Re: AW: AW: [agi] Language learning (was Re: Defining AGI)
On Thu, Oct 23, 2008 at 12:55 AM, Matt Mahoney wrote: I suppose you are right. Instead of encoding mathematical rules as a grammar, with enough training data you can just code all possible instances that are likely to be encountered. For example, instead of a grammar rule to encode the commutative law of addition, 5 + 3 = a + b = b + a = 3 + 5 a model with a much larger training data set could just encode instances with no generalization: 12 + 7 = 7 + 12 92 + 0.5 = 0.5 + 92 etc. I believe this is how Google gets away with brute force n-gram statistics instead of more sophisticated grammars. It's language model is probably 10^5 times larger than a human model (10^14 bits vs 10^9 bits). Shannon observed in 1949 that random strings generated by n-gram models of English (where n is the number of either letters or words) look like natural language up to length 2n. For a typical human sized model (1 GB text), n is about 3 words. To model strings longer than 6 words we would need more sophisticated grammar rules. Google can model 5-grams (see http://googleresearch.blogspot.com/2006/08/all-our-n-gram-are-belong-to-you.html ), so it is able to generate and recognize (thus appear to understand) sentences up to about 10 words. Gigantic databases are indeed Google's secret sauce. See: http://googleresearch.blogspot.com/2008/09/doubling-up.html Quote: Monday, September 29, 2008 Posted by Franz Josef Och Machine translation is hard. Natural languages are so complex and have so many ambiguities and exceptions that teaching a computer to translate between them turned out to be a much harder problem than people thought when the field of machine translation was born over 50 years ago. At Google Research, our approach is to have the machines learn to translate by using learning algorithms on gigantic amounts of monolingual and translated data. Another knowledge source is user suggestions. This approach allows us to constantly improve the quality of machine translations as we mine more data and get more and more feedback from users. A nice property of the learning algorithms that we use is that they are largely language independent -- we use the same set of core algorithms for all languages. So this means if we find a lot of translated data for a new language, we can just run our algorithms and build a new translation system for that language. As a result, we were recently able to significantly increase the number of languages on translate.google.com. Last week, we launched eleven new languages: Catalan, Filipino, Hebrew, Indonesian, Latvian, Lithuanian, Serbian, Slovak, Slovenian, Ukrainian, Vietnamese. This increases the total number of languages from 23 to 34. Since we offer translation between any of those languages this increases the number of language pairs from 506 to 1122 (well, depending on how you count simplified and traditional Chinese you might get even larger numbers). - BillK --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Language learning (was Re: Defining AGI)
I have already proved something stronger What would you consider your best reference/paper outlining your arguments? Thanks in advance. - Original Message - From: Matt Mahoney [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Wednesday, October 22, 2008 8:55 PM Subject: Re: AW: AW: [agi] Language learning (was Re: Defining AGI) --- On Wed, 10/22/08, Dr. Matthias Heger [EMAIL PROTECTED] wrote: You make the implicit assumption that a natural language understanding system will pass the turing test. Can you prove this? If you accept that a language model is a probability distribution over text, then I have already proved something stronger. A language model exactly duplicates the distribution of answers that a human would give. The output is indistinguishable by any test. In fact a judge would have some uncertainty about other people's language models. A judge could be expected to attribute some errors in the model to normal human variation. Furthermore, it is just an assumption that the ability to have and to apply the rules are really necessary to pass the turing test. For these two reasons, you still haven't shown 3a and 3b. I suppose you are right. Instead of encoding mathematical rules as a grammar, with enough training data you can just code all possible instances that are likely to be encountered. For example, instead of a grammar rule to encode the commutative law of addition, 5 + 3 = a + b = b + a = 3 + 5 a model with a much larger training data set could just encode instances with no generalization: 12 + 7 = 7 + 12 92 + 0.5 = 0.5 + 92 etc. I believe this is how Google gets away with brute force n-gram statistics instead of more sophisticated grammars. It's language model is probably 10^5 times larger than a human model (10^14 bits vs 10^9 bits). Shannon observed in 1949 that random strings generated by n-gram models of English (where n is the number of either letters or words) look like natural language up to length 2n. For a typical human sized model (1 GB text), n is about 3 words. To model strings longer than 6 words we would need more sophisticated grammar rules. Google can model 5-grams (see http://googleresearch.blogspot.com/2006/08/all-our-n-gram-are-belong-to-you.html ) , so it is able to generate and recognize (thus appear to understand) sentences up to about 10 words. By the way: The turing test must convince 30% of the people. Today there is a system which can already convince 25% http://www.sciencedaily.com/releases/2008/10/081013112148.htm It would be interesting to see a version of the Turing test where the human confederate, machine, and judge all have access to a computer with an internet connection. I wonder if this intelligence augmentation would make the test easier or harder to pass? -Matthias 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules It must have the rules and apply them to pass the Turing test. -- Matt Mahoney, [EMAIL PROTECTED] -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?; Powered by Listbox: http://www.listbox.com --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: [agi] Language learning (was Re: Defining AGI)
--- On Tue, 10/21/08, Dr. Matthias Heger [EMAIL PROTECTED] wrote: Sorry, but this was no proof that a natural language understanding system is necessarily able to solve the equation x*3 = y for arbitrary y. 1) You have not shown that a language understanding system must necessarily(!) have made statistical experiences on the equation x*3 =y. A language model is a probability distribution P over text of human origin. If you can compute P(x) for given text string x, then you can pass the Turing test because for any question Q and answer A you can compute P(A|Q) = P(QA)/P(Q) using the same distribution that a human would use to answer the question. This includes any math questions that the average human could answer. 2) you give only a few examples. For a proof of the claim, you have to prove it for every(!) y. You originally allowed *any* y. To quote your earlier email: For instance, I doubt that anyone can prove that any system which understands natural language is necessarily able to solve the simple equation x *3 = y for a given y. Anyway I did the experiment for y = 12. You can try the experiment for other values of y if you wish. Let me know what happens. 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules It must have the rules and apply them to pass the Turing test. -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: AW: [agi] Language learning (was Re: Defining AGI)
You make the implicit assumption that a natural language understanding system will pass the turing test. Can you prove this? Furthermore, it is just an assumption that the ability to have and to apply the rules are really necessary to pass the turing test. For these two reasons, you still haven't shown 3a and 3b. By the way: The turing test must convince 30% of the people. Today there is a system which can already convince 25% http://www.sciencedaily.com/releases/2008/10/081013112148.htm -Matthias 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules It must have the rules and apply them to pass the Turing test. -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Language learning (was Re: Defining AGI)
--- On Wed, 10/22/08, Dr. Matthias Heger [EMAIL PROTECTED] wrote: You make the implicit assumption that a natural language understanding system will pass the turing test. Can you prove this? If you accept that a language model is a probability distribution over text, then I have already proved something stronger. A language model exactly duplicates the distribution of answers that a human would give. The output is indistinguishable by any test. In fact a judge would have some uncertainty about other people's language models. A judge could be expected to attribute some errors in the model to normal human variation. Furthermore, it is just an assumption that the ability to have and to apply the rules are really necessary to pass the turing test. For these two reasons, you still haven't shown 3a and 3b. I suppose you are right. Instead of encoding mathematical rules as a grammar, with enough training data you can just code all possible instances that are likely to be encountered. For example, instead of a grammar rule to encode the commutative law of addition, 5 + 3 = a + b = b + a = 3 + 5 a model with a much larger training data set could just encode instances with no generalization: 12 + 7 = 7 + 12 92 + 0.5 = 0.5 + 92 etc. I believe this is how Google gets away with brute force n-gram statistics instead of more sophisticated grammars. It's language model is probably 10^5 times larger than a human model (10^14 bits vs 10^9 bits). Shannon observed in 1949 that random strings generated by n-gram models of English (where n is the number of either letters or words) look like natural language up to length 2n. For a typical human sized model (1 GB text), n is about 3 words. To model strings longer than 6 words we would need more sophisticated grammar rules. Google can model 5-grams (see http://googleresearch.blogspot.com/2006/08/all-our-n-gram-are-belong-to-you.html ), so it is able to generate and recognize (thus appear to understand) sentences up to about 10 words. By the way: The turing test must convince 30% of the people. Today there is a system which can already convince 25% http://www.sciencedaily.com/releases/2008/10/081013112148.htm It would be interesting to see a version of the Turing test where the human confederate, machine, and judge all have access to a computer with an internet connection. I wonder if this intelligence augmentation would make the test easier or harder to pass? -Matthias 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules It must have the rules and apply them to pass the Turing test. -- Matt Mahoney, [EMAIL PROTECTED] -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: [agi] Language learning (was Re: Defining AGI)
Sorry, but this was no proof that a natural language understanding system is necessarily able to solve the equation x*3 = y for arbitrary y. 1) You have not shown that a language understanding system must necessarily(!) have made statistical experiences on the equation x*3 =y. 2) you give only a few examples. For a proof of the claim, you have to prove it for every(!) y. 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules In my opinion a natural language understanding system must have a lot of linguistic knowledge. Furthermore a system which can learn natural languages must be able to gain linguistic knowledge. But both systems do not have necessarily(!) the ability to *work* with this knowledge as it is essential for AGI. And for this reason natural language understanding is not AGI complete at all. -Matthias -Ursprüngliche Nachricht- Von: Matt Mahoney [mailto:[EMAIL PROTECTED] Gesendet: Dienstag, 21. Oktober 2008 05:05 An: agi@v2.listbox.com Betreff: [agi] Language learning (was Re: Defining AGI) --- On Mon, 10/20/08, Dr. Matthias Heger [EMAIL PROTECTED] wrote: For instance, I doubt that anyone can prove that any system which understands natural language is necessarily able to solve the simple equation x *3 = y for a given y. It can be solved with statistics. Take y = 12 and count Google hits: string count -- - 1x3=12 760 2x3=12 2030 3x3=12 9190 4x3=12 16200 5x3=12 1540 6x3=12 1010 More generally, people learn algebra and higher mathematics by induction, by generalizing from lots of examples. 5 * 7 = 35 - 35 / 7 = 5 4 * 6 = 24 - 24 / 6 = 4 etc... a * b = c - c = b / a It is the same way we learn grammatical rules, for example converting active to passive voice and applying it to novel sentences: Bob kissed Alice - Alice was kissed by Bob. I ate dinner - Dinner was eaten by me. etc... SUBJ VERB OBJ - OBJ was VERB by SUBJ. In a similar manner, we can learn to solve problems using logical deduction: All frogs are green. Kermit is a frog. Therefore Kermit is green. All fish live in water. A shark is a fish. Therefore sharks live in water. etc... I understand the objection to learning math and logic in a language model instead of coding the rules directly. It is horribly inefficient. I estimate that a neural language model with 10^9 connections would need up to 10^18 operations to learn simple arithmetic like 2+2=4 well enough to get it right 90% of the time. But I don't know of a better way to learn how to convert natural language word problems to a formal language suitable for entering into a calculator at the level of an average human adult. -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?; Powered by Listbox: http://www.listbox.com --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: [agi] Language learning (was Re: Defining AGI)
There is another point which indicates that the ability to understand language or to learn language does not imply *general* intelligence. You can often observe in school that linguistic talents are poor in mathematics and vice versa. - Matthias --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: [agi] Language learning (was Re: Defining AGI)
This really seems more like arguing that there is no such thing as AI-complete at all. That is certainly a possibility. It could be that there are only different competences. This would also seem to mean that there isn't really anything that is truly general about intelligence, which is again possible. I guess one thing we're seeing here is a basic example of mathematics as having underlying separate mechanisms from other features of language. The Lakoff and Nunez talk about subitizing (judging small numbers of things at a glance) as one core competancy, and counting as another. These are things you can see in animals that do not use language. So, sure, mathematics could be a separate realm of intelligence. Of course, my response to that is that this kind of basic mathematical ability is needed to understand language. Of course, people who favor language use my not exercise their mathematical ability and it can become weak, but I think it generally has to be there for full competance. And there are some more abstract concepts that could be hard for people to get, and maybe some people don't have what it takes to get some concepts, so the don't have infinite potential. andi Matthias wrote: Sorry, but this was no proof that a natural language understanding system is necessarily able to solve the equation x*3 = y for arbitrary y. 1) You have not shown that a language understanding system must necessarily(!) have made statistical experiences on the equation x*3 =y. 2) you give only a few examples. For a proof of the claim, you have to prove it for every(!) y. 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules In my opinion a natural language understanding system must have a lot of linguistic knowledge. Furthermore a system which can learn natural languages must be able to gain linguistic knowledge. But both systems do not have necessarily(!) the ability to *work* with this knowledge as it is essential for AGI. And for this reason natural language understanding is not AGI complete at all. -Matthias -Ursprüngliche Nachricht- Von: Matt Mahoney [mailto:[EMAIL PROTECTED] Gesendet: Dienstag, 21. Oktober 2008 05:05 An: agi@v2.listbox.com Betreff: [agi] Language learning (was Re: Defining AGI) --- On Mon, 10/20/08, Dr. Matthias Heger [EMAIL PROTECTED] wrote: For instance, I doubt that anyone can prove that any system which understands natural language is necessarily able to solve the simple equation x *3 = y for a given y. It can be solved with statistics. Take y = 12 and count Google hits: string count -- - 1x3=12 760 2x3=12 2030 3x3=12 9190 4x3=12 16200 5x3=12 1540 6x3=12 1010 More generally, people learn algebra and higher mathematics by induction, by generalizing from lots of examples. 5 * 7 = 35 - 35 / 7 = 5 4 * 6 = 24 - 24 / 6 = 4 etc... a * b = c - c = b / a It is the same way we learn grammatical rules, for example converting active to passive voice and applying it to novel sentences: Bob kissed Alice - Alice was kissed by Bob. I ate dinner - Dinner was eaten by me. etc... SUBJ VERB OBJ - OBJ was VERB by SUBJ. In a similar manner, we can learn to solve problems using logical deduction: All frogs are green. Kermit is a frog. Therefore Kermit is green. All fish live in water. A shark is a fish. Therefore sharks live in water. etc... I understand the objection to learning math and logic in a language model instead of coding the rules directly. It is horribly inefficient. I estimate that a neural language model with 10^9 connections would need up to 10^18 operations to learn simple arithmetic like 2+2=4 well enough to get it right 90% of the time. But I don't know of a better way to learn how to convert natural language word problems to a formal language suitable for entering into a calculator at the level of an average human adult. -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?; Powered by Listbox: http://www.listbox.com --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?; Powered by Listbox: http://www.listbox.com --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: [agi] Language learning (was Re: Defining AGI)
I agree. But the vaguely-human-mind-like-architecture is a huge additional assumption. If you have a system that can solve problem x and has in addition a human-mind-like-architecture then obviously you obtain AGI for *any* x. The whole AGI-completeness would essentially depend on this additional assumption. A human-mind-like-architecture even would imply the ability to learn natural language understanding - Matthias Ben wrote I wouldn't argue that any software system capable of learning human language, would necessarily be able to learn mathematics However, I strongly suspect that any software system **with a vaguely human-mind-like architecture** that is capable of learning human language, would also be able to learn basic mathematics ben On Tue, Oct 21, 2008 at 2:30 AM, Dr. Matthias Heger [EMAIL PROTECTED] wrote: Sorry, but this was no proof that a natural language understanding system is necessarily able to solve the equation x*3 = y for arbitrary y. 1) You have not shown that a language understanding system must necessarily(!) have made statistical experiences on the equation x*3 =y. 2) you give only a few examples. For a proof of the claim, you have to prove it for every(!) y. 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules In my opinion a natural language understanding system must have a lot of linguistic knowledge. Furthermore a system which can learn natural languages must be able to gain linguistic knowledge. But both systems do not have necessarily(!) the ability to *work* with this knowledge as it is essential for AGI. And for this reason natural language understanding is not AGI complete at all. -Matthias -Ursprüngliche Nachricht- Von: Matt Mahoney [mailto:[EMAIL PROTECTED] Gesendet: Dienstag, 21. Oktober 2008 05:05 An: agi@v2.listbox.com Betreff: [agi] Language learning (was Re: Defining AGI) --- On Mon, 10/20/08, Dr. Matthias Heger [EMAIL PROTECTED] wrote: For instance, I doubt that anyone can prove that any system which understands natural language is necessarily able to solve the simple equation x *3 = y for a given y. It can be solved with statistics. Take y = 12 and count Google hits: string count -- - 1x3=12 760 2x3=12 2030 3x3=12 9190 4x3=12 16200 5x3=12 1540 6x3=12 1010 More generally, people learn algebra and higher mathematics by induction, by generalizing from lots of examples. 5 * 7 = 35 - 35 / 7 = 5 4 * 6 = 24 - 24 / 6 = 4 etc... a * b = c - c = b / a It is the same way we learn grammatical rules, for example converting active to passive voice and applying it to novel sentences: Bob kissed Alice - Alice was kissed by Bob. I ate dinner - Dinner was eaten by me. etc... SUBJ VERB OBJ - OBJ was VERB by SUBJ. In a similar manner, we can learn to solve problems using logical deduction: All frogs are green. Kermit is a frog. Therefore Kermit is green. All fish live in water. A shark is a fish. Therefore sharks live in water. etc... I understand the objection to learning math and logic in a language model instead of coding the rules directly. It is horribly inefficient. I estimate that a neural language model with 10^9 connections would need up to 10^18 operations to learn simple arithmetic like 2+2=4 well enough to get it right 90% of the time. But I don't know of a better way to learn how to convert natural language word problems to a formal language suitable for entering into a calculator at the level of an average human adult. -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/? https://www.listbox.com/member/?; Powered by Listbox: http://www.listbox.com --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/? https://www.listbox.com/member/?; Powered by Listbox: http://www.listbox.com -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] Nothing will ever be attempted if all possible objections must be first overcome - Dr Samuel Johnson _ agi | https://www.listbox.com/member/archive/303/=now Archives https://www.listbox.com/member/archive/rss/303/ | https://www.listbox.com/member/?; 7 Modify Your Subscription http://www.listbox.com --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription:
AW: AW: [agi] Language learning (was Re: Defining AGI)
Andi wrote This really seems more like arguing that there is no such thing as AI-complete at all. That is certainly a possibility. It could be that there are only different competences. This would also seem to mean that there isn't really anything that is truly general about intelligence, which is again possible. No. This arguing shows that there are very basic features which do not imply necessarily from natural language understanding: Usage of knowledge. The example to solve a equation is just one of many examples. If you can talk about things this does not imply that you can do things. I guess one thing we're seeing here is a basic example of mathematics as having underlying separate mechanisms from other features of language. The Lakoff and Nunez talk about subitizing (judging small numbers of things at a glance) as one core competancy, and counting as another. These are things you can see in animals that do not use language. So, sure, mathematics could be a separate realm of intelligence. It is not just mathematics. A natural language understanding system can talk about shopping. But from this ability you can't prove that it can do shopping. There are essential features of intelligence missing in natural language understanding. And that's the reason why natural language understanding is not AGI-complete. Of course, my response to that is that this kind of basic mathematical ability is needed to understand language. This argumentation is nothing else than making a non-AGI-complete system AGI complete by adding more and more features. If you suppose for a arbitrary still unsolved problem P that everything is which is needed to solve AGI is also necessary to solve P then it becomes trivial that P is AGI-complete. But this argumentation is similar to the doubters of AGI who essentially suppose for an arbitrary given still unsolved problem P that P is not computable at all. -Matthias Matthias wrote: Sorry, but this was no proof that a natural language understanding system is necessarily able to solve the equation x*3 = y for arbitrary y. 1) You have not shown that a language understanding system must necessarily(!) have made statistical experiences on the equation x*3 =y. 2) you give only a few examples. For a proof of the claim, you have to prove it for every(!) y. 3) you apply rules such as 5 * 7 = 35 - 35 / 7 = 5 but you have not shown that 3a) that a language understanding system necessarily(!) has this rules 3b) that a language understanding system necessarily(!) can apply such rules In my opinion a natural language understanding system must have a lot of linguistic knowledge. Furthermore a system which can learn natural languages must be able to gain linguistic knowledge. But both systems do not have necessarily(!) the ability to *work* with this knowledge as it is essential for AGI. And for this reason natural language understanding is not AGI complete at all. -Matthias -Ursprüngliche Nachricht- Von: Matt Mahoney [mailto:[EMAIL PROTECTED] Gesendet: Dienstag, 21. Oktober 2008 05:05 An: agi@v2.listbox.com Betreff: [agi] Language learning (was Re: Defining AGI) --- On Mon, 10/20/08, Dr. Matthias Heger [EMAIL PROTECTED] wrote: For instance, I doubt that anyone can prove that any system which understands natural language is necessarily able to solve the simple equation x *3 = y for a given y. It can be solved with statistics. Take y = 12 and count Google hits: string count -- - 1x3=12 760 2x3=12 2030 3x3=12 9190 4x3=12 16200 5x3=12 1540 6x3=12 1010 More generally, people learn algebra and higher mathematics by induction, by generalizing from lots of examples. 5 * 7 = 35 - 35 / 7 = 5 4 * 6 = 24 - 24 / 6 = 4 etc... a * b = c - c = b / a It is the same way we learn grammatical rules, for example converting active to passive voice and applying it to novel sentences: Bob kissed Alice - Alice was kissed by Bob. I ate dinner - Dinner was eaten by me. etc... SUBJ VERB OBJ - OBJ was VERB by SUBJ. In a similar manner, we can learn to solve problems using logical deduction: All frogs are green. Kermit is a frog. Therefore Kermit is green. All fish live in water. A shark is a fish. Therefore sharks live in water. etc... I understand the objection to learning math and logic in a language model instead of coding the rules directly. It is horribly inefficient. I estimate that a neural language model with 10^9 connections would need up to 10^18 operations to learn simple arithmetic like 2+2=4 well enough to get it right 90% of the time. But I don't know of a better way to learn how to convert natural language word problems to a formal language suitable for entering into a calculator at the level of an average human adult. -- Matt Mahoney, [EMAIL PROTECTED] --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed:
