognitive abilities. However, it is a simple matter to prove that
neural networks can do anything that symbolic processors can do, since
nets can be constructed that mimic a computer's circuits. So the
objection can not be that connectionist models are unable to account
for higher cognition; it is rather that they can do so only if they
implement the classicist's symbolic processing tools.
Implementational connectionism may succeed, but radical connectionists
will never be able to account for the mind.



Fodor and Pylyshyn's often cited paper (1988) launches a debate
of this kind. They identify a feature of human intelligence called
systematicity which they feel connectionists cannot explain. The
systematicity of language refers to the fact that the ability to
produce/understand/think some sentences is intrinsically connected to
the ability to produce/understand/think others of related structure.
For example, no one with a command of English who understands
"John loves Mary" can fail to understand "Mary loves
John." From the classical point of view, the connection between
these two abilities can easily be explained by assuming that masters
of English represent the constituents ("John",
"loves" and "Mary") of "John loves
Mary" and compute its meaning from the meanings of these
constituents. If this is so, then understanding a novel sentence like
"Mary loves John" can be accounted for as another instance
of the same symbolic process. In a similar way, symbolic processing
would account for the systematicity of reasoning, learning and
thought. It would explain why there are no people who are capable of
concluding *P* from *P* & (*Q* &
*R*), but incapable of concluding *P* from *P*
& *Q*, why there are no people capable of learning to
prefer a red cube to green square who cannot learn to prefer a green
cube to the red square, and why there isn't anyone who can think
that John loves Mary who can't also think that Mary loves
John.



Fodor and McLaughlin (1990) argue in detail that connectionists do not
account for systematicity. Although connectionist models can be
trained to be systematic, they can also be trained, for example, to
recognize "John loves Mary" without being able to
recognize "Mary loves John." Since connectionism does not
guarantee systematicity, it does not explain why systematicity is
found so pervasively in human cognition. Systematicity may exist in
connectionist architectures, but where it exists, it is no more than a
lucky accident. The classical solution is much better, because in
classical models, pervasive systematicity comes for free.



The charge that connectionist nets are disadvantaged in explaining
systematicity has generated a lot of interest. Chalmers (1993) points
out that Fodor and Pylyshyn's argument proves too much, for it
entails that all neural nets, even those that implement a classical
architecture, do not exhibit systematicity. Given the uncontroversial
conclusion that the brain is a neural net, it would follow that
systematicity is impossible in human thought. Another often mentioned
point of rebuttal (Aizawa 1997b; Matthews 1997; Hadley 1997b) is that
classical architectures do no better at explaining systematicity.
There are also classical models that can be programmed to recognize
"John loves Mary" without being able to recognize
"Mary loves John," for this depends on exactly which
symbolic rules govern the classical processing. The point is that
neither the use of connectionist architecture alone nor the use of
classical architecture alone enforces a strong enough constraint to
explain pervasive systematicity. In both architectures, further
assumptions about the nature of the processing must be made to ensure
that "Mary loves John" and "John loves Mary"
are treated alike.



A discussion of this point should mention Fodor and McLaughlin's
requirement that systematicity be explained as a matter of nomic
necessity, that is, as a matter of natural law. The complaint against
connectionists is that while they may implement systems that exhibit
systematicity, they will not have explained it unless it follows from
their models as a nomic necessity. However, the demand for nomic
necessity is a very strong one, and one that classical architectures
clearly cannot meet either. So the only tactic for securing a telling
objection to connectionists along these lines would be to weaken the
requirement on the explanation of systematicity to one which classical
architectures can and connectionists cannot meet. A convincing case of
this kind has yet to be made.



As the systematicity debate has evolved, attention has been focused on
defining the benchmarks that would answer Fodor and Pylyshyn's
challenge. Hadley (1994a, 1994b) distinguishes three brands of
systematicity. Connectionists have clearly demonstrated the weakest of
these by showing that neural nets can learn to correctly recognize
novel sequences of words (e.g., "Mary loves John") that
were not in the training set. However, Hadley claims that a convincing
rebuttal must demonstrate strong systematicity, or better, strong
semantical systematicity. Strong systematicity would require (at
least) that "Mary loves John" be recognized even if
"Mary" never appears in the subject position in any
sentence in the training set. Strong semantical systematicity would
require as well that the net show abilities at correct semantical
processing of the novel sentences rather than merely distinguishing
grammatical from ungrammatical forms. Niklasson and van Gelder (1994)
have claimed success at strong systematicity, though Hadley complains
that this is at best a borderline case. Hadley and Hayward (1997)
tackle strong semantical systematicity, but by Hadley's own
admission it is not clear that they have avoided the use of a
classical architecture. Boden and Niklasson (2000) claim to have
constructed a model that meets at least the spirit of strong
semantical systematicity, but Hadley (2004) argues that even strong
systematicity has not been demonstrated there. Whether one takes a
positive or a negative view of these attempts, it is safe to say that
no one has met the challenge of providing a neural net capable of
learning complex semantical processing that generalizes to a full
range of truly novel inputs.



Research on nets that clearly demonstrate strong systematicity has
continued. Jansen and Watter (2012) provide a good summary of more
recent efforts along these lines, and propose an interesting basis for
solving the problem. They use a more complex architecture that
combines unsupervised self-organizing maps with features of simple
recurrent nets. However, the main innovation is to allow codes for the
words being processed to represent sensory-motor features of what the
words represent. Once trained, their nets displayed very good accuracy
in distinguishing the grammatical features of sentences whose words
never even appeared in the training set. This may appear to be
cheating since the word codes might surreptitiously represent
grammatical categories, or at least they may unfairly facilitate
learning those categories. Jansen and Watter note however, that the
sensory-motor features of what a word represents are apparent to a
child who has just acquired a new word, and so that information is not
off-limits in a model of language learning. They make the interesting
observation that a solution to the systematicity problem may require
including sources of environmental information that have so far been
ignored in theories of language learning. This work complicates the
systematicity debate, since it opens a new worry about what
information resources are legitimate in responding to the challenge.
However, this reminds us that architecture alone (whether classical or
connectionist) is not going to solve the systematicity problem in any
case, so the interesting questions concern what sources of
supplemental information are needed to make the learning of grammar
possible.



Kent Johnson (2004) argues that the whole systematicity debate is
misguided. Attempts at carefully defining the systematicity of
language or thought leaves us with either trivialities or falsehoods.
Connectionists surely have explaining to do, but Johnson recommends
that it is fruitless to view their burden under the rubric of
systematicity. Aizawa (2014) also suggests the debate is no longer
germane given the present climate in cognitive science. What is needed
instead is the development of neurally plausible connectionist models
capable of processing a language with a recursive syntax, which react
immediately to the introduction of new items in the lexicon without
introducing the features of classical architecture. The
"systematicity" debate may have already gone as Johnson
advises, for Hadley's demand for strong semantical systematicity
may be thought of as the requirement that connectionists exhibit
success in that direction.



Recent work (Loula, Baroni, & Lake 2018) sheds new light on the
controversy. Here recurrent neural nets were trained to interpret
complex commands in a simple language that includes primitives such as
"jump", "walk", "left",
"right", "opposite" and "around".
"Opposite" is interpreted as a request to perform a
command twice, and "around" to do so four times. So
"jump around left" requests a left jump four times. The
authors report that their nets showed very accurate generalization at
tasks that qualify for demonstrating strong semantic systematicity.
The nets correctly parsed commands in the test set containing
"jump around right" even though this phrase never appeared
in the training set. Nevertheless the net's failures at more
challenging tasks point to limitations in their abilities to
generalize in ways that would demonstrate genuine systematicity. The
nets exhibited very poor performance when commands in the test set
were longer (or even shorter), than those presented in the training
set. So they appeared unable to spontaneously compose the meaning of
complex expressions from the meanings of their parts. New research is
needed to understand the nature of these failures, whether they can be
overcome in non-classical architectures, and the extent to which
humans would exhibit similar mistakes under analogous
circumstances.



It has been almost thirty years since the systematicity debate first
began, with over 3,000 citations to Fodor and Pylyshyn's
original paper. So this brief account is necessarily incomplete.
Aizawa (2003) provides an
excellent view of the literature, and Calvo and Symons (2014) serves
as another more recent resource. 


## 8. Connectionism and Semantic Similarity



One of the attractions of distributed representations in connectionist
models is that they suggest a solution to the problem of providing a
theory of how brain states could have meaning. The idea is that the
similarities and differences between activation patterns along
different dimensions of neural activity record semantical information.
So the similarity properties of neural activations provide intrinsic
properties that determine meaning. However, when it comes to
compositional linguistic representations, Fodor and Lepore (1992: Ch.
6) challenge similarity based accounts, on two fronts. The first
problem is that human brains presumably vary significantly in the
number of and connections between their neurons. Although it is
straightforward to define similarity measures on two nets that contain
the same number of units, it is harder to see how this can be done
when the basic architectures of two nets differ. The second problem
Fodor and Lepore cite is that even if similarity measures for meanings
can be successfully crafted, they are inadequate to the task of
meeting the desiderata which a theory of meaning must satisfy.



Churchland (1998) shows that the first of these two objections can be
met. Citing the work of Laakso and Cottrell (2000) he explains how
similarity measures between activation patterns in nets with radically
different structures can be defined. Not only that, Laakso and
Cottrell show that nets of different structures trained on the same
task develop activation patterns which are strongly similar according
to the measures they recommend. This offers hope that empirically well
defined measures of similarity of concepts and thoughts across
different individuals might be forged.



On the other hand, the development of a traditional theory of meaning
based on similarity faces severe obstacles (Fodor & Lepore 1999),
for such a theory would be required to assign sentences truth
conditions based on an analysis of the meaning of their parts, and it
is not clear that similarity alone is up to such tasks as fixing
denotation in the way a standard theory demands. However, most
connectionists who promote similarity based accounts of meaning reject
many of the presupposition of standard theories. They hope to craft a
working alternative which either rejects or modifies those
presuppositions while still being faithful to the data on human
linguistic abilities.



Calvo Garzon (2003) complains that there are reasons to think
that connectionists must fail. Churchland's response has no
answer to the collateral information challenge. That problem is that
the measured similarities between activation patterns for a concept
(say: grandmother) in two human brains are guaranteed to be very low
because two people's (collateral) information on their
grandmothers (name, appearance, age, character) is going to be very
different. If concepts are defined by everything we know, then the
measures for activation patterns of our concepts are bound to be far
apart. This is a truly deep problem in any theory that hopes to define
meaning by functional relationships between brain states. Philosophers
of many stripes must struggle with this problem. Given the lack of a
successfully worked out theory of concepts in either traditional or
connectionist paradigms, it is only fair to leave the question for
future research.


## 9. Connectionism and the Elimination of Folk Psychology



Another important application of connectionist research to
philosophical debate about the mind concerns the status of folk
psychology. Folk psychology is the conceptual structure that we
spontaneously apply to understanding and predicting human behavior.
For example, knowing that John desires a beer and that he believes
that there is one in the refrigerator allows us to explain why John
just went into the kitchen. Such knowledge depends crucially on our
ability to conceive of others as having desires and goals, plans for
satisfying them, and beliefs to guide those plans. The idea that
people have beliefs, plans and desires is a commonplace of ordinary
life; but does it provide a faithful description of what is actually
to be found in the brain?



Its defenders will argue that folk psychology is too good to be false
(Fodor 1988: Ch. 1). What more can we ask for the truth of a theory
than that it provides an indispensable framework for successful
negotiations with others? On the other hand, eliminativists will
respond that the useful and widespread use of a conceptual scheme does
not argue for its truth (Churchland 1989: Ch. 1). Ancient astronomers
found the notion of celestial spheres useful (even essential) to the
conduct of their discipline, but now we know that there are no
celestial spheres. From the eliminativists' point of view, an
allegiance to folk psychology, like allegiance to folk (Aristotelian)
physics, stands in the way of scientific progress. A viable psychology
may require as radical a revolution in its conceptual foundations as
is found in quantum mechanics.



Eliminativists are interested in connectionism because it promises to
provide a conceptual foundation that might replace folk psychology.
For example Ramsey, Stich, & Garon (1991) have argued that certain
feed-forward nets show that simple cognitive tasks can be performed
without employing features that could correspond to beliefs, desires
and plans. Presuming that such nets are faithful to how the brain
works, concepts of folk psychology fare no better than do celestial
spheres. Whether connectionist models undermine folk psychology in
this way is still controversial. There are two main lines of response
to the claim that connectionist models support eliminativist
conclusions. One objection is that the models used by Ramsey et
al. are feed forward nets, which are too weak to explain some of the
most basic features of cognition such as short term memory. Ramsey et
al. have not shown that beliefs and desires must be absent in a class
of nets adequate for human cognition. A second line of rebuttal
challenges the claim that features corresponding to beliefs and
desires are necessarily absent even in the feed forward nets at issue
(Von Eckardt 2005).



The question is complicated further by disagreements about the nature
of folk psychology. Many philosophers treat the beliefs and desires
postulated by folk psychology as brain states with symbolic contents.
For example, the belief that there is a beer in the refrigerator is
thought to be a brain state that contains symbols corresponding to
beer and a refrigerator. From this point of view, the fate of folk
psychology is strongly tied to the symbolic processing hypothesis. So
if connectionists can establish that brain processing is essentially
non-symbolic, eliminativist conclusions will follow. On the other
hand, some philosophers do not think folk psychology is essentially
symbolic, and some would even challenge the idea that folk psychology
is to be treated as a theory in the first place. Under this
conception, it is much more difficult to forge links between results
in connectionist research and the rejection of folk psychology.


## 10. Predictive Coding Models of Cognition



As connectionist research has matured from its "Golden
Age" in the 1980s, the main paradigm has radiated into a number
of distinct approaches. Two important trends worth mention are
predicative coding and deep learning (which will be covered in the
following section). Predictive coding is a well-established
information processing tool with a wide range of applications. It is
useful, for example, in compressing the size of data sets. Suppose you
wish to transmit a picture of a landscape with a blue sky. Since most
of the pixels in the top half of your image are roughly the same
shade, it is very inefficient to record the color value (say Red: 46
Green: 78 Blue: FF in hexadecimal) over and over again for each pixel
in the top half of the image. Since the value of one pixel strongly
predicts the value of its neighbor, the efficient thing to do is
record at each pixel location, the difference between the predicted
value (an average of its neighbors) and the actual value for that
pixel. (In the case of representing an even shaded sky, we would only
need to record the blue value once, followed by lots of zeros.) This
way, major coding resources are only needed to keep track of points in
the image (such as edges) where there are large changes, that is
points of "surprise" or "unexpected"
variation.



It is well known that early visual processing in the brain involves
taking differences between nearby values, (for example, to identify
visual boundaries). It is only natural then to explore how the brain
might take advantage of predictive coding in perception, inference, or
even action. (See Clark 2013 for an excellent summary and entry point
to the literature.) There is wide variety in the models presented in
the predictive coding paradigm, and they tend to be specified at a
higher level of generality than are connectionist models so far
discussed. Assume we have a neural net with input, hidden and output
levels that has been trained on a task (say face recognition) and so
presumably has information about faces stored in the weights
connecting the hidden level nodes. Three features would classify this
net as a predictive coding (PC) model. First, the model will have
downward connections from the higher levels that are able to predict
the next input for that task. (The prediction might be a
representation of a generic face.) Second, the data sent to the higher
levels for a given input is not the value recorded at the input nodes,
but the difference between the predicted values and the values
actually present. (So in the example, the data provided tracks the
differences between the face to be recognized and the generic face.)
In this way the data being received by the net is already preprocessed
for coding efficiency. Third, the model is trained by adjusting the
weights in such a way that the error is minimized at the inputs. In
other words, the trained net reduces as much as possible the
"surprise" registered in the difference between the raw
input and its prediction. In so doing it comes to be able to predict
the face of the individual to be recognized to eliminate the error.
Some advocates of predictive coding models suggest that this scheme
provides a unified account of all cognitive phenomena, including
perception, reasoning, planning and motor control. By minimizing
prediction error in interacting with the environment, the net is
forced to develop the conceptual resources to model the causal
structure of the external world, and so navigate that world more
effectively. 



The predictive coding (PC) paradigm has attracted a lot of attention.
There is ample evidence that PC models capture essential details of
visual function in the mammalian brain (Rao & Ballard 1999; Huang
& Rao 2011). For example, when trained on typical visual input, PC
models spontaneously develop functional areas for edge, orientation
and motion detection known to exist in visual cortex. This work also
raises the interesting point that the visual architecture may develop
in response to the statistics of the scenes being encountered, so that
organisms in different environments have visual systems specially
tuned to their needs.



It must be admitted that there is still no convincing evidence that
the essential features of PC models are directly implemented as
anatomical structures in the brain. Although it is conjectured that
superficial pyramidal cells may transmit prediction error, and deep
pyramidal cells predictions, we do not know that that is how they
actually function. On the other hand, PC models do appear more
neurally plausible than backpropagation architectures, for there is no
need for a separate process of training on an externally provided set
of training samples. Instead, predictions replace the role of the
training set, so that learning and interacting with the environment
are two sides of a unified unsupervised process. 



PC models also show promise for explaining higher-level cognitive
phenomena. An often-cited example is binocular rivalry. When presented
with entirely different images in two eyes, humans report an
oscillation between the two images as each in turn comes into
"focus". The PC explanation is that the system succeeds in
eliminating error by predicting the scene for one eye, but only to
increase the error for the other eye. So the system is unstable,
"hunting" from one prediction to the other. Predictive
coding also has a natural explanation for why we are unaware of our
blind spot, for the lack of input in that area amounts to a report of
no error, with the result that one perceives "more of the
same".



PC accounts of attention have also been championed. For example, Hohwy
(2012) notes that realistic PC models, which must tolerate noisy
inputs, need to include parameters that track the desired precision to
be used in reporting error. So PC models need to make predictions of
the error precision relevant for a given situation. Hohwy explores the
idea that mechanisms for optimizing precision expectations map onto
those that account for attention, and argues that attentional
phenomena such as change blindness can be explained within the PC
paradigm. 



Predictive coding has interesting implications for themes in the
philosophy of cognitive science. By integrating the processes of
top-down prediction with bottom-up error detection, the PC account of
perception views it as intrinsically theory-laden. Deployment of the
conceptual categorization of the world embodied in higher levels of
the net is essential to the very process of gathering data about the
world. This underscores, as well, tight linkages between belief,
imaginative abilities, and perception (Grush 2004). The PC paradigm
also tends to support situated or embodied conceptions of cognition,
for it views action as a dynamic interaction between the
organism's effects on the environment, its predictions
concerning those effects (its plans), and its continual monitoring of
error, which provides feedback to help ensure success.



It is too early to evaluate the importance and scope of PC models in
accounting for the various aspects of cognition. Providing a unified
theory of brain function in general is, after all, an impossibly high
standard. Clark's target article (2013) provides a useful forum
for airing complaints against PC models and some possible responses.
One objection that is often heard is that an organism with a PC brain
can be expected to curl up in a dark room and die, for this is the
best way to minimize error at its sensory inputs. However, that view
may take too narrow a view of the sophistication of the predictions
available to the organism. If it is to survive at all, its genetic
endowment coupled with what it can learn along the way may very well
endow it with the expectation that it go out and seek needed resources
in the environment. Minimizing error for that prediction of its
behavior will get it out of the dark room. However, it remains to be
seen whether a theory of biological urges is usefully recast in PC
terminology in this way, or whether PC theory is better characterized
as only part of the explanation. Another complaint is that the
top-down influence on our perception coupled with the constraint that
the brain receives error signals rather than raw data would impose an
unrealistic divide between a represented world of fantasy and the
world as it really is. It is hard to evaluate whether that qualifies
as a serious objection. Were PC models actually to provide an account
of our phenomenological experience, and characterize the relations
between that experience and what we count as real, then skeptical
conclusions to be drawn would count as features of the view rather
than objections to it. A number of responders to Clark's target
article also worry that PC-models count as overly general. In trying
to explain everything they explain nothing. Without sufficient
constraints on the architecture, it is too easy to pretend to explain
cognitive phenomena by merely redescribing them in a story written in
the vocabulary of prediction, comparison, error minimization, and
optimized precision. The real proof of the pudding will come with the
development of more complex and detailed computer models in the PC
framework that are biologically plausible, and able to demonstrate the
defining features of cognition.