Interactions Between Data Labeling and Ratio of Hebbian to Error-Driven Learning in Mixed-Model Networks

Cognitive models using mixed-model (that is, combining both task and model learning) learning algorithms, such as Leabra (O’Reilly, 2001), have typically been simulated with supervised-only paradigms. Despite decades of research on learning from partial data (e.g., Dempster, Laird, & Rubin, 1997), only recently have paradigms such as semi-supervised and active learning been applied to more psychologically-oriented models (Love, Medin, & Gureckis, 2004; Robare, 2004). This has been driven, at least in part, by a concern for creating models more reflective of real-world learning environments (Elwin et al., 2007; Li, Farkas, & MacWhinney, 2004; Robare, 2004), which should make mixed-model algorithms and semi-supervised and active learning paradigms more popular in the future. As paradigms like semi-supervised learning are applied to connectionist networks, often used to model cognitive phenomena in an explicitly brain-based fashion, some unexpected interactions have been observed. Leabra users know that the ratio of task to model learning (the lmix variable in the PDP++ software; O’Reilly et al., 1995) interacts with learning rate, k-winners-take-all inhibition (kWTA), and the number of epochs needed to train the network (O’Reilly & Munakata, 2000). The ratio of labeled to unlabeled data also interacts with these variables. Although similar interactions have been explored in earlier research on semi-supervised learning and its related paradigms (e.g., Nigam et al., 2000), particularly in the doman of training duration, related as it is to the cost reduction for which semi-supervised learning was initially developed, with the application of semi-supervised learning to connectionist models it is worthwhile to study these interactions anew. There are two primary reasons for this. First, when the goal of cognitive modeling is not the solving of a computational problem or the development of an artificial intelligence but the explication of human cognition, a different set of considerations apply. Time and cost of human labor, a driving force in other semisupervised learning research (e.g., Nigam et al., 2000; Yarowsky, 1995), becomes less relevant (though cost may be important in other ways; Antrobus, personal communication, March 2007). Neuroscience provides constraints absent from purely computational research (Sejnowski, 1986), and O’Reilly (1998) has argued persuasively for other constraints on connectionist networks that follow from the requirement for biological plausibility. These constraints mean, or may mean, that the labeled:unlabeled data ratio interacts differently with other variables in a biologically plausible connectionist network than in other kinds of cognitive architectures. Second, because the drive for using semi-supervised learning in psychologically-oriented models comes not from neuroscience-based constraints but from environment-based constraints, the specific interactions of labeled:unlabeled data ratios with other network variables may have implications for the way we study feedback and reinforcement in real-world environments. Only recently has the notion of selective feedback moved outside the realm of respondent (Rescorla & Wagner, 1972) and operant (Hemmes & Eckerman, 1972) conditioning into cognitive research (Elwin et al., 2007). If we understand, in our models, the relationship between the labeled:unlabeled data ratio and the variables with which it interacts, we will be better able to predict the results of empirical studies on partial and selective feedback and be able to direct observations on the nature of feedback in real-world environments. The current work focuses on the interaction between the labeled:unlabeled data ratio and the task learning: model learning ratio as applied in Leabra. The Leabra algorithm is a natural fit for semi-supervised paradigms, and the interaction between these two variables is particularly important. The changes wrought in the brain by contact with environmental feedback that is inconstant, incomplete, or absent (Elwin et al., 2007; Li, Farkas, & MacWhinney, 2004; Love, Medin, & Gureckis, 2004; Robare, 2004) will depend on the parameters in the brain that determine changes in synaptic strength. For example, holding constant kWTA at 0.1 and learning rate at 0.01, for a task learning:model learning ratio of 19:1 (that is, 5% of the weight change comes from Hebbian learning), adding unlabeled data to the training set for a 2:1 ratio of labeled: unlabeled data lowers learning performance, whereas a 3:4 ratio of labeled: unlabeled data improves it. However, when 7.5% of the weight change is from Hebbian learning (a In Proceedings of ICCM 2007Eighth International Conference on Cognitive Modeling. 305 305. Oxford, UK: Taylor & Francis/Psychology Press.