Game Theory
A mathematical formalism used to study human games, economics,
military conflicts, and biology. The goal of game theory is to find
the optimal strategy for one player to use when his opponent also
plays optimally. A strategy may incorporate randomness, in which
case it is referred to as a mixed strategy.
Gaussian
Normally distributed (with a bell-shaped curve) and having a mean
at the center of the curve with tail widths proportional to the
standard deviation of the data about the mean.
Generalized Delta Rule
Another name for backpropagation.
Genetic Algorithm (GA)
A method of simulating the action of evolution within a
computer. A population of fixed-length strings is evolved with a
GA by employing crossover and mutation operators along with
a fitness function that determines how likely individuals
are to reproduce. GAs perform a type of search in a
fitness landscape.
Genetic Programming (GP)
A method of applying simulated evolution on programs or
program fragments. Modified forms of mutation and crossover
are used along with a fitness function.
Glider
A simple object in Conway's Game of Life that swims diagonally
through the grid space.
Glider Gun
An object in Conway's Game of Life that builds and emits
gliders, which can then be collided in purposeful ways to
construct more complicated objects.
Global Minimum (Maximum)
In a search space, the lowest (or highest) point of the surface,
which usually represents the best possible solution in the space with
respect to some problem.
Gödel Number
A natural number computed via a Gödelization procedure
that uniquely corresponds to a string.
Gödelization
A method for mapping arbitrary strings to natural numbers
such that the process is one-to-one and invertible. The
process usually exploits the properties of prime numbers. Since
Gödelization can be defined as a computable
function, and since functions can be Gödelized, some
functions (or programs) can assert statements about other
functions or programs, or themselves.
Gödel's Incompleteness Theorem
Any sufficiently interesting formal system can express true
statements for which there can be no proof in the original
formal system.
Gödel's Statement
Given the formal statement ``There does not exist any proof
for the statement with Gödel number x applied to x,'' which
has it own Gödel number, g, Gödel's statement paraphrased is
``There does not exist a proof of the statement with Gödel number
g applied to itself.'' Gödel's statement is true, but cannot be
proven true in the formal system in which it is constructed,
which leads to Gödel's Incompleteness Theorem.
Gradient
A vector of partial derivatives of a function that
operates on vectors. Intuitively, the gradient represents the slope
of a high-dimensional surface.
Graph
A construct that consists of many nodes connected with edges. The
edges usually represent a relationship between the objects represented
by the nodes. For example, if the nodes are cities, then the edges
may have numerical values that correspond to the distances between the
cities. A graph can be equivalently represented as a matrix.
