Jim, > I do believe that projection, first produced from primal or a programmed > methods and then later from learned reactions is obviously a necessary part > of general intelligence.
I think you're talking about instincts, conditioned responses, & analogues. No, they're not part of GI, - there's nothing general about them. > Since they are obviously necessary, I don't see any reason not to amp them up > so long as they do not interfere with the ability of an AGI program to do > some genuine learning from induction-like methods. My point is that you can't put the cart before the horse. Deduction / pattern projection is a feedback, to serve GI it must be directly determined by previously discovered patterns. Well, unless you're doing pure math, but that's not part of our basic learning algorithm. Lot's of intelligent people are totally clueless about math. > It will take me some time to figure out what you are saying in the rest of > the message. Strange, I thought it was crystal-clear :). Boris, It is going to take some time for me to understand what you wrote. But I do have a quick reaction to something easy to understand. You said: This reflects on our basic disagreement, - you (& most logicians, mathematicians, & programmers) start from deduction / pattern projection, which is based on direct operations. And I think real GI must start from induction / pattern discovery, which is intrinsically an inverse operation. It's pretty dumb to generate / project patterns at random, vs. first discovering them in the real world & projecting accordingly. Well, no and yes. No I don't disagree that GI must start from induction and pattern discovery, but I do believe that projection, first produced from primal or a programmed methods and then later from learned reactions is obviously a necessary part of general intelligence. Since they are obviously necessary, I don't see any reason not to amp them up so long as they do not interfere with the ability of an AGI program to do some genuine learning from induction-like methods. It will take me some time to figure out what you are saying in the rest of the message. Jim. On Wed, Aug 8, 2012 at 10:21 AM, Boris Kazachenko <bori...@verizon.net> wrote: Jim, I agree with your focus on binary computational compression, but, as you said, that efficiency depends on specific operands. Even though low-power operations (addition) are more efficient for most data, it's the exceptions that matter. Most data is noise, what we care about is patterns. So, to improve both representational & computational compression, we need to quantify it for each operand ) operation. And the atomic operation that quantifies compression is what I call comparison, which starts with an inverse, vs. direct arithmetic operation. This reflects on our basic disagreement, - you (& most logicians, mathematicians, & programmers) start from deduction / pattern projection, which is based on direct operations. And I think real GI must start from induction / pattern discovery, which is intrinsically an inverse operation. It's pretty dumb to generate / project patterns at random, vs. first discovering them in the real world & projecting accordingly. This is how I proposed to quantify compression (pattern strength) in my intro, part 2: "AIT quantifies compression for sequences of inputs, while I define match for comparisons among individual inputs. On this level, a match is a lossless compression by replacing a larger comparand with its derivative (miss), relative to the smaller comparand. In other words, a match a complementary of a miss. That’s a deeper level of analysis, which I think can enable a far more incremental (thus potentially scalable) approach. Given incremental complexity of representation, initial inputs should have binary resolution. However, average binary match won’t justify the cost of comparison, which adds a syntactic overhead of newly differentiated match & miss to positionally distinct inputs. Rather, these binary inputs are compressed by digitization: a selective carry, aggregated & then forwarded up the hierarchy of digits. This is analogous to hierarchical search, explained in the next chapter, where selected templates are compared & conditionally forwarded up the hierarchy of expansion levels: a “digital hierarchy” of a corresponding coordinate. Digitization is done on inputs within a shared coordinate, the resolution of which is adjusted by feedback. This resolution must form average integers that are large enough for an average match between them (a subset of their magnitude) to merit the above-mentioned costs of comparison. Hence, the next order of compression is comparison across coordinates (initially defined with binary resolution as before | after input). Any comparison is an inverse arithmetic operation of incremental power: Boolean AND, subtraction, division, logarithm, & so on. Binary match is a sum of AND: partial identity of uncompressed bit strings, & miss is !AND. Binary comparison is useful for digitization, but it won’t further compress the integers produced thereby. In general, the products of a given-power comparison are further compressed only by a higher-power comparison between them, where match is the *additive* compression. Thus, initial comparison between digitized integers is done by subtraction, which increases match by compressing miss from !AND to difference, in which opposite-sign bits cancel each other via carry | borrow. The match is increased because it is a complimentary of difference, equal to the smaller of the comparands. All-to-all comparison across 1D queue of pixels forms signed derivatives, complemented by which new inputs can losslessly & compressively replace older templates. At the same time, current input match determines whether individual derivatives are also compared (vs. aggregated), forming successively higher derivatives. “Atomic” comparison is between a single-variable input & a template (older input): Comparison: match= min (input, template), miss= dif (i-t): aggregated over the span of constant sign. Evaluation: match - average_match_per_average_difference_match, formed on the next search level. This evaluation is for comparing higher derivatives, vs. evaluation for higher-level inputs explained in part 3. It can also be increasingly complex, but I will need a meaningful feedback to elaborate. Division further reduces difference to a ratio, which can then be reduced to a logarithm, & so on. Thus, complimentary match is increased with the power of comparison. But the costs may grow even faster, for both operations & incremental syntax to record incidental sign, fraction, irrational fraction. The power of comparison is increased if current match plus miss predict an improvement, as indicated by higher-order comparison between the results from different powers of comparison. This meta-comparison can discover algorithms, or meta-patterns..." http://www.cognitivealgorithm.info/2012/01/cognitive-algorithm.html From: Jim Bromer Sent: Wednesday, August 08, 2012 9:08 AM To: AGI Subject: [agi] Re: Addition is the Engine of Computation Rereading my original message I realized that what I said may not have been very easy to read. It is, however, interesting and serious programmers should be aware of it. An algorithm can be (and usually is) like a procedural compression method. (I have sometimes called it a transformational compression method.) That is not to say that algorithms typically compress data, but that they are extremely efficient. For instance, multiplication is defined as the repeated addition of a particular number. However, the standard multiplier algorithm is much more efficient than doing the repeated additions because it is, what I am calling, a procedural compression method. Furthermore, both addition and multiplication can use binary numbers which, as I explained, are extremely efficient compressions of the representations of values. It is difficult to compare the complexity (that is the efficiency) of these compressed procedural methods, so one way to do so is to expand the algorithm into a true formula of Boolean Logic where only AND, OR, Negation and parentheses are used with atomic Boolean variables. If you can find the shortest Boolean Formula then we can say (if we agree to do so) that this is a measure of the complexity of the algorithm. Most programmers (including myself) do not know how you go about it and the problem of efficiently finding the most efficient Boolean Formula may be a problem that has probably not yet been solved. However, we can expand some algorithms into Boolean formulas and at least get an intuitive sense of just how efficient these algorithms are. What I said in this thread is that I was surprised to find that the real engine of efficiency in arithmetic procedures is found in additions of multiple addends. Multiplication is more efficient than repeated addition for one class of multiple addends, but even there it is my opinion that the real power of multiplication comes from the addition of the multiple partial products. Most examples of compressed data cannot be used without decompressing the data. The benefits of addition and multiplication is that it is not necessary to 'decompress' the binary representations of values in order to use them in arithmetic operations. So addition and multiplication (and of the computational-numerical methods which are derived from addition) are not only procedural compressions but they also use data in it's compressed form without first decompressing it! This is an amazing power, and I believe that it is exactly where the power of computation comes from. What does this have to do with you? It is my opinion, based on this analysis, that if you can -effectively- use multiple addend addition in your programs you would be well advised to consider doing so. The problem with many supposed numerical 'solutions' to AGI is that no one has been able to find an effective method to use numbers to represent or model the problem space of AGI. Jim Bromer AGI | Archives | Modify Your Subscription AGI | Archives | Modify Your Subscription AGI | Archives | Modify Your Subscription ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
