The computational origin of representation

Abstract

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations-whatever they are-must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give rise to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an "assembly language" for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems.

Figure 1:

Learners observe relations in the world, like the successor relationship between seasons. Their goal is to create an internal mental representation which obeys the same dynamics. This is achieved by mapping each observed token to a simple expression written in a universal mental language whose constructs/concepts specify interactions between elements. This system uses a logic for function compositions that is capable of universal computation.

Figure 2:

An overview of the encoding of LCL dynamics into a connectionist architecture. Schemes like Smolensky (1990)’s tensor product encoding allow tree operations and structure (e.g. first, rest, pair), which can be used to implement the structures necessary for combinatory logic as well as the evaluator. The structures built in combinatory logic, as shown in this paper, create symbolic concepts which participate in theories and whose meaning is derived through conceptual role in those theories. It is possible that the intermediate levels below LCL are superfluous, and that dynamics like combinatory logic could be encoded directly in biological neurons (dotted line).