context sensitivity of representations

[mherrmann@informatik.uni-leipzig.dbp.de]

Andy Clark (andyc at cogs.sussex.ac.uk) asks:

> Must [the representational] process bottom out somewhere in a
> set of microfeatures which are genuinely SEMANTIC (genuinely
> contentful but which are NOT prone to contextual infection?

I believe that it is possible to build a representational system
in which all the components are context-sensitive, and that it
*may* be necessary to do so in order to achieve sophisticated
behaviour such as analogical reasoning.  (This belief is not
based on empirical work - so those who don't like speculation on
this mailing list will probably want to leave right now.)

I want to break up Andy's question into four areas: bottoming out
of data structures, bottoming out of meaning, context
sensitivity, and semantic primitives.

BOTTOMING OUT OF DATA STRUCTURES

My interest is in analogical reasoning - a domain that demands
sophisticated data structures.  So I will assume that we are
talking about representational systems capable of implementing
complex structures.

Traditional symbolic AI systems often have tree-structured
representations.  Repeated application of a decomposition
operator (CAR or CDR for LISP) will eventually bottom out at a
leaf of the tree.  However, this needn't always be the case: e.g.
the underlying structure might be a network.  If you wanted a
system that reasoned about unobserved parts of instances you
might have: a tree representing the component structure of an
instance and a semantic net encoding default class information. 
Application of a decomposition operator to a leaf of the instance
tree would cause the leaf to be expanded with a fringe of
information resulting from binding instance information into
semantic net information.  Thus the tree would *appear* to be
unbounded.

In the connectionist domain, Bruce MacLennan (1991) discussed
knowledge representation in infinite-dimensional vector spaces. 
A decomposition operator is just a function that can be applied
to any pattern to yield a component pattern of the same
dimensionality as the parent.  Repeated decomposition *may* yield
nonsense patterns - but, in principle, it should be possible to
construct a cyclic structure that never bottoms out, like a
semantic net.  MacLennan also points out the possibility of
multiple decomposition operators (not necessarily restricted to
the inverse of a single composition operator).  I suspect that
systems designed to generate multiply decomposable
representations will be very interesting.

BOTTOMING OUT OF MEANING

Consider a dictionary.  The definitions form a network with each
word defined in terms of other words.  There are no semantic
primitives here.  Each word is as fuzzily defined as any other,
although analysis may reveal that some words are more central
than others.  The amazing fact is that dictionaries are actually
useful - it is possible to gain some understanding of the meaning
of a word from a dictionary even though it contains no semantic
primitives.  But this only works if there is an environment that
is understood by the reader and represented by the dictionary. 

Stevan Harnad (1990), in discussing the symbol-grounding problem,
makes the point that it is impossible to learn Chinese from a
Chinese to Chinese dictionary.  Purely formal systems (like
maths) are predicated on internal consistency, can be understood
with no reference to external environments, and would be nonsense
without semantic primitives.  Representational systems *can* be
based on semantic primitives, as in classical AI, but I suspect
that they are crippled when used to represent an environment of
greater intrinsic complexity than the complexity of the
representation language.  Representational systems *can* be built
that are not dependent on semantic primitives, as in the case of
the dictionary, provided that an external environment is
available for grounding of the meaning.

CONTEXT SENSITIVITY

Andy Clark gives an example of context sensitivity where the
pattern representing the to-be-represented-object varies
depending on the context in which the object occurs.  In this
case the micro-structure of the representation varies (although
it begs the question of how the system 'knows' that the different
patterns represent the same thing.  It seems to me that there are
other types of context-sensitivity.

Looking at the outermost perceptual end of the system there are
context sensitivities in the encoding process.  For example there
are many perceptual adaptation phenomena and simultaneous
contrast phenomena.  From the point of view of an external
observer the encoding of some external quantity into a neural
firing rate is dependent on the environmental context.  From the
point of view of up-stream processing, a given firing level does
not have a constant mapping to the external physical quantity.

The process of transduction from the perceptual to cognitive
domains is also context dependent.  Dave Chalmers et al (1991)
argue very strongly for the context sensitivity of the
representational process.  Their contention is that the
information extracted from the perceptual flow *must* depend on
the cognitive states (current goals, beliefs etc) of the system. 
In this case the individual components of the representation are
*not necessarily* context dependent, but the overall
representational structure that is extracted from the perceptual
data must be depend on the context.  Similarly, cognitive
activities (such as reasoning) might be seen as similar to the
perceptual process (interpreting one structure to yield another)
and could also be expected to be context-sensitive.

Returning to the Chinese dictionary example given earlier, it is
obvious that the interpretation of the components is context-
sensitive (cf Wittgenstein on the impossibility of precise
definition) but the actual words themselves (representational
atoms) are discrete and context-free.

Someone with a flair for maths might be able to come up with a
proof for the inevitability of context-sensitivity.  An organism
is constrained to make inferences under conditions of extreme
uncertainty: it must respond to an environment that is more
complex than can be represented exactly, it operates under
resource constraints of computational power and response time,
and the number of observations available is far too small to
uniquely constrain a mental model.  Under such conditions the
best strategy may well be to allow underconstrained mental models
with the low bandwidth input being used as a source of
confirmation of model predictions rather than being directly
transduced into the model.

SEMANTIC PRIMITIVES

Andy couches his explanation of context-sensitivity in terms of
microfeatures.  Conceiving of representations in this way makes
it difficult to see how representations can be based on other
than context-free atoms, because microfeatures *are* context-
free atoms (if we ignore the low-level perceptual context-
sensitivity mentioned above).  The term 'micro-features' conjures
up associations of grandmother cells and hand-coded
representations of the type argued against by Chalmers et al.

It should be obvious from my earlier comments that I don't think
semantic primitives are necessary for grounded systems.  This
begs the question of how the system could be grounded.  The prime
requirement is that the environmental input can be predicted (or
at least checked for consistency) from the representation.  This
obviously doesn't *necessarily* require direct representation of
the environmental patterns in the cognitive structure - only that
such patterns can be generated or checked at the point of
transduction.  Many symbolic AI representations are based on the
notion of objects (and I believe that to be a useful
abstraction), and while there may be objects in the real world
each individual perceptual input says next to nothing about
objects.  That is, objects are an internal construction, not a
simple re-coding of the perceptual input.

Another possibility is that the representations are based on
system dynamics rather than direct encoding of an 'external
reality'.  The usual view is to see representations as passive
objects (like computer data structures) that are acted upon - but
is also possible to see representations as active entities that
transform other representations (a little akin to procedural
representations in AI).  Janet Wiles et al (1991) have argued
that activation patterns in recurrent networks can be seen dually
as static representations and as dynamic operators.  The trick
with this approach is that the representations must be
functional and cannot be arbitrary - so the hard party is to
learn/construct representations so that the dynamic effect when
the representation is applied as an operator has the correct
semantics as confirmed by the environment.

The same argument can be applied to perceptual inputs.  The usual
conception of perceptual processing has a direct signal path from
lower to higher levels with the signal being recoded along the
way.  A more indirect, context-sensitive, interpretive approach
would view the main signal flow as being confined within the
higher levels and view the perceptual input as modulating the
processing parameters of the high-level signal transformations
rather than directly inserting signals into that flow. 
Confirmation of accuracy of modelling the environment could be
by the perceptual signals modulating the parameters of a cost
function on the cognitive representation rather than entering
directly into the cost function.

SUMMARY

Data structures don't have to bottom out.

Meaning doesn't have to bottom out in semantic primitives.

You do need an environment to ground the symbols.

There are different types of context-sensitivity.

Everything *should* be context-sensitive if you want to build a
sophisticated system.

The representation doesn't have to *directly* represent the
environment.

REFERENCES

Chalmers, D.J., French, R.M., & Hofstadter, D.R. (1991). High-
     level perception, representation and analogy: A critique of
     artificial intelligence methodology. Indiana University,
     Bloomington, CRCC technical report 49.

Harnad, S. (1990) The symbol grounding problem.  "Physica D" 42:
     335-346.

MacLennan, B. (1991) Continuous symbol systems: The logic of
     connectionism. University of Tennessee, Knoxville,
     Department of Computer Science technical report CS-91-145.

Wiles, J., Stewart, J.E.M., & Bloesch, A. (1991) Patterns of
     activations are operators in recurrent networks. Proceedings
     of the 2nd Australian Conference on Neural Networks, 44-48.

----------------
I will let you know when I get this to work.  Don't hold your
breath.

Ross Gayler
ross at psych.psy.uq.oz.au