REN, K., GARDNER-MEDWIN, A.R.
Department of Physiology, University College London, London WC1E 6BT,
A PROPER KNOWLEDGE MEASURE AND ITS IMPLICATIONS FOR LEARNING
Learning increases knowledge of the environment, in the
sense that an animal becomes better able to choose actions that lead to
beneficial consequences. We define knowledge as the ability to predict,
with appropriate confidence, the outcome of events or the consequences
of actions. It has clear biological value, but has not generally
been held to have a well defined measure. We show first that a satisfactory
measure for knowledge or lack of knowledge does exist within certain constraints.
We define assessment procedures and show that the results are invariant
with details of these procedures. Furthermore, this invariance renders
our measure uniquely satisfactory amongst the possible options. The
measures and procedures apply equally to knowledge of individual facts,
sets of interconnected facts and their implications, or stochastic events.
Quantitative treatment of knowledge can lead to neurobiological
insights. An animal that predicts events with a high level of accuracy
and confidence (i.e. a high estimated probability for the actual outcome)
has low nescience (our formal measure for missing knowledge). This
means that it can store information identifying the actual events more
compactly: minimum required storage capacity is directly proportional to
average nescience for the events. With stochastic events, low nescience
implies that an animal's confidence judgements are close to the true probabilities.
This is precisely what is required if confidence judgements are to form
the basis for optimal selection between different courses of action.
Low nescience can also lead to quicker and more accurate stimulus identification,
where this involves sequential matching of predicted inputs to sensory
Mechanisms by which knowledge can be acquired and represented
in neural systems and can lead to improved efficiency will be illustrated
with neural network models.