Abstract
Modular connectionist systems comprise autonomous, communicating modules, achieving a behaviour more complex than that of a single neural network. The component modules, possibly of different topologies, may operate under various learning algorithms. Some modular connectionist systems are constrained at the representational level, in that the connectivity of the modules is hard-wired by the modeller; others are constrained at an architectural level, in that the modeller explicitly allocates each module to a specific subtask. Our approach aims to minimise these constraints, thus reducing the bias possibly introduced by the modeller. This is achieved, in the first case, through the introduction of adaptive connection weights and, in the second, by the automatic allocation of modules to subtasks as part of the learning process. The efficacy of a minimally constrained system, with respect to representation and architecture, is demonstrated by a simulation of numerical development amongst children. The modular connectionist system MASCOT (Modular Architecture for Subitising and Counting Over Time) is a dual-routed model simulating the quantification abilities of subitising and counting. A gating network learns to integrate the outputs of the two routes in determining the final output of the system. MASCOT simulates subitising through a numerosity detection system comprising modules with adaptive weights that self-organise over time. The effectiveness of MASCOT is demonstrated in that the distance effect and Fechner's law for numbers are seen to be consequences of this learning process. The automatic allocation of modules to subtasks is illustrated in a simulation of learning to count. Introducing feedback into one of two competing expert networks enables a mixture-of-experts model to perform decomposition of a task into static and temporal subtasks, and to allocate appropriate expert networks to those subtasks. MASCOT successfully performs decomposition of the counting task with a two-gated mixture-of-experts model and exhibits childlike counting errors.