1 Neural Networks and Statistics: Intelligence and the Self Prof Bruce Curry and Dr Peter Morgan Cardiff Business School, UK

2 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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4 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.

5 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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7 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

8 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

9 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!!

10 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.

11 (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.

12 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

13 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?

14 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.

15 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?

16 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

17 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.

18 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’.