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Asymmetries in the Bidirectional Associative Strengths Between Events in Cue Competition for Causes and Effects

Asymmetries in the Bidirectional Associative Strengths Between Events in Cue Competition for Causes and Effects Deanah Kim (kmkim@usc.edu) Department of Psychology, University of Southern California Los Angeles, CA 90089-1061 Stephen J. Read (read@usc.edu) Department of Psychology, University of Southern California Los Angeles, CA 90089-1061 Abstract Lopez, Cano, Almaraz & Shanks, 2002) interpret the find- ings as consistent with associative learning theories. Others (e.g., Matute et al., 1996; Miller & Matute, 1998) assert that the findings are more consistent with contiguity theory, which assumes that associations are learned noncompeti- tively and bi-directionally through simple contiguity, and that cue competition takes place at judgment. In contrast, proponents of causal model theory (e.g., Waldmann & Holyoak 1992; Melz, Cheng, Holyoak & Waldmann, 1993; Waldmann, 2000) deny the evidence for cue competition for effects, suggesting that whereas causes compete, effects do not. They argue that multiple effects should not compete with each other because they provide new information about the effects of a common cause. The goal of this paper is to contrast the predictions of a recurrent neural network, with associative learning theory, causal model theory and contiguity theory’s predictions for cue competition for causes as well as for effects. Two experiments designed to test the different predictions for the occurrence of cue competition between effects will be pre- sented. These experiments use various social behaviors as target stimuli for cues and outcomes in an attempt to extend the research in multiple cue contingency learning beyond the traditional settings of biological, physical or abstract events and their consequences. In addition, these studies assess both directions of rea- soning between causes and effects. Typical research in this domain only investigates one direction of reasoning and thus cannot say anything about the relative strength of the forward link from causes to effects and the backward link from effects to causes. Two experiments using social stimuli tested a recurrent neural network model’s predictions for cue competition for causes and effects. The delta-rule based model predicts the presence of cue competition for effects as well as for causes as a result of an asymmetry in the bidirectional associative strengths between the relevant cue-outcome pairs. This model can capture cue competition for effects when cues are encountered in the cause-effect direction, unlike associative and feed- forward models. Results support the model’s prediction of cue competition for both effects and causes. The implications of these results for causal model theory and for various associative accounts of cue competition are discussed. Introduction Since the advent of research on causal induction many re- searchers have focused on causal models that explain the competitive nature of learning cues that predict or indicate the occurrence of an event (e.g., Rescorla & Wagner, 1972; Gluck & Bower, 1988; Shanks, 1991; Waldmann & Holyoak, 1992). The first account of competitive learning of cues was the Rescorla-Wagner (1972) model. When multiple cues are present preceding an event, these cues compete with each other for predictive strength, resulting in the competitive learning of cues. A classic example of this is blocking, whereupon learning that stimulus A predicts outcome X during initial training, there is a deficit in learning that B also perfectly predicts X when AB are presented together preceding X in the second training phase. Although cue competition of causes is well established in both the animal and human causal learning literature, the question of whether competition occurs among multiple effects of a common cause has produced somewhat inconsistent findings and has resulted in a heated debate (e.g., Shanks, 1991; Waldmann & Holyoak, 1992; Van Hamme & Wasserman, 1993; Price & Yates, 1995; Matute, Arcediano & Miller, 1996; Shanks, & Lopez, 1996). Cue competition for effects describes a two-stage conditioning phenomenon whereupon first learning that cause A perfectly predicts the occurrence of effect X during Phase 1 of training, there is a deficit in subsequently learning that cause A also perfectly predicts the occurrence of effect Y when the XY compound is presented together after the presentation of cause A during the Phase 2 training. A number of researchers have provided evidence for cue competition for effects. Some researchers (e.g., Shanks, 1991; Shanks & Lopez, 1996; Price & Yates, 1995; Cobos, Cue Competition in Associative Models The Rescorla-Wagner (R-W) model (Rescorla & Wagner, 1972) formally describes the change in associative strength during learning by: ∆V cs(n) = a cs b us(n) (l us(n) – V total(n) ), where ∆V cs(n) is the change in the associative strength (V) of CS as a result of a pairing with US on trial n; a cs is the learning rate parameter of the CS; b us(n) is the learning rate parameter of the US on trial n; l us(n) is the asymptote of learning or the maximum associative strength that the US can support on trial n; and V total(n) is the sum of associative strengths of all CSs present on trial n, or the extent to which the US is pre- dicted on trial n. The basic principle behind the R-W model is that associative learning is determined by the extent to which an US is surprising, represented by the difference