Summation in causal learning: elemental processing or configural generalization?

Spontaneous recovery from overexpectation in an insect

In associative learning in mammals, it is widely accepted that learning is determined by the prediction error, i.e., the error between the actual reward and the reward predicted by the animal. However, it is unclear whether error-based learning theories are applicable to the learning occurring in other non-mammalian species. Here, we examined whether overexpectation, a phenomenon that supports error-based learning theories, occurs in crickets. Crickets were independently trained with two different conditioned stimuli (CSs), an odour and a visual pattern, that were followed by an appetitive unconditioned stimulus (US). Then the two CSs were presented simultaneously as a compound, followed by the same US. This treatment resulted in a reduced conditioned response to the odour CS when tested immediately after training. However, the response to the CS was partially recovered after 1 day. These results are the first to show overexpectation and its spontaneous recovery in an invertebrate species. While the results showing overexpectation are in agreement with the prediction by the Rescorla-Wagner model, a major form of error-based learning theories, the ones showing spontaneous recovery are not. Our results suggest that conventional error-based learning models account for some, but not for all essential features of Pavlovian conditioning in crickets.

Causal invariance as a tacit aspiration: Analytic knowledge of invariance functions

For causal knowledge to be worth learning, it must remain valid when that knowledge is applied. Because unknown background causes are potentially present, and may vary across the learning and application contexts, extricating the strength of a candidate cause requires an assumption regarding the decomposition of the observed outcome into the unobservable influences from the candidate and from background causes. Acquiring stable, useable causal knowledge is challenging when the search space of candidate causes is large, such that the reasoner's current set of candidates may fail to include a cause that generalizes well to an application context. We have hypothesized that an indispensable navigation device that shapes our causal representations toward useable knowledge involves the concept of causal invariance - the sameness of how a cause operates to produce an effect across contexts. Here, we tested our causal invariance hypothesis by making use of the distinct mathematical functions expressing causal invariance for two outcome-variable types: continuous and binary. Our hypothesis predicts that, given identical prior domain knowledge, intuitive causal judgments should vary in accord with the causal-invariance function for a reasoner's perceived outcome-variable type. The judgments are made as if the reasoner aspires to formulate causally invariant knowledge. Our experiments involved two cue-competition paradigms: blocking and overexpectation. Results show that adult humans tacitly use the appropriate causal-invariance functions for decomposition. Our analysis offers an explanation for the apparent elusiveness of the blocking effect and the adaptiveness of intuitive causal inference to the representation-dependent reality in the mind.

Exploring the Effect of Stimulus Similarity on the Summation Effect in Causal Learning

Several contemporary models anticipate that the summation effect is modulated by the similarity between the cues forming a compound. Here, we explore this hypothesis in a series of causal learning experiments. Participants were presented with two visual cues that separately predicted a common outcome and later asked for the outcome predicted by the compound of the two cues. Similarity was varied between groups through changes in shape, spatial position, color, configuration, and rotation. In variance with the predictions of these models, we observed similar and strong levels of summation in both groups across all manipulations of similarity. The effect, however, was significantly reduced by manipulations intended to impact assumptions about the causal independence of the cues forming the compound, but this reduction was independent of stimulus similarity. These results are problematic for similarity-based models and can be more readily explained by rational approaches to causal learning.

Why are some dimensions integral? Testing two hypotheses through causal learning experiments

Compound generalization and dimensional generalization are traditionally studied independently by different groups of researchers, who have proposed separate theories to explain results from each area. A recent extension of Shepard's rational theory of dimensional generalization allows an explanation of data from both areas within a single framework. However, the conceptualization of dimensional integrality in this theory (the direction hypothesis) is different from that favored by Shepard in his original theory (the correlation hypothesis). Here, we report two experiments that test differential predictions of these two notions of integrality. Each experiment takes a design from compound generalization and translates it into a design for dimensional generalization by replacing discrete stimulus components with dimensional values. Experiment 1 showed that an effect analogous to summation is found in dimensional generalization with separable dimensions, but the opposite effect is found with integral dimensions. Experiment 2 showed that the analogue of a biconditional discrimination is solved faster when stimuli vary in integral dimensions than when stimuli vary in separable dimensions. These results, which are analogous to more "non-linear" processing with integral than with separable dimensions, were predicted by the direction hypothesis, but not by the correlation hypothesis. This confirms the assumptions of the unified rational theory of stimulus generalization and reveals interesting links between compound and dimensional generalization phenomena.

Mechanisms of object recognition: what we have learned from pigeons

Behavioral studies of object recognition in pigeons have been conducted for 50 years, yielding a large body of data. Recent work has been directed toward synthesizing this evidence and understanding the visual, associative, and cognitive mechanisms that are involved. The outcome is that pigeons are likely to be the non-primate species for which the computational mechanisms of object recognition are best understood. Here, we review this research and suggest that a core set of mechanisms for object recognition might be present in all vertebrates, including pigeons and people, making pigeons an excellent candidate model to study the neural mechanisms of object recognition. Behavioral and computational evidence suggests that error-driven learning participates in object category learning by pigeons and people, and recent neuroscientific research suggests that the basal ganglia, which are homologous in these species, may implement error-driven learning of stimulus-response associations. Furthermore, learning of abstract category representations can be observed in pigeons and other vertebrates. Finally, there is evidence that feedforward visual processing, a central mechanism in models of object recognition in the primate ventral stream, plays a role in object recognition by pigeons. We also highlight differences between pigeons and people in object recognition abilities, and propose candidate adaptive specializations which may explain them, such as holistic face processing and rule-based category learning in primates. From a modern comparative perspective, such specializations are to be expected regardless of the model species under study. The fact that we have a good idea of which aspects of object recognition differ in people and pigeons should be seen as an advantage over other animal models. From this perspective, we suggest that there is much to learn about human object recognition from studying the "simple" brains of pigeons.

Explaining compound generalization in associative and causal learning through rational principles of dimensional generalization

How do we apply learning from one situation to a similar, but not identical, situation? The principles governing the extent to which animals and humans generalize what they have learned about certain stimuli to novel compounds containing those stimuli vary depending on a number of factors. Perhaps the best studied among these factors is the type of stimuli used to generate compounds. One prominent hypothesis is that different generalization principles apply depending on whether the stimuli in a compound are similar or dissimilar to each other. However, the results of many experiments cannot be explained by this hypothesis. Here, we propose a rational Bayesian theory of compound generalization that uses the notion of consequential regions, first developed in the context of rational theories of multidimensional generalization, to explain the effects of stimulus factors on compound generalization. The model explains a large number of results from the compound generalization literature, including the influence of stimulus modality and spatial contiguity on the summation effect, the lack of influence of stimulus factors on summation with a recovered inhibitor, the effect of spatial position of stimuli on the blocking effect, the asymmetrical generalization decrement in overshadowing and external inhibition, and the conditions leading to a reliable external inhibition effect. By integrating rational theories of compound and dimensional generalization, our model provides the first comprehensive computational account of the effects of stimulus factors on compound generalization, including spatial and temporal contiguity between components, which have posed long-standing problems for rational theories of associative and causal learning.

Two heads are better than one, but how much? Evidence that people's use of causal integration rules does not always conform to normative standards

Many theories of causal learning and causal induction differ in their assumptions about how people combine the causal impact of several causes presented in compound. Some theories propose that when several causes are present, their joint causal impact is equal to the linear sum of the individual impact of each cause. However, some recent theories propose that the causal impact of several causes needs to be combined by means of a noisy-OR integration rule. In other words, the probability of the effect given several causes would be equal to the sum of the probability of the effect given each cause in isolation minus the overlap between those probabilities. In the present series of experiments, participants were given information about the causal impact of several causes and then they were asked what compounds of those causes they would prefer to use if they wanted to produce the effect. The results of these experiments suggest that participants actually use a variety of strategies, including not only the linear and the noisy-OR integration rules, but also averaging the impact of several causes.

Reduced Summation with Common Features in Causal Judgments

In three experiments human participants received training in a causal judgment task. After learning which patterns were associated with an outcome, participants rated the likelihood of the outcome in the presence of a novel combination of the patterns. The first two experiments used two conditions in which two visual patterns were associated with the outcome. In one condition these patterns shared a common feature. The third experiment only used the common feature condition. According to an elemental theory ( Rescorla & Wagner, 1972 ) the response to the novel test pattern should have exceeded that made to the individual training patterns, a summation effect, and this effect should have been reduced by the addition of a common feature. Summation was observed but since the common feature condition abolished, rather than merely reduced, summation the results were not consistent with the Rescorla-Wagner Model (RWM) nor with a configural alternative ( Pearce, 1994 ). Instead, it is necessary to consider models which allow the possibility of both elemental and configural strategies in causal learning. The Replaced Elements Model ( Wagner, 2003 ) is a development of the RWM which can best predict the patterns of summation and summation failure in these experiments.

Generality of the summation effect in human causal learning

Considerable research has examined the contrasting predictions of the elemental and configural association theories proposed by Rescorla and Wagner (1972) and Pearce (1987), respectively. One simple method to distinguish between these approaches is the summation test, in which the associative strength attributed to a novel compound of two separately trained cues is examined. Under common assumptions, the configural view predicts that the strength of the compound will approximate to the average strength of its components, whereas the elemental approach predicts that the strength of the compound will be greater than the strength of either component. Different studies have produced mixed outcomes. In studies of human causal learning, Collins and Shanks (2006) suggested that the observation of summation is encouraged by training, in which different stimuli are associated with different submaximal outcomes, and by testing, in which the alternative outcomes can be scaled. The reported experiments further pursued this reasoning. In Experiment 1, summation was more substantial when the participants were trained with outcomes identified as submaximal than when trained with simple categorical (presence/absence) outcomes. Experiments 2 and 3 demonstrated that summation can also be obtained with categorical outcomes during training, if the participants are encouraged by instruction or the character of training to rate the separately trained components with submaximal ratings. The results are interpreted in terms of apparent performance constraints in evaluations of the contrasting theoretical predictions concerning summation.