340,503 research outputs found
Ultimate Intelligence Part I: Physical Completeness and Objectivity of Induction
We propose that Solomonoff induction is complete in the physical sense via
several strong physical arguments. We also argue that Solomonoff induction is
fully applicable to quantum mechanics. We show how to choose an objective
reference machine for universal induction by defining a physical message
complexity and physical message probability, and argue that this choice
dissolves some well-known objections to universal induction. We also introduce
many more variants of physical message complexity based on energy and action,
and discuss the ramifications of our proposals.Comment: Under review at AGI-2015 conference. An early draft was submitted to
ALT-2014. This paper is now being split into two papers, one philosophical,
and one more technical. We intend that all installments of the paper series
will be on the arxi
Bounded Arithmetic in Free Logic
One of the central open questions in bounded arithmetic is whether Buss'
hierarchy of theories of bounded arithmetic collapses or not. In this paper, we
reformulate Buss' theories using free logic and conjecture that such theories
are easier to handle. To show this, we first prove that Buss' theories prove
consistencies of induction-free fragments of our theories whose formulae have
bounded complexity. Next, we prove that although our theories are based on an
apparently weaker logic, we can interpret theories in Buss' hierarchy by our
theories using a simple translation. Finally, we investigate finitistic G\"odel
sentences in our systems in the hope of proving that a theory in a lower level
of Buss' hierarchy cannot prove consistency of induction-free fragments of our
theories whose formulae have higher complexity
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
Complicating to Persuade?
This paper addresses a common criticism of certification processes: that they simultaneously generate excessive complexity, insuficient scrutiny and high rates of undue validation. We build a model of persuasion in which low and high types pool on their choice of complexity. A natural criterion based on forward induction selects the high-type optimal pooling equilibrium.When the receiver prefers rejection ex ante, the sender simplifies her report. When the receiver prefers validation ex ante, however, more complexity makes the receiver less selective, and we provide sufficient conditions that lead to complexity inflation in equilibrium
FASTSUBS: An Efficient and Exact Procedure for Finding the Most Likely Lexical Substitutes Based on an N-gram Language Model
Lexical substitutes have found use in areas such as paraphrasing, text
simplification, machine translation, word sense disambiguation, and part of
speech induction. However the computational complexity of accurately
identifying the most likely substitutes for a word has made large scale
experiments difficult. In this paper I introduce a new search algorithm,
FASTSUBS, that is guaranteed to find the K most likely lexical substitutes for
a given word in a sentence based on an n-gram language model. The computation
is sub-linear in both K and the vocabulary size V. An implementation of the
algorithm and a dataset with the top 100 substitutes of each token in the WSJ
section of the Penn Treebank are available at http://goo.gl/jzKH0.Comment: 4 pages, 1 figure, to appear in IEEE Signal Processing Letter
- …