Dr Nathan Duran Nathan.Duran@uwe.ac.uk
Lecturer in Artificial Intelligence
Abstract
Responding to the relationships between stimuli (i.e., relational responding) plays a central role in human intelligence (Colbert, 2017, Cassidy, 2016). Decades of psychological research have shown how relational responding behaviour is first learned and then generalised to become the basis for language and higher order cognitive functioning. Relational Frame Theory (RFT, Hayes et al, 2001) describes how as relational responding becomes increasingly generalised, human beings become increasingly able to respond to socially defined (i.e., symbolic) qualities of a stimulus, not just its physical properties, such as when a child chooses a 20 pence coin rather than a 10 pence coin, which although larger, is also ‘worth’ less. The ability to respond symbolic qualities is understood by RFT to be the basis of human abstract thought and ultimately intelligence.
While human relational responding has been modelled in a machine, to date there are no studies describing how this relational responding itself emerges from a particular learning history.
According to RFT, the most basic relational response is mutual entailment, often called symmetry. Symmetry describes how if stimulus A is related to stimulus B (i.e., AB) in some way, then the reversed relation (i.e., BA) can be automatically derived without any further training. While symmetry represents a deceptively simple and basic process, engineering a computer system able to learn generalised stimulus bi-directionality is a more significant challenge.
Machine Learning (ML) attempts to derive a computational model which is capable of emulating real-world knowledge, or behaviours. Conventionally, this is achieved via a set of training data which is representative of the problem in question. While this data is always, to some extent, an abstraction, it nonetheless contains discernible and problem-specific features. For example, we may wish to train a neural network (NN) to discriminate between images of cats and dogs. The training images may vary, but they still contain a multitude of visual features that are unique to these two species. Thus, the NN is able to differentiate between these features and predict which animal the image contains.
However, due to their transductive nature, most conventional NN architectures will be unable to learn generalised symmetry relations. Instead, we look to architectures
that are intended for relational learning, Graph Neural Networks (GNN) (Scarselli, F., et al., 2009). Rather than considering data samples in isolation, GNNs can operate on graph-structured data. We can then formulate the problem of relational symmetry as nodes, representing stimuli, and edges, the relations between them.
In this paper we describe the construction of a directed multigraph dataset, with arbitrary stimuli represented as pseudo-random numbers and edges representing symmetry relations. We then conduct a series of experiments using the GraphSAGE (SAmple and aggreGatE) architecture (Hamilton, W.L., Ying, R. and Leskovec, J., 2017), which is capable of inductive inference on previously unseen elements of a graph. We first train the GNN on a set of stimulus pairs in both directions, e.g. (A -> B) and (B -> A), with the objective of predicting if a relation (edge) exists between the stimuli or not. We then show that, with further training on novel stimulus pairs in only one direction (X -> Y), the GNN is able to correctly reverse that relation (Y -> X) without being explicitly trained.
To the best of our knowledge this is the first application of GNNs to the problem of learning generalised symmetry relations within the context of RFT. The wider impact of modelling basic relational processes for the development of artificial general intelligence is also discussed.
