Connectionist models are computational paradigms that model cognitive processes through networks of simple, parallel-working units, whose connections are represented by weighted edges.
Formally, a connectionist model can be described as a directed graph \( G = (V, E) \) with nodes \( V \) and weighted edges \( E \subseteq V \times V \), where each node has an activation function \( f: \mathbb{R} \rightarrow \mathbb{R} \).
The state update typically occurs through
\[ a_j(t+1) = f\left( \sum_i w_{ij} a_i(t) + b_j \right) \]
where \( a_j(t) \) is the activation of node \( j \) at time \( t \), \( w_{ij} \) is the weight of the connection from node \( i \) to \( j \), and \( b_j \) is a bias term.
Learning is based on optimization methods such as gradient descent to minimize an error measure over training data.
Connectionist models form the basis of many modern neural networks and are central to understanding distributed information processing.
Definition:
“Connectionist models are computational structures that represent cognitive functions through interconnected, parallel-working units with weighted connections, where knowledge is distributedly encoded in the connection strengths.”
Source:
Rumelhart, D. E., McClelland, J. L., & PDP Research Group (1986). Parallel Distributed Processing: Explorations in the Microstructure of Cognition. MIT Press.