Complexity, universal predictors, wrong answers, and psychotic episodes

From: James Rogers (
Date: Fri May 17 2002 - 13:34:23 MDT

On Thu, 2002-05-16 at 21:20, Ben Goertzel wrote:
> Yes, but the catch is that for a complex problem, the "best approximation"
> may be a very bad one ;>

This is very literally true in a number of ways, though increasing
improbable as the size of the UP model increases in the most critical
sense. This leads me to an interesting thought worth bringing up.

Universal predictors of all types do not have a perfectly nice linear
relationship between their available resources, the complexity of the
problem, and the accuracy of their conclusions. "Non-optimal" UPs have
this same characteristic and cover a huge swath of design and
architecture for intelligent systems, encompassing just about everything
that would fall under the umbrella of AGI. The value of a "non-optimal"
UPs in the real world is that under certain complexity constraints they
can give better results, but the accuracy of their results do not
converge as fast in the general case (i.e. when the complexity exceeds a
certain trivial level).

Of specific interest, for every UP ("optimal" or not) it is possible to
construct a pattern (usually way out on the edge of the complexity limit
for a given predictor) that will break the universal predictor in such a
way that it makes conclusions/predictions WORSE than what you would
expect to get by random chance. In a sense, there is a very narrow
boundary condition under which the predictor will behave in an
"irrational" manner. The larger the predictor, the more improbable it is
that you will find a pattern that can break the predictor by chance, but
such patterns exist nonetheless. (Hey, this reminds me of GEB when they
discuss Godel's Incompleteness Theorem.)

Implication: Any Friendliness theory for AGI that requires perfect
rationality cannot be guaranteed to stay Friendly. Ironically, the best
prophylactic for this (other than not doing it at all) would be to make
the AI as big as possible to make the probability of a "psychotic
episode" vanishingly small.

An opinion on this from a "Friendliness" expert (Eliezer?) would be

I just thought of this today so I haven't really thought it through, but
I don't see anything obviously wrong with my conclusion either. It would
seem that some level of irrationality is intrinsic to any workable model
for AGI (e.g. neural networks, AIC, etc). It probably wouldn't manifest
itself as it does in humans, but an analog is certainly possible in any
such system.

> Sure, but inadequate memory on a single machine can be turned into adequate
> memory on a distributed system, at the cost of accepting a significant
> slowdown!

This is quite correct, and getting more correct every day. As someone
who works at a company delivering obscene bandwidth to the masses, I
should know this as well as anyone. Throw in 64-bit OS and boxen, and
you can effectively have very large usable memories on the cheap.

One thing that I want to try doing is turning a solid-state disk array
(not cheap by any means, but a lot cheaper than buying a box that can
support and address, say, 128-Gb of RAM directly) and turning it into a
giant swap partition on a 64-bit box. The idea being that this is a back
door way to get really large blocks of addressable RAM without buying a
mainframe, while being a few orders of magnitude faster than a hard


-James Rogers

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