In the context of AIXI, intelligence is measured by an accumulated reward signal, and compression is defined by the size of a program (with respect to some fixed universal Turing machine) guessed by the agent that is consistent with the observed interaction with the environment. I don't believe it is true that better compression implies higher intelligence (by these definitions) for every possible agent, environment, universal Turing machine and pair of guessed programs. I also don't believe Hutter's paper proved it to be a general trend (by some reasonable measure). But I wouldn't doubt it. -- Matt Mahoney, [EMAIL PROTECTED]
----- Original Message ---- From: Mark Waser <[EMAIL PROTECTED]> To: agi@v2.listbox.com Sent: Thursday, November 16, 2006 12:18:46 PM Subject: Re: [agi] A question on the symbol-system hypothesis 1. The fact that AIXI is intractable is not relevant to the proof that compression = intelligence, any more than the fact that AIXI is not computable. In fact it is supporting because it says that both are hard problems, in agreement with observation. Wrong. Compression may (and, I might even be willing to admit, does) equal intelligence under the conditions of perfect and total knowledge. It is my contention, however, that without those conditions that compression does not equal intelligence and AIXI does absolutely nothing to disprove my contention since it assumes (and requires) those conditions -- which emphatically do not exist. 2. Do not confuse the two compressions. AIXI proves that the optimal behavior of a goal seeking agent is to guess the shortest program consistent with its interaction with the environment so far. This is lossless compression. A typical implementation is to perform some pattern recognition on the inputs to identify features that are useful for prediction. We sometimes call this "lossy compression" because we are discarding irrelevant data. If we anthropomorphise the agent, then we say that we are replacing the input with perceptually indistinguishable data, which is what we typically do when we compress video or sound. I haven't confused anything. Under perfect conditions, and only under perfect conditions, does AIXI prove anything. You don't have perfect conditions so AIXI proves absolutely nothing. ----- Original Message ----- From: "Matt Mahoney" <[EMAIL PROTECTED]> To: <agi@v2.listbox.com> Sent: Wednesday, November 15, 2006 7:20 PM Subject: Re: [agi] A question on the symbol-system hypothesis 1. The fact that AIXI^tl is intractable is not relevant to the proof that compression = intelligence, any more than the fact that AIXI is not computable. In fact it is supporting because it says that both are hard problems, in agreement with observation. 2. Do not confuse the two compressions. AIXI proves that the optimal behavior of a goal seeking agent is to guess the shortest program consistent with its interaction with the environment so far. This is lossless compression. A typical implementation is to perform some pattern recognition on the inputs to identify features that are useful for prediction. We sometimes call this "lossy compression" because we are discarding irrelevant data. If we anthropomorphise the agent, then we say that we are replacing the input with perceptually indistinguishable data, which is what we typically do when we compress video or sound. -- Matt Mahoney, [EMAIL PROTECTED] ----- Original Message ---- From: Mark Waser <[EMAIL PROTECTED]> To: agi@v2.listbox.com Sent: Wednesday, November 15, 2006 3:48:37 PM Subject: Re: [agi] A question on the symbol-system hypothesis >> The connection between intelligence and compression is not obvious. The connection between intelligence and compression *is* obvious -- but compression, particularly lossless compression, is clearly *NOT* intelligence. Intelligence compresses knowledge to ever simpler rules because that is an effective way of dealing with the world. Discarding ineffective/unnecessary knowledge to make way for more effective/necessary knowledge is an effective way of dealing with the world. Blindly maintaining *all* knowledge at tremendous costs is *not* an effective way of dealing with the world (i.e. it is *not* intelligent). >>1. What Hutter proved is that the optimal behavior of an agent is to guess >>that the environment is controlled by the shortest program that is >>consistent with all of the interaction observed so far. The problem of >>finding this program known as AIXI. >> 2. The general problem is not computable [11], although Hutter proved >> that if we assume time bounds t and space bounds l on the environment, >> then this restricted problem, known as AIXItl, can be solved in O(t2l) >> time Very nice -- except that O(t2l) time is basically equivalent to incomputable for any real scenario. Hutter's proof is useless because it relies upon the assumption that you have adequate resources (i.e. time) to calculate AIXI -- which you *clearly* do not. And like any other proof, once you invalidate the assumptions, the proof becomes equally invalid. Except as an interesting but unobtainable edge case, why do you believe that Hutter has any relevance at all? ----- Original Message ----- From: "Matt Mahoney" <[EMAIL PROTECTED]> To: <agi@v2.listbox.com> Sent: Wednesday, November 15, 2006 2:54 PM Subject: Re: [agi] A question on the symbol-system hypothesis Richard, what is your definition of "understanding"? How would you test whether a person understands art? Turing offered a behavioral test for intelligence. My understanding of "understanding" is that it is something that requires intelligence. The connection between intelligence and compression is not obvious. I have summarized the arguments here. http://cs.fit.edu/~mmahoney/compression/rationale.html -- Matt Mahoney, [EMAIL PROTECTED] ----- Original Message ---- From: Richard Loosemore <[EMAIL PROTECTED]> To: agi@v2.listbox.com Sent: Wednesday, November 15, 2006 2:38:49 PM Subject: Re: [agi] A question on the symbol-system hypothesis Matt Mahoney wrote: > Richard Loosemore <[EMAIL PROTECTED]> wrote: >> "Understanding" 10^9 bits of information is not the same as storing 10^9 >> bits of information. > > That is true. "Understanding" n bits is the same as compressing some > larger training set that has an algorithmic complexity of n bits. Once > you have done this, you can use your probability model to make predictions > about unseen data generated by the same (unknown) Turing machine as the > training data. The closer to n you can compress, the better your > predictions will be. > > I am not sure what it means to "understand" a painting, but let's say that > you understand art if you can identify the artists of paintings you > haven't seen before with better accuracy than random guessing. The > relevant quantity of information is not the number of pixels and > resolution, which depend on the limits of the eye, but the (much smaller) > number of features that the high level perceptual centers of the brain are > capable of distinguishing and storing in memory. (Experiments by Standing > and Landauer suggest it is a few bits per second for long term memory, the > same rate as language). Then you guess the shortest program that > generates a list of feature-artist pairs consistent with your knowledge of > art and use it to predict artists given new features. > > My estimate of 10^9 bits for a language model is based on 4 lines of > evidence, one of which is the amount of language you process in a > lifetime. This is a rough estimate of course. I estimate 1 GB (8 x 10^9 > bits) compressed to 1 bpc (Shannon) and assume you remember a significant > fraction of that. Matt, So long as you keep redefining "understand" to mean whatever something trivial (or at least, something different in different circumstances), all you do is reinforce the point I was trying to make. In your definition of "understanding" in the context of art, above, you specifically choose an interpretation that enables you to pick a particular bit rate. But if I chose a different interpretation (and I certainly would - an art historian would never say they understood a painting just because they could tell the artist's style better than a random guess!), I might come up with a different bit rate. And if I chose a sufficiently subtle concept of "understand", I would be unable to come up with *any* bit rate, because that concept of "understand" would not lend itself to any easy bit rate analysis. The lesson? Talking about bits and bit rates is completely pointless .... which was my point. You mainly identify the meaning of "understand" as a variant of the meaning of "compress". I completely reject this - this is the most idiotic development in AI research since the early attempts to do natural language translation using word-by-word lookup tables - and I challenge you to say why anyone could justify reducing the term in such an extreme way. Why have you thrown out the real meaning of "understand" and substituted another meaning? What have we gained by dumbing the concept down? As I said in previously, this is as crazy as redefining the complex concept of "happiness" to be "a warm puppy". Richard Loosemore > Landauer, Tom (1986), “How much do people > remember? Some estimates of the quantity > of learned information in long term memory”, Cognitive Science (10) pp. > 477-493 > > Shannon, Cluade E. (1950), “Prediction and > Entropy of Printed English”, Bell Sys. Tech. J (3) p. 50-64. > > Standing, L. (1973), “Learning 10,000 Pictures”, > Quarterly Journal of Experimental Psychology (25) pp. 207-222. > > > > -- Matt Mahoney, [EMAIL PROTECTED] > > ----- Original Message ---- > From: Richard Loosemore <[EMAIL PROTECTED]> > To: agi@v2.listbox.com > Sent: Wednesday, November 15, 2006 9:33:04 AM > Subject: Re: [agi] A question on the symbol-system hypothesis > > Matt Mahoney wrote: >> I will try to answer several posts here. I said that the knowledge >> base of an AGI must be opaque because it has 10^9 bits of information, >> which is more than a person can comprehend. By opaque, I mean that you >> can't do any better by examining or modifying the internal >> representation than you could by examining or modifying the training >> data. For a text based AI with natural language ability, the 10^9 bits >> of training data would be about a gigabyte of text, about 1000 books. Of >> course you can sample it, add to it, edit it, search it, run various >> tests on it, and so on. What you can't do is read, write, or know all of >> it. There is no internal representation that you could convert it to >> that would allow you to do these things, because you still have 10^9 >> bits of information. It is a limitation of the human brain that it can't >> store more information than this. > > "Understanding" 10^9 bits of information is not the same as storing 10^9 > bits of information. > > A typical painting in the Louvre might be 1 meter on a side. At roughly > 16 pixels per millimeter, and a perceivable color depth of about 20 bits > that would be about 10^8 bits. If an art specialist knew all about, > say, 1000 paintings in the Louvre, that specialist would "understand" a > total of about 10^11 bits. > > You might be inclined to say that not all of those bits count, that many > are redundant to "understanding". > > Exactly. > > People can easily comprehend 10^9 bits. It makes no sense to argue > about degree of comprehension by quoting numbers of bits. > > > Richard Loosemore > > ----- > This list is sponsored by AGIRI: http://www.agiri.org/email > To unsubscribe or change your options, please go to: > http://v2.listbox.com/member/?list_id=303 > > > > ----- > This list is sponsored by AGIRI: http://www.agiri.org/email > To unsubscribe or change your options, please go to: > http://v2.listbox.com/member/?list_id=303 > > ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303 ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303 ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303 ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303 This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303 ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
