Generalization,similarity, and Bayesian inference

Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models.     

Influence of auditory and audiovisual stimuli on the right–left prevalence effect

When auditory stimuli are used in two-dimensional spatial compatibility tasks, where the stimulus and response configurations vary along the horizontal and vertical dimensions simultaneously, a right–left prevalence effect occurs in which horizontal compatibility dominates over vertical compatibility. The right–left prevalence effects obtained with auditory stimuli are typically larger than that obtained with visual stimuli even though less attention should be demanded from the horizontal dimension in auditory processing. In the present study, we examined whether auditory or visual dominance occurs when the two-dimensional stimuli are audiovisual, as well as whether there will be cross-modal facilitation of response selection for the horizontal and vertical dimensions. We also examined whether there is an additional benefit of adding a pitch dimension to the auditory stimulus to facilitate vertical coding through use of the spatial-musical association of response codes (SMARC) effect, where pitch is coded in terms of height in space. In Experiment 1, we found a larger right–left prevalence effect for unimodal auditory than visual stimuli. Neutral, non-pitch coded, audiovisual stimuli did not result in cross-modal facilitation, but did show evidence of visual dominance. The right–left prevalence effect was eliminated in the presence of SMARC audiovisual stimuli, but the effect influenced horizontal rather than vertical coding. Experiment 2 showed that the influence of the pitch dimension was not in terms of influencing response selection on a trial-to-trial basis, but in terms of altering the salience of the task environment. Taken together, these findings indicate that in the absence of salient vertical cues, auditory and audiovisual stimuli tend to be coded along the horizontal dimension and vision tends to dominate audition in this two-dimensional spatial stimulus–response task.     

Adding Types,But Not Tokens,Affects Property Induction

The extent to which we generalize a novel property from a sample of familiar instances to novel instances depends on the sample composition. Previous property induction experiments have only used samples consisting of novel types (unique entities). Because real-world evidence samples often contain redundant tokens (repetitions of the same entity), we studied the effects on property induction of adding types and tokens to an observed sample. In Experiments 1–3, we presented participants with a sample of birds or flowers known to have a novel property and probed whether this property generalized to novel items varying in similarity to the initial sample. Increasing the number of novel types (e.g., new birds with the target property) in a sample produced tightening, promoting property generalization to highly similar stimuli but decreasing generalization to less similar stimuli. On the other hand, increasing the number of tokens (e.g., repeated presentations of the same bird with the target property) had little effect on generalization. Experiment 4 showed that repeated tokens are encoded and can benefit recognition, but appear to be given little weight when inferring property generalization. We modified an existing Bayesian model of induction (Navarro, Dry, & Lee, 2012) to account for both the information added by new types and the discounting of information conveyed by tokens.     

The role of observing and attention in establishing stimulus control.

Early theorists (Skinner, Spence) interpreted discrimination learning in terms of the strengthening of the response to one stimulus and its weakening to the other. But this analysis does not account for the increasing independence of the two performances as training continues or for increases in control by dimensions of a stimulus other than the one used in training. Correlation of stimuli with different densities of reinforcement produces an increase in the behavior necessary to observe them, and greater observing of and attending to the relevant stimuli may account for the increase in control by these stimuli. The observing analysis also encompasses errorless training, and the selective nature of observing explains the feature-positive effect and the relatively shallow gradients of generalization generated by negative discriminative stimuli. The effectiveness of the observing analysis in handling these special cases adds to the converging lines of evidence supporting its integrative power and thus its validity.     

Shepard's universal law supported by honeybees in spatial generalization

An animal that is rewarded for a response in one situation (the S+) is likely to respond to similar but recognizably different stimuli, the ubiquitous phenomenon of stimulus generalization. On the basis of functional analyses of the probabilistic structure of the world, Shepard formulated a universal law of generalization, claiming that generalization gradients, as a function of the appropriately scaled distance of a stimulus from S+, should be exponential in shape. This law was tested in spatial generalization in honeybees. Based on theoretically derived scales, generalization along both the dimensions of the distance from a landmark and the direction to a landmark followed Shepard's law. Support in an invertebrate animal increases the scope of the law, and suggests that the ecological structure of the world may have driven the evolution of cognitive structures in diverse animals.     

Stimulus control of differential-reinforcement-of-low-rate responding

Five pigeons were given single-stimulus training on an 8-sec differential-reinforcement-of-low-rate schedule followed by steady-state generalization training using 12 wavelength stimuli. Three birds had a high percentage of reinforced responses on the training schedule and flat generalization gradients of total responses. The birds with fewer reinforced responses had much steeper generalization gradients. Generalization gradients plotted as a function of both stimulus wavelength and interresponse time showed that for most birds, stimulus control was restricted to responses with long interresponse times. Responses with very short interresponse times were not under stimulus control and there was some evidence of inhibitory control of short interresponse times. Interresponse-times-per-opportunity functions, plotted as a function of stimulus wavelength, showed that stimulus wavelength controlled the temporal distribution of responses, rather than the overall rate of response. The data indicate that the differential-reinforcement-of-low-rate schedule generates several response categories that are controlled in different ways by wavelength and time-correlated stimuli, and that averaging responses regardless of interresponse-time length obscures this control.     

Rate of response as a visual social stimulus

In Exp. 1, a high rate of responding (chain pulling) of a stimulus monkey was established as a visual positive discriminative stimulus for the operant behavior (bar pressing) of an observer monkey. The terminal performance of the observer under conditions in which a high rate of response of the stimulus monkey alternated in a variable temporal arrangement with a zero rate of response of the stimulus monkey (negative discriminative stimulus) was essentially the same as when nonbehavioral stimuli are correlated with the availability of reinforcement. By manipulating the schedule of reinforcement to change the rate of responding of the stimulus subject without changing its rate of reinforcement, Exp. 2 showed that the effective behavioral stimulus for the observer was the rate of chain pulling by the stimulus subject. A novel intermediate rate of responding by the stimulus monkey resulted in an intermediate rate (generalization) on the part of the observer during an extinction test. These experiments demonstrated that the rate of responding of one organism can function as a discriminative stimulus to control the rate of responding of another organism; and that the rate of responding is similar to other physical stimuli in terms of discrimination and generalization.     

General attentiveness effects of discriminative training

Using a design that permitted the simultaneous assessment of intra-, inter-, and extradimensional effects of discriminative training, the generality of discriminative effects that have been said to reflect increases in “general attentiveness” was assessed. Pigeons received either discriminative training with two stimuli correlated with reinforcement and one stimulus correlated with nonreinforcement, or nondifferential reinforcement (control) training. One positive stimulus was part of an intradimensional task and the other was not. After training, generalization tests were conducted to assess stimulus control along several dimensions. Discriminative training resulted in increased control along dimensions of the positive stimulus involved in the intradimensional task, but not along any dimensions of the other positive stimulus. The results suggested that discriminative training leads to increases in attention that are neither so general as suggested by the “general attentiveness” view nor so specific as to be revealed solely by intradimensional effects.     

Stimulus dimensions or stimulus aspects

Summary The questionableness of geometric models of stimulus similarity has led to the development of an alternative approach by Tversky which makes no dimensional or metric assumptions. Rather, stimuli are described as sets of qualitative stimulus aspects and stimulus similarity as a function of common and non-common aspects. According to Restle's model of stimulus similarity, however, the perception of stimuli of a categorial nature can be organized along dimensions because stimulus aspects form dimensions under certain conditions. The present study supports the empirical validity of this assumption. Further it is suggested that contrary to the present opinion quantitative stimulus characteristics are probably not perceived as dimensions in the sense of the geometric models but only dimensions as described in the Restle model.     

Stimulus generalization following extra-dimensional training in educationally subnormal (severely) children.

The use of discrimination learning paradigms in the study of attentional transfer is discussed. The technique of go/no-go discrimination learning followed by stimulus generalization testing is contrasted with the more familiar simultaneous learning paradigm followed by a shift in the relevant cues. In the former paradigm the effect of training a discrimination on one dimension on the slope of the stimulus generalization gradient on an independent gradient dimension (extra-dimensional training) is assessed. A steepening of the gradient relative to appropriate control procedures is taken as evidence of positive attentional transfer. The relevance of the technique to the detailed study of attentional transfer in educationally subnormal (severely) (ESN(S)) children is considered. In Expt. I nine ESN(S) children were trained in a go/no-go discrimination involving stimuli differing in orientation, and were generalization tested on a dimension that was orthogonal, namely hue. Of the six subjects who learnt the discrimination five showed clear decremental gradients on the hue dimension. In contrast a Pseudo-Discrimination group (PD) of eight subjects matched to those in the TD group showed no gradients. These subjects were not trained in the orientation discrimination, but were reinforced for responding on 50 per cent of each of the S+ and S- stimulus presentations. They thus received equal exposure to, but no differential training on, the orientation dimension. An S+ only group of four subjects who received no exposure to the orientation stimuli showed no gradients when stimulus generalization testing on the hue continuum was carried out. The result is discussed in terms of transfer deriving from stimulus control by relational aspects of the stimuli; in terms of control by constant irrelevant stimuli; and in terms of the study of stimulus control in ESN(S) children. In Expt. II the influence of the codability of the colours on the location of the peak of the stimulus generalization gradients in the TD group is investigated.     

Limits on the generalizability of context-driven control

Context-driven control refers to the fast and flexible weighting of stimulus dimensions that may be applied at the onset of a stimulus. Evidence for context-driven control comes from interference tasks in which participants encounter a high proportion of incongruent trials at one location and a high proportion of congruent trials at another location. Since the size of the congruency effect varies as a function of location, this suggests that stimulus dimensions are weighted differently based on the context in which they appear. However, manipulations of condition proportion are often confounded by variations in the frequency with which particular stimuli are encountered. To date, there is limited evidence for the context-driven control in the absence of stimulus frequency confounds. In the current paper, we attempt to replicate and extend one such finding [Crump, M. J. C., & Milliken, B. (2009). The flexibility of context-specific control: Evidence for context-driven generalization of item-specific control settings. The Quarterly Journal of Experimental Psychology, 62, 1523–1532]. Across three experiments we fail to find evidence for context-driven control in the absence of stimulus frequency confounds. Based on these results, we argue that consistency in the informativeness of the irrelevant dimension may be required for context-driven control to emerge.     

Stimulus–response correspondence effect as a function of temporal overlap between relevant and irrelevant information processing

The stimulus–response correspondence (SRC) effect refers to advantages in performance when stimulus and response correspond in dimensions or features, even if the common features are irrelevant to the task. Previous research indicated that the SRC effect depends on the temporal course of stimulus information processing. The current study investigated how the temporal overlap between relevant and irrelevant stimulus processing influences the SRC effect. In this experiment, the irrelevant stimulus (a previously associated tone) preceded the relevant stimulus (a coloured rectangle). The irrelevant and relevant stimuli onset asynchrony was varied to manipulate the temporal overlap between the irrelevant and relevant stimuli processing. Results indicated that the SRC effect size varied as a quadratic function of the temporal overlap between the relevant stimulus and irrelevant stimulus. This finding extends previous experimental observations that the SRC effect size varies in an increasing or decreasing function with reaction time. The current study demonstrated a quadratic function between effect size and the temporal overlap.     

Multidimensional Fechnerian Scaling: Perceptual Separability

A new definition of the perceptual separability of stimulus dimensions is given in terms of discrimination probabilities. Omitting technical details, stimulus dimensions are considered separable if the following two conditions are met: (a) the probability of discriminating two sufficiently close stimuli is computable from the probabilities with which one discriminates the projections of these stimuli on the coordinate axes; (b) the psychometric differential for discriminating two sufficiently close stimuli that differ in one coordinate only does not depend on the value of their matched coordinates (the psychometric differential is the difference between the probability of discriminating a comparison stimulus from a reference stimulus and the probability with which the reference is discriminated from itself). Thus defined perceptual separability is analyzed within the framework of the regular variation version of multidimensional Fechnerian scaling. The result of this analysis is that the Fechnerian metric of a stimulus space with perceptually separable dimensions has the structure of a Minkowski power metric with respect to these dimensions. The exponent of this metric equals the psychometric order of the stimulus space, or 1, whichever is greater.     

Facilitatory spatial interaction with percutaneous electrical stimuli

To measure the effect of a rectangular percutaneous conditioning shock to one finger on subjective magnitude of a suprathreshold test shock to an adjacent finger, Ss equated a contralateral matching stimulus to the test shock. The conditioning shock generally increased the apparent intensity of the test shock. This facilitation was a negatively accelerated function of test-shock current. Larger conditioning stimuli produced greater facilitation. Over limited intervals, time between conditioning and test or test and matching stimuli had no systematic effects.     

ASSESSING STIMULUS CONTROL IN NATURAL SETTINGS: AN ANALYSIS OF STIMULI THAT ACQUIRE CONTROL DURING TRAINING

When a learner is taught a new response, the stimuli that influence its display are often unknown. The presence or absence of these stimuli alters the probability of occurrence of the response. By identifying the stimuli influencing the probability of newly acquired responses, interventionists may program for their generalization more effectively and efficiently. This investigation describes the application of an operant methodology to assess functional relationships between responses and specific stimulus variables. Four young adults with moderate mental retardation were taught to include “please” as part of requests they made in school. Four environmental stimuli, present during training, were assessed for the controlling properties they acquired. Each of the four was assessed prior to and after training by presenting it in isolation (i.e., the other three were varied). If the presence of a single stimulus associated with training did not occasion “please,” then pairs of stimuli were probed. The results revealed that single-stimulus probing occasioned responding by only 1 learner; paired-stimulus probing set the occasion for including “please” by 2 others. Control of the 4th learner's responding was lost before training was introduced, because he began including “please” in his requests during baseline. The implications of these results are discussed in terms of analyzing stimulus control and promoting stimulus generalization.     

On Stimulus Generalization and Stimulus Classes

Stimulus generalization has been defined as the spread of effect of reinforcement for responses emitted in the presence of one stimulus to different stimuli presented under extinction conditions. As a result of stimulus generalization, novel stimuli come to exert stimulus control over members of the response class. Studies in the applied behavior analysis literature, however, have reported experimental preparations that included prompting and reinforcement procedures during what were claimed to be stimulus generalization conditions. These studies violated the procedural requirement that stimulus generalization be tested under extinction conditions. Responses that come under the control of a class of stimuli may do so by direct training or by stimulus generalization. It is desirable for organisms to respond in the presence of members of an appropriately constructed stimulus class, but we should understand the mechanism of entry into the class by its members. If inaccurate claims of stimulus generalization are made when training procedures are used in the ostensible generalization conditions, the robustness of the original training procedures will be over estimated. By adhering to the operational requirements of behavioral definitions, we could better understand the power and limits of our educational and training procedures.     

Superordinate categorization via learned stimulus equivalence: quantity of reinforcement, hedonic value, and the nature of the mediator

Three experiments examined superordinate categorization via stimulus equivalence training in pigeons. Experiment 1 established superordinate categories by association with a common number of food pellet reinforcers, plus it established generalization to novel photographic stimuli. Experiment 2 documented generalization of choice responding from stimuli signaling different numbers of food pellets to stimuli signaling different delays to food reinforcement. Experiment 3 indicated that different numbers of food pellets did not substitute as discriminative stimuli for the photographic stimuli with which the food pellets had been paired. The collective results suggest that the effective mediator of superordinate categories that are established via learned stimulus equivalence is not likely to be an accurate representation of the reinforcer, neither is it likely to be a distinctive response that is made to the discriminative stimulus. Motivational or emotional mediation is a more likely account.     

When can non‐commutative statistical inference be Bayesian?

Based on recalling two characteristic features of Bayesian statistical inference in commutative probability theory, a stability property of the inference is pointed out, and it is argued that that stability of the Bayesian statistical inference is an essential property which must be preserved under generalization of Bayesian inference to the non‐commutative case. Mathematical no‐go theorems are recalled then which show that, in general, the stability can not be preserved in non‐commutative context. Two possible interpretations of the impossibility of generalization of Bayesian statistical inference to the non‐commutative case are offered, none of which seems to be completely satisfying.     

The transfer of specific and general consequential functions through simple and conditional equivalence relations

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.     

Attitude formation through exploration: valence asymmetries

The formation of attitudes toward novel objects was examined as a function of exploratory behavior. An initial experiment, in which participants played a computer game that required them to learn which stimuli, when sampled, produced favorable or unfavorable outcomes, demonstrated learning, attitude formation, and generalization to novel objects. The findings also revealed 2 interesting valence asymmetries: a learning asymmetry involving better learning for negatively valenced than positively valenced objects and a generalization asymmetry involving stronger generalization as a function of negative than of positive attitudes. Findings from 4 experiments led to an explanation of the learning asymmetry in terms of information gain being contingent on approach behavior and related the generalization asymmetry to a negativity bias that weighs resemblance to a known negative more heavily than resemblance to a positive.