Mathematical Tractability of Neural Nets

[Elizabeth Bates]

I must object to the argument that "Neurologists know with great
specificity how to predict the effects of lesions...".  In fact, the
more we know about structural and functional brain imaging, the less
clear the localization story becomes.  For example, Basso et al.
have reviewed CT or MRI records for 1,500 patients, and find that
the classical teaching is contradicted (re type of lesion and type
of aphasia) in at least 20% of the cases (e.g. fluent aphasias
with a frontal lesion; non-fluent aphasias with a posterior lesion,
and so forth).  Antonio Damasio has a lovely paper that is titled
something like "Where is Broca's area?"  It turns out that it is not
at all obvious where that is!!  There are cases of syndromes with
very specific behavioral impairments (e.g. the famous Hart, Berndt
and Caramazza case who had a particularly severe problem naming
fruits and vegetables; see also Warrington's patients).  But there is
a real mystery in that category-specific literature as well: most (though
not all) of the reported cases of very very specific impairments come
from patients with very global forms of encephalopathy, e.g. diffuse
forms of brain injury.  The real facts are that the localization
story has been grossly OVERSOLD to the outside world.  Insiders (e.g.
members of the Academy of Aphasia) know all too well how approximate
and often non-specific the relationships are between lesion site and
syndrome type.  For example, I suspect that many of you believe that
there is a sound relationship between lesions to anterior cortex and
damage to grammar (e.g. the Broca's-aphasia-as-agrammatism story).  But
how many know about the 1983 study by Linebarger et al. (followed by
many replications, in several different languages) showing that
so-called agrammatic Broca's aphasics can make spectacularly good
and quite fine-grained judgments of grammaticality?  How do you square
that finding with the claim that Broca's area is the "grammar box"?  In
our own cross-linguistic research, we have found that Turkish Broca's
aphasics look radically different from Serbo-Croatians, who look
radically different from Italians, who look radically different from
English-speakers, and so on.  In studies with a Patient Group by
Language Group design (e.g. Broca's and Wernicke's in several different
languages) it is invariably the case that Language accounts for
4 - 5 times more variance than aphasia group!  You can predict more
of the linguistic behavior of a brain-damaged patient by knowing his
premorbid language than you can by knowing his lesion site and/or his
aphasic classification.  These findings can ONLY be explained if we
assume that a great deal (if not all) of linguistic knowledge is spared.
Aphasics suffer from some poorly-understood problems in accessing and
deploying this knowledge (and there are a lot of new proposals on board
right now to try and explain the nature of these performance deficits).
But the specificity is far less than textbook stories would have you
believe.

The Good News for Connectionists: the "real" data from patients with
focal brain injury are in fact much more compatible with a neural
network story (i.e. a story in which representations are broadly
distributed and activated by degree) than they are with an old-fashioned
19th century Thing-In-a-Box theory of the brain.  -liz bates