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353 hunch net-2009-05-08-Computability in Artificial Intelligence


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Introduction: Normally I do not blog, but John kindly invited me to do so. Since computability issues play a major role in Artificial Intelligence and Machine Learning, I would like to take the opportunity to comment on that and raise some questions. The general attitude is that AI is about finding efficient smart algorithms. For large parts of machine learning, the same attitude is not too dangerous. If you want to concentrate on conceptual problems, simply become a statistician. There is no analogous escape for modern research on AI (as opposed to GOFAI rooted in logic). Let me show by analogy why limiting research to computational questions is bad for any field. Except in computer science, computational aspects play little role in the development of fundamental theories: Consider e.g. set theory with axiom of choice, foundations of logic, exact/full minimax for zero-sum games, quantum (field) theory, string theory, … Indeed, at least in physics, every new fundamental theory seems to


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sentIndex sentText sentNum sentScore

1 Since computability issues play a major role in Artificial Intelligence and Machine Learning, I would like to take the opportunity to comment on that and raise some questions. [sent-2, score-0.431]

2 The general attitude is that AI is about finding efficient smart algorithms. [sent-3, score-0.476]

3 For large parts of machine learning, the same attitude is not too dangerous. [sent-4, score-0.186]

4 If you want to concentrate on conceptual problems, simply become a statistician. [sent-5, score-0.166]

5 Except in computer science, computational aspects play little role in the development of fundamental theories: Consider e. [sent-8, score-0.585]

6 set theory with axiom of choice, foundations of logic, exact/full minimax for zero-sum games, quantum (field) theory, string theory, … Indeed, at least in physics, every new fundamental theory seems to be less computable than previous ones. [sent-10, score-0.438]

7 Of course, once a subject has been formalized, further research (a) analyzes the structure of the theory and (b) tries to compute efficient approximations. [sent-11, score-0.262]

8 Only in (b) do computational aspects play a role. [sent-12, score-0.395]

9 Here are some unconvincing arguments I’ve heard: A) Because AI is a subfield of computer science , and the task of computer scientists is to find (efficient) algorithms for well-defined problems? [sent-14, score-0.411]

10 I think it does not do any (real-world) problem any good to confine it to computer science. [sent-15, score-0.166]

11 B) Because formalizing AI and finding efficient smart programs goes hand-in-hand? [sent-17, score-0.432]

12 I am not aware of any convincing argument that separating the issues of “axiomatizing a field” and “finding efficient solutions” will (likely) fail for AI. [sent-19, score-0.499]

13 For instance, von Neumann’s minimax solution for games, albeit infeasible for most games, is the cornerstone of most practical approximations. [sent-22, score-0.166]

14 Sure, you could say that intelligence is by definition about computationally efficient decision making. [sent-24, score-0.363]

15 D) Because AI is trivial if computational issues are ignored? [sent-29, score-0.373]

16 All conceptual problems have already been solved? [sent-30, score-0.244]

17 For instance, optimal minimax play of a zero-sum game or solving NP complete problems are conceptually trivial, i. [sent-33, score-0.472]

18 The Turing test is informal (involves a human judge in the loop), maximizing expected reward (the true distribution is not known, so expectation w. [sent-37, score-0.179]

19 Conceptual and computational problems in AI should be studied jointly as well as separately , but the latter is not (yet) fashionable. [sent-44, score-0.238]

20 When AI was more logic oriented, some good logicians helped develop the foundations of “deductive” AI. [sent-45, score-0.213]


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