Forgetting curves: implications for connectionist models

Forgetting in long-term memory, as measured in a recall or a recognition test, is faster for items encoded more recently than for items encoded earlier. Data on forgetting curves fit a power function well. In contrast, many connectionist models predict either exponential decay or completely flat forgetting curves. This paper suggests a connectionist model to account for power-function forgetting curves by using bounded weights and by generating the learning rates from a monotonically decreasing function. The bounded weights introduce exponential forgetting in each weight and a power-function forgetting results when weights with different learning rates are averaged. It is argued that these assumptions are biologically reasonable. Therefore power-function forgetting curves are a property that may be expected from biological networks. The model has an analytic solution, which is a good approximation of a power function displaced one lag in time. This function fits better than any of the 105 suggested two-parameter forgetting-curve functions when tested on the most precise recognition memory data set collected by. Unlike the power-function normally used, the suggested function is defined at lag zero. Several functions for generating learning rates with a finite integral yield power-function forgetting curves; however, the type of function influences the rate of forgetting. It is shown that power-function forgetting curves cannot be accounted for by variability in performance between subjects because it requires a distribution of performance that is not found in empirical data. An extension of the model accounts for intersecting forgetting curves found in massed and spaced repetitions. The model can also be extended to account for a faster forgetting rate in item recognition (IR) compared to associative recognition in short but not long retention intervals.     

An attempt to discriminate different types of executive functions in the Wisconsin Card Sorting Test

This study examined the roles of the phonological working memory and the central executive in the Wisconsin Card Sorting Test by altering the materials and the procedure of the task and using a dual-task design, in which cognitive abilities of normal participants were manipulated by performance of the secondary tasks selectively taxing the phonological loop or the central executive. The present study used three novel versions of the Wisconsin Card Sorting Test, namely the WCST-4 stimuli, the WCST-12-stimuli, and the WCST-12-stimuli-box, in all of which the participants were given the exact sorting criterion. So the tasks did not involve processes such as maintenance of inferences about the sorting criterion which would require phonological memory load. However, the tasks were assumed to require the executive process of response inhibition. In the WCST-4-stimuli condition no change was made to the WCST materials. In the other two conditions, relying on the assumption that the three-dimensional nature of the cards triggers inappropriate responses, unidimensional stimulus cards were used instead of the four normal three-dimensional WCST stimulus cards. The difference between these two conditions was that, in the WCST-12-stimuli-box condition, boxes were used to conceal the response cards previously sorted. The results supported Dunbar and Sussman's (1995) argument that some executive processes in the Wisconsin Card Sorting Test require the use of phonological store, and the present design was able to differentiate the type of executive functions that do not involve the use of a phonological loop from the ones that do. In addition, the results concerning manipulations of the visual aspects of the Wisconsin Card Sorting Test suggest that the three-dimensional nature of the WCST stimulus cards leads to an increase in the number of inappropriate responses produced with the executive secondary task interference.     

Automatic mimicry reactions as related to differences in emotional empathy

The hypotheses of this investigation were derived by conceiving of automatic mimicking as a component of emotional empathy. Differences between subjects high and low in emotional empathy were investigated. The parameters compared were facial mimicry reactions, as represented by electromyographic (EMG) activity when subjects were exposed to pictures of angry or happy faces, and the degree of correspondence between subjects' facial EMG reactions and their self-reported feelings. The comparisons were made at different stimulus exposure times in order to elicit reactions at different levels of information processing. The high-empathy subjects were found to have a higher degree of mimicking behavior than the low-empathy subjects, a difference that emerged at short exposure times (17-40 ms) that represented automatic reactions. The low-empathy subjects tended already at short exposure times (17-40 ms) to show inverse zygomaticus muscle reactions, namely "smiling" when exposed to an angry face. The high-empathy group was characterized by a significantly higher correspondence between facial expressions and self-reported feelings. No differences were found between the high- and low-empathy subjects in their verbally reported feelings when presented a happy or an angry face. Thus, the differences between the groups in emotional empathy appeared to be related to differences in automatic somatic reactions to facial stimuli rather than to differences in their conscious interpretation of the emotional situation.     

Returning the tables: language affects spatial reasoning

Li and Gleitman (Turning the tables: language and spatial reasoning. Cognition, in press) seek to undermine a large-scale cross-cultural comparison of spatial language and cognition which claims to have demonstrated that language and conceptual coding in the spatial domain covary (see, for example, Space in language and cognition: explorations in linguistic diversity. Cambridge: Cambridge University Press, in press; Language 74 (1998) 557): the most plausible interpretation is that different languages induce distinct conceptual codings. Arguing against this, Li and Gleitman attempt to show that in an American student population they can obtain any of the relevant conceptual codings just by varying spatial cues, holding language constant. They then argue that our findings are better interpreted in terms of ecologically-induced distinct cognitive styles reflected in language. Linguistic coding, they argue, has no causal effects on non-linguistic thinking--it simply reflects antecedently existing conceptual distinctions. We here show that Li and Gleitman did not make a crucial distinction between frames of spatial reference relevant to our line of research. We report a series of experiments designed to show that they have, as a consequence, misinterpreted the results of their own experiments, which are in fact in line with our hypothesis. Their attempts to reinterpret the large cross-cultural study, and to enlist support from animal and infant studies, fail for the same reasons. We further try to discern exactly what theory drives their presumption that language can have no cognitive efficacy, and conclude that their position is undermined by a wide range of considerations.     

At what age do children learn to discriminate between act and actor?

Children's ability to make moral judgements about an act on the basis of aspects of the act rather than on liking and preconceived ideas about the actor was investigated. 85 children of 4 age groups (preschool, Grades 1, 2, and 3, age range 5-9 years) participated. Act/Actor discrimination was investigated with a test consisting of 8 cartoons. In 4, a rabbit was behaving aggressively against a wolf; the other 4 portrayed identical acts with the wolf as aggressor and the rabbit as victim. Participants made moral evaluations of each cartoon. IQ was measured with Raven's Standard Progressive Matrices, and the general level of moral development was measured in accord with Piaget's (1932) criteria. Age, IQ, and general moral development correlated with discriminative ability for Act and Actor. In Piagetian terms, children at the heteronomous level were not capable of such discrimination, while children at the autonomous level (above 7 years of age) in general were.     

Hierarchical modeling of paired comparison data

The method of paired comparisons belongs to a small group of techniques that provide explicit information about the consistency of individual and aggregated choices. This article investigates the link between the individual- and group-level judgments by extending R. D. Luce's (1959) model, which was originally developed for individual choice behavior, to a mixed-effects paired comparison model. It is shown that standard multilevel software for binary data can be used to estimate the model. The interpretation of the paired comparison parameters and statistical model tests are discussed in detail. An extensive analysis of an experimental study illustrates the usefulness of a hierarchical approach in modeling multiple pairwise judgments.     

The role of attribution of motivation in producing postsuppressional rebound

Three studies demonstrated that postsuppressional rebound (PSR) may be both reduced and enhanced by manipulating people's attributions about why they experience difficulty during suppression. Telling participants that suppression failures indicate a high motivation to use the suppressed construct produced more PSR than telling them that suppression failures indicate a low motivation to use the construct (Study 1). Telling participants that an external stimulus would make suppression easy produced more PSR than telling them that it would make suppression difficult (Study 2). Telling participants that suppressing a stereotype is difficult and unindicative of prejudice eliminated PSR (Study 3). These results support the notion that PSR occurs because people infer from the difficulty experienced during suppression and from suppression failures that they are motivated to use the suppressed construct.     

Set-Theoretic Absoluteness and the Revision Theory of Truth

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.     

Familial correlates of social anxiety in children and adolescents

Retrospective studies suggest a relationship between parental rearing practices and social phobia. The present study investigated whether socially anxious children perceive their current parental rearing as rejecting, overprotective, and lacking emotional warmth, and as emphasizing the importance of other's opinion, and de-emphasizing social initiatives and family sociability. Furthermore, we examined whether parents of socially anxious children report to rely on such rearing practices, and suffer themselves from social fears. A regression analysis as well as extreme group comparisons were applied. Little support was found for the presumed role of the assessed family rearing aspects in the development of social anxiety in children. Solely family sociability (children's and mothers' report) and children's perception of overprotection of the mother predicted social anxiety in the regression analysis. Given the influence of the mentioned rearing practices, social anxiety of the mother still significantly predicted social anxiety of the child. In the extreme group comparisons, differences in the expected direction were found between socially anxious and normal children on parental rejection, emotional warmth, and family sociability. However, the lack of differences between socially anxious and clinical control children suggests that these variables do not form a specific pathway to social fears.     

Body dissatisfaction and irrational beliefs

To test the hypothesis that the irrational evaluative beliefs, postulated by Rational-Emotive Behavior Therapy, are associated with body dissatisfaction, 94 women (21 diagnosed with an eating disorder, 38 with high body dissatisfaction but without an eating disorder, and 35 with low body dissatisfaction) completed the Survey of Personal Beliefs and the Eating Disorders Inventory. Analysis showed no significant difference in body dissatisfaction between the Eating Disordered and High Body Dissatisfaction subgroups. No significant correlations between body dissatisfaction and irrational beliefs were found for the Eating Disordered subgroup. For the High Body Dissatisfaction subgroup, significant but low correlations were found between scores on body dissatisfaction and irrational standards for self and others and with negative self-rating. In terms of irrational beliefs the Eating Disordered and High Body Dissatisfaction subgroups showed a significantly greater tendency towards Catastrophizing, Low Frustration Tolerance, and Negative self-rating, compared to the controls, without any significant difference between the former two groups. The Eating Disordered subgroup but not the High Body Dissatisfaction subgroup differed significantly from the controls in terms of more Self-directed demands.