  In the artificial intelligence field, learning often corresponds to changing
the parameters of a parameterized function. A learning rule is an algorithm or
mathematical expression that specifies precisely how the parameters should be
changed. When creating an artificial intelligence system, we must make two
decisions: what representation should be used (i.e., what parameterized
function should be used) and what learning rule should be used to search
through the resulting set of representable functions. Using most learning
rules, these two decisions are coupled in a subtle (and often unintentional)
way. That is, using the same learning rule with two different representations
that can represent the same sets of functions can result in two different
outcomes. After arguing that this coupling is undesirable, particularly when
using artificial neural networks, we present a method for partially decoupling
these two decisions for a broad class of learning rules that span unsupervised
learning, reinforcement learning, and supervised learning.
