Neural Networks and Statistics:

chickenchairwomanAI and Robotics

Oct 19, 2013 (3 years and 9 months ago)

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Neural Networks and Statistics:

Intelligence and the Self





Prof Bruce Curry and Dr Peter Morgan



Cardiff Business School, UK

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NEURAL NETWORKS ( NNs)



Generally seen as part of the discipline of AI, although to us they are
statistical devices.



They originated as models of the workings of the brain



‘A Logical Calculus of Ideas Immanent in Nervous Activity’



This implies they are an alternative to symbolic computation, eg. rule based
methods



Rules and chaining methods, inference through formal logic.


NNs carry out sub
-
symbolic computation


They copy the physical workings of the brain


Neurons + connections

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Some Details



Feedforward networks


Inputs, Outputs, Hidden Nodes


Hidden Node activation: step functions or sigmoids.
These are fuzzified steps


Hidden nodes provide the intelligence we seek to model


They are like specialised parts of the brain brought into
action when needed


They can describe Fuzzy IF/THEN rules.


Hence we don’t need a strict distinction between NNs
and rule based methods.

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NN learning


Learning is an essential component of intelligence



NN’s can learn rules


Learning through weight adjustment and optimisation


Minimum RMS (equivalent to least squares)


Universal Approximation through use of a flexible functional form


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Hence in statistical terms we have a form
of nonlinear regression


The network learns the underlying shape
describing the relationship between Y and
X.


Example, Mexican Hat

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NNs , Statistics and Intelligence



Hence NNs are statistical devices


Supervised and unsupervised learning


NNs provide nonlinear alternatives to standard
statistical methods


They are applied to traditional statistical tasks

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BUT



Statistics, in its aims, is almost antithetical to intelligence


The aim is automated judgment based on standard
methods


This is achieved by standard numerical measures, for
example of the strength of a conclusion


The prime example is testing hypotheses, where we
have a significance level or ‘p value’


Everyone is supposed to agree that for example


p = .001 gives a strong conclusion, with in fact less than
1% chance of being wrong


This is in practice rather idealistic!!

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CONTROVERSIES IN PHILOSOPHICAL ASPECTS OF COMPUTING




(a) The nature of the Self and the Mind Body Problem.



This includes issues involving consciousness.



(b) The nature of Intelligence and the limits of Strong AI



AI texts generally insist that the subject is concerned with computer models
which operate in a way we would perceive as being intelligent. This has
implications for the Turing test. A simple version of the test involving just
outward behaviour or evidence would not be sufficient for intelligence.
Interestingly, the attacks by Searle (through his ‘Chinese room’) on ‘Strong
AI’ or ‘Computationalism’ have a similar flavour. It has been argued that a
connectionist approach provides an escape from the problem.

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(c) Gödel’s theorems and their implications for
AI. The theorems serve to identify a difference
between truth and provability, in which case
machine intelligence inevitably has limitations. It
has been argued that a system which can learn,
for example a Neural Network, can escape from
the implications of the Gödel theorems. However,
because the difficulties arise specifically with
self
-
referential statements in formal systems this
is unlikely to be true.

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DISCUSSION



Our networks are detailed numeric models, which although based
on some sophisticated methods are still quite simple and
unintelligent


They find optimal weight values through blind search


They learn through weight adjustment


They are statistical devices they also don’t embody intelligence


They can be analysed using the standard tools of applied
mathematics


They are too detailed and too primitive to be regarded as models of
intelligence as such ( as opposed to the underlying processes
which produce intelligence)


However, we can build specialised networks to model for example
consciousness

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The Self



A Self is not necessary for intelligence, but it is for ‘higher’ levels of
intelligence


E.g. My cat is intelligent, an ant colony displays aspects of intelligence>
neither has a self


The self is the driver of the brain, but where and what is it?


If we physically reverse engineer a brain, in such a way that the copy
functions exactly as the original, where is the self?


This is in fact a connectionist approach


What happens with the self and NN’s?


Our types of network are basic low level number processors, which can in
fact be given higher level interpretations


Can in fact simulate consciousness ( the self) in more specialised networks


This is not ‘real’ but simulated consciousness. There can be a model of the
self and consciousness of the self.


Can we simulate a person who controls his/her self?

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Searle Argument: Chinese Room



Anti
-
computation view:


passing Turing test does not necessarily imply intelligence ( test
based on the end result not the process)


Chinese language translation is just a mechanical linking of symbols,
with syntactic rules. Maybe like an electronic dictionary. What about
a human interpreter: does he/she operate mechanically?


Symbols have no internal meaning, so AI is not attainable. (There is
no self, to achieve understanding).


But, we can simulate some of the process of human reasoning, eg.
using Prolog.


Partial simulation/ emulation of intelligence is attainable, even if the
mind is not simply a digital computer


But we must pass the Turing test in a way regarded as being
intelligent.

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NNs, Connectionism and Searle?



As above, our own networks are just mechanical
devices, without intelligence


Connectionist answer to Searle? Intelligence as
manifested in the brain consists of symbol
manipulation plus lower level ( sub symbolic)
processes). Therefore AI is possible.


But, refer back to point above about perfect
physical replica of the brain. Where in this
perfect replica is intelligence and the self?

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GOEDEL theorems



These show distinction between truth +
provability


Hence incompleteness of any system of axioms


Only arises with self referential statements: ‘This
sentence is unprovable’


Show limitations of computationalist approach,
but don’t destroy it. Can still simulate/emulate
human thought processes to some degree

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This is because it shows limitations of human
intelligence


Maths and reasoning are about derivation from
initial axioms, therefore the truth of those axioms
is unprovable. In this sense the Goedel
theorems don’t do much damage.


Theoretically possible to have computational
intelligence which has proofs but also
axioms/beliefs.


Also, Goedel theorems deal with ‘perfect’
reasoning: human reasoning may be imperfect
and this may be simulated.

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Importance for NNs?


Can’t argue that learning allows an escape: but
learning of non self
-
referential statements is OK


What happens with NN’s and self learning?


Can simulate consciousness in the network, by
having specialist nodes


but isn’t this still limited by Goedel?


Goedel theorems help with AI; they show that all
reasoning is subject to limitations and axioms
need to be ‘imported’.