On 8/15/06, Matt Mahoney <[EMAIL PROTECTED]> wrote:



I realize it is tempting to use lossy text compression as a test for AI
because that is what the human brain does when we read text and recall it in
paraphrased fashion.  We remember the ideas and discard details about the
expression of those ideas.  A lossy text compressor that did the same thing
would certainly demonstrate AI.

But there are two problems with using lossy compression as a test of AI:
1. The test is subjective.
2. Lossy compression does not imply AI.

Lets assume we solve the subjectivity problem by having human judges
evaluate whether the decompressed output is "close enough" to the input.  We
already do this with lossy image, audio and video compression (without much
consensus).

The second problem remains: ideal lossy compression does not imply passing
the Turing test.  For lossless compression, it can be proven that it does.
Let p(s) be the (unknown) probability that s will be the prefix of a text
dialog.  Then a machine that can compute p(s) exactly is able to generate
response A to question Q with the distribution p(QA)/p(Q) which is
indistinguishable from human.  The same model minimizes the compressed size,
E[log 1/p(s)].

This proof is really not useful.  The Turing test is subjective; all
you are saying is that lossy compression is lossy, and lossless
compression is not.  A solution to the first problem would also solve
the second problem.

It is necessary to allow lossy compression in order for this
compression test to be useful for AI, because lossless and
uncomprehending compression is already bumping up against the
theoretical limits for text compression.

- Phil

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