A random perceptron is a model of random linear measurements of a weight vector, with constraints or weights imposed through a scalar function of each measurement. For independent
pattern vectors 
with independent standard normal coordinates, a common
measurement convention is 
. At pattern density 
, there are 
patterns, with 
the floor function.
For a single-pattern log-weight 
, its partition
function is
 |
The Ising perceptron uses uniform probability on binary weight vectors, and the spherical
perceptron uses uniform probability on a sphere
of radius 
. Hard constraints instead assign zero weight to vectors
violating a prescribed measurement inequality. The
geometry of the weight space and the pattern distribution are part of the model.
