If connectionism is to be an adequate theory of mind, we must have a theory of representation for neural networks that allows for individual differences in weighting and architecture while preserving sameness, or at least similarity, of content. In this paper we propose a procedure for measuring sameness of content of neural representations. We argue that the correct way to compare neural representations is through analysis of the distances between neural activations, and we present a method for doing so. We (...) then use the technique to demonstrate empirically that different artificial neural networks trained by backpropagation on the same categorization task, even with different representational encodings of the input patterns and different numbers of hidden units, reach states in which representations at the hidden units are similar. We discuss how this work provides a rebuttal to Fodor and Lepore's critique of Paul Churchland's state space semantics. (shrink)

Conscious experiences are characterized by mental qualities, such as those involved in seeing red, feeling pain, or smelling cinnamon. The standard framework for modeling mental qualities represents them via points in geometrical spaces, where distances between points inversely correspond to degrees of phenomenal similarity. This paper argues that the standard framework is structurally inadequate and develops a new framework that is more powerful and flexible. The core problem for the standard framework is that it cannot capture precision structure: for example, (...) consider the phenomenal contrast between seeing an object as crimson in foveal vision versus merely as red in peripheral vision. The solution I favor is to model mental qualities using regions, rather than points. I explain how this seemingly simple formal innovation not only provides a natural way of modeling precision, but also yields a variety of further theoretical fruits: it enables us to formulate novel hypotheses about the space and structures of mental qualities, formally differentiate two dimensions of phenomenal similarity, generate a quantitative model of the phenomenal sorites, and define a measure of discriminatory grain. A noteworthy consequence is that the structure of the mental qualities of conscious experiences is fundamentally different from the structure of the perceptible qualities of external objects. (shrink)