  Does the brain construct an efficient representation of the sensory world? We
review progress on this question, focusing on a series of experiments in the
last decade which use fly vision as a model system in which theory and
experiment can confront each other. Although the idea of efficient
representation has been productive, clearly it is incomplete since it doesn't
tell us which bits of sensory information are most valuable to the organism. We
suggest that an organism which maximizes the (biologically meaningful) adaptive
value of its actions given fixed resources should have internal representations
of the outside world that are optimal in a very specific information theoretic
sense: they maximize the information about the future of sensory inputs at a
fixed value of the information about their past. This principle contains as
special cases computations which the brain seems to carry out, and it should be
possible to test this optimization directly. We return to the fly visual system
and report the results of preliminary experiments that are in encouraging
agreement with theory.
