Connectionists: Fw: TR on NN semantics

[Michael Healy]

The following technical report is available at http://hdl.handle.net/1928/31783 :


Title: The Neural Representation of Concepts at the Sensor Level


Author(s):

Healy, Michael John

Caudell, Thomas Preston


Abstract:

This report presents a mathematical model of the semantics, or

meaning, of the connectionist structure and stimulus activity of a neural

network, whether artificial or biological. The mathematical model

associates concepts about sensed objects with the neuron-like nodes in

a neural network and composable concept relationships with the

connection pathways in the network. Category-theoretic constructs,

specifically colimits, limits, and functors, organize the concept structure

and map it to a formal neural network in a structure-preserving manner.

Starting with a simple example of a neural vision system, we show that

this mathematical model of neural network structure and activity can be

used to derive connectionist architectures that work as intended. We

also claim an additional advantage of this approach: A properly functioning

connectionist architecture has an accompanying concept

representation and this representation is both local and distributed.

These properties are derived from the category-theoretic formalism

described here.


Sincerely,

Mike Healy

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