Gödel machines overcome certain limitations of
and of non- self- referential
Universal learning algorithms
and the asymptotically "fastest" algorithm
for all problems
and of our previous
Disclaimer: Gödel machines can be implemented on
traditional computers! No
hypothetical super- Turing capabilities and the like.
Is the GM conscious?
Is consciousness the ability to execute unlimited
self- inspection and provably useful self-change
(modulo limits of computability and
provability)? Then the Goedel machine's
Global Optimality Theorem provides
the first technical justification
of consciousness in the context of general problem solving.
We present the first class of mathematically rigorous, general, fully
self-referential, self-improving, optimally efficient problem solvers.
Inspired by Kurt Gödel's celebrated self-referential formulas (1931),
a Gödel machine (or `Goedel machine' but not `Godel machine')
rewrites any part of its own code as soon
as it has found a proof that the rewrite is useful, where the
problem-dependent utility function and the hardware and the entire
initial code are described by axioms encoded in an initial proof
searcher which is also part of the initial code. The searcher
systematically and efficiently tests
computable proof techniques (programs whose outputs are proofs)
until it finds a provably useful, computable self-rewrite. We show
that such a self-rewrite is
globally optimal - no local maxima!
- since the code first had to prove that it is not useful to continue the
proof search for alternative self-rewrites. Unlike previous
non-self-referential methods based on hardwired proof searchers, ours
not only boasts an optimal order of complexity but can optimally
reduce any slowdowns hidden by the O()-notation, provided the utility
of such speed-ups is provable at all. (FAQ)
Gödel machine papers:
B. R. Steunebrink, J. Schmidhuber. Towards an Actual Gödel Machine Implementation. In P. Wang, B. Goertzel, eds.,
Theoretical Foundations of Artificial General Intelligence.
B. Steunebrink, J. Schmidhuber.
A Family of Gödel Machine Implementations.
In Proc. Fourth Conference on Artificial General Intelligence (AGI-11),
Google, Mountain View, California, 2011.
Ultimate Cognition à la Gödel.
Cognitive Computation 1(2):177-193, 2009. PDF.
Completely Self-Referential Optimal Reinforcement Learners.
In W. Duch et al. (Eds.):
Proc. Intl. Conf. on Artificial Neural Networks ICANN'05,
LNCS 3697, pp. 223-233, Springer-Verlag Berlin Heidelberg, 2005
Fully Self-Referential Optimal Universal Self-Improvers.
In B. Goertzel and C. Pennachin, eds.: Artificial
General Intelligence, p. 119-226, 2006.
4. J. Schmidhuber.
A Technical Justification of Consciousness.
9th annual meeting of the Association for the
Scientific Study of Consciousness ASSC,
Caltech, Pasadena, CA, 2005.
3. J. Schmidhuber. Goedel machines:
Towards a Technical Justification of Consciousness.
In D. Kudenko, D. Kazakov, and E. Alonso, eds.:
Adaptive Agents and Multi-Agent Systems III
LNCS 3394, p. 1-23, Springer, 2005.
Section on Goedel machines on page 235 of: J. Schmidhuber,
Machine Learning, 54, 211-254, 2004.
(The editors also offered to publish the entire original Goedel machine
paper instead of the OOPS paper, but
the latter came first chronologically).
(2003, revised Dec 2006)
Invited talks on Gödel machine and general
reinforcement learners and New AI:
15 Jan 2011: Winter Intelligence Conference, Oxford
(on universal AI and theory of fun). See
3 Oct 2009: Singularity Summit, New York City.
6 Mar 2009: Keynote for Artificial General
27 July 2006: Artificial Life, Jena
27 May 2006: Turing Days, Istanbul
31 Jan 2006: Dagstuhl Castle: Kolmogorov complexity
Sept 11-15 2005: Plenary talk at ICANN'05, Warsaw, Poland
Dec 9 2004: Keynote talk at Neuro-IT'04, Munich, Germany
Nov 9 2004: Plenary talk at ANNIE'04, St. Louis, US
Jun 4 2004: ETH Zuerich, Switzerland
Apr 1 2004: Univ. Birmingham, UK
Mar 30 2004: Keynote talk at 4th Symposium on
Adaptive Agents and Multi-Agent Systems, Univ. Leeds, UK
Feb 19 2004: Univ. Newcastle upon Tyne, UK
Jan 30 2004: Univ. Amsterdam, NL
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