On the effectiveness of including meaningful pictures in the formation of equivalence classes

Relating in the Wild: Toward an Analysis of Equivalence Relations Under More Naturalistic Conditions

Since the first proposal 50 years ago, numerous experiments have documented how arbitrarily related stimuli can become functionally interchangeable. These studies have sought to understand how different variables can moderate the probability of equivalence class formation. However, the well-established evidence regarding this phenomenon in experimental settings does not necessarily guarantee an understanding about how equivalence relations are produced in natural settings. In typical experiments, experimenters control critical variables to produce equivalence relations, such as, the requirement of proficiency with baseline relations, the number of opportunities to relate two or more stimuli, the efforts to promote stimulus control topography coherent with the experimenter-defined relations, etc. All these variables, however, are not controlled in our daily lives. The present article elucidates how some differences between experimental and natural settings can likely affect how the phenomenon of equivalence relations can occur in noncontrolled, naturalistic environments. Furthermore, we suggest new areas of research to promote the generalization of basic experimental data to contingencies in our daily lives.

A mediational theory of equivalence relations and transformation of function

In this article, we describe a mediational theory of emergent or derived relations resulting from matching-to-sample procedures that produce equivalence and transformation of function. According to a mediational theory, behaviors that occur at the time of reinforcement mediate subsequent behavioral relations referred to as "derived" or "emergent." Such relations have been documented for decades in studies using mostly matching-to-sample procedures with humans and nonhumans. In both verbal human and nonhuman participants, the mediating behaviors consist of differential responding to the sample stimulus. In humans, such behaviors are mostly, but not necessarily, verbal; in nonhumans they include a variety of sample-specific responses, sometimes called "coding." The proposed mediational theory, based only on the four-term contingency and the basic principles of operant learning, makes specific predictions and explains results from a broad range of experiments. There are at least three important implications of a mediational theory. First, if by "derived" or "emergent" one means untrained or unreinforced, then derived relations may not exist. Second, if there are no derived relations, then theories of such relations may not be necessary. Third, a mediational theory of relational responding has potentially important implications for clinical practice.

The effects of a training package to teach note taking on the formation of equivalence classes

Effective note taking may enhance learning outcomes for students and serve as a directly observable form of mediation within a test context. Frampton et al. (2023) used stimulus fading to teach note taking in the form of a graphic organizer (GO) during matching-to-sample baseline relations training (MTS-BRT). Moderately high yields were observed with young adults despite the use of linear series training, abstract stimuli, and five-member classes. The present study taught the same note taking strategy using an intervention package including video illustration, voice-over instructions, and feedback to eight college students. Participants were taught to construct the GO during MTS-BRT with three three-member classes of familiar stimuli. Then the effects of MTS-BRT alone with three five-member classes of abstract stimuli was evaluated. Participants efficiently completed training with familiar stimuli and passed the posttest on the first attempt. With the abstract stimuli, participants engaged in GO construction during MTS-BRT and the six participants that demonstrated high levels of fidelity to the trained note taking strategy passed the posttest on the first attempt. These results replicate findings from Frampton et al. while using a more efficient intervention package. Benefits of teaching overt mediation responses are discussed as well as future directions for translation to applied contexts.

More complex incidental bidirectional naming results from exposure alone

Incidental bidirectional naming (Inc-BiN) has been defined as a verbal developmental cusp whereby children demonstrate learning the names of things as listener and speaker as a function of observation alone. Stimulus characteristics have been found to affect performance in tests for Inc-BiN. To further explore this effect, Experiment 1 compared untaught listener and speaker responses for novel familiar-type versus novel nonfamiliar-type stimuli with 20 first-grade students following naming experiences in which the participants observed each visual stimulus five times while hearing its name. Participants performed significantly better with familiar-type than with nonfamiliar-type stimuli. Experiment 2 examined the effects of a repeated-probe intervention to induce Inc-BiN with nonfamiliar-type stimuli. Participants were six first-grade students who demonstrated incidental unidirectional naming (i.e., acquired names as listener from exposure alone). Implementation of the intervention was staggered across dyads of participants in a multiple-probe, simultaneous-treatments design. One participant in each dyad received the intervention with nonfamiliar-type stimuli only and the other with both nonfamiliar- and familiar-type stimuli. Pre- and postintervention Inc-BiN probes with stimuli not included in the intervention suggested both conditions were effective in establishing Inc-BiN for nonfamiliar-type stimuli. These findings have implications for understanding the mechanisms underlying Inc-BiN.

Computational models of stimulus equivalence: An intersection for the study of symbolic behavior

Stimulus equivalence is a central paradigm in the analysis of symbolic behavior, language, and cognition. It describes emergent relations between stimuli that were not explicitly trained and cannot be explained by primary stimulus generalization. In recent years, researchers have developed computational models to simulate the learning of equivalence relations. These models have been used to address primary theoretical and methodological issues in this field, such as exploring the underlying mechanisms that explain emergent equivalence relations and analyzing the effects of training and testing protocols on equivalence outcomes. Nonetheless, although these models build upon general learning principles, their operation is usually obscure for nonmodelers, and in the field of stimulus equivalence computational models have been developed with a variety of approaches, architectures, and algorithms that make it difficult to understand the scope and contributions of these tools. In this paper, we present the state of the art in computational modeling of stimulus equivalence. We seek to provide concise and accessible descriptions of the models' functioning and operation, highlight their main theoretical and methodological contributions, identify the existing software available for researchers to run experiments, and suggest future directions in the emergent field of computational modeling of stimulus equivalence.

Reexamining nodality in equivalence classes

Equivalence classes are defined according to the substitutability, or functional similarity, of the stimuli within a stimulus class. Several studies have demonstrated that the degree of functional similarity between stimuli in a class is dependent, in part, upon the number of nodes (intervening stimuli) between the stimuli. Higher nodal number is related to lower functional similarity. This effect is referred to as "nodality." There are three key factors that have not been simultaneously controlled for in the relevant studies: priming effects, reinforcement during training, and multiple stimulus functions of stimuli (sample, comparison, or both). In the present experiment, controlling for these factors, two 6-member, 4-node equivalence classes were established, and a within-class preference assessment was used to evaluate nodality. Of 12 participants, five achieved criterion accuracy (90%) during testing. These participants demonstrated nodality, showing preference for stimuli that were nodally proximal to a sample in the preference test. When distal comparisons were chosen, participants took longer, on average, to make the selection compared to selections of proximal stimuli. These findings are consistent with earlier studies demonstrating nodality, which suggests that nodality is a robust phenomenon and not an artifact of the factors that were controlled for in the present study.

Merger and expansion of equivalence classes via meaningful stimuli

The present experiments evaluated the effect of meaningful stimuli on the inclusion of a set of extra-experimental meaningful pictures into equivalence classes using within- and between-subjects designs. There were 35 adult participants in total (N_EXP1 = 22; N_EXP2 = 13). In both experiments, participants were first trained on 6 baseline relations with abstract stimuli (A, B, and C) and assessed on the emergence of three 3-member equivalence classes. Next, they were trained on DA relations and assessed on the inclusion of the D stimuli and a set of meaningful pictures in the equivalence classes. In Experiment 1, D1 and D2 were meaningful written words and D3 was a written pseudoword. In Experiment 2, for 2 groups, D1, D2, and D3 were meaningful words; for another group, D1, D2, and D3 were pseudowords. In both experiments, participants formed the ABC classes and included the D stimuli in the classes. When D was a meaningful word, participants also included a set of pictures potentially related to the word in the ABC class established experimentally. The results have implications for the definition of meaningfulness and contribute to discussions on the impact of test arrangements on emergent responding.

Effects of Limited Hold on Equivalence Class Formation

In an attempt to limit the opportunity to engage in mediating behavior, two groups of adult participants received preliminary training in identity matching with limited hold levels (LH) for responding of 0.7 s for the sample and 1.2 s for the comparisons. The two groups were subsequently trained to form three 5-member classes, using the same LH levels, where the A, B, D, and E stimuli were abstract stimuli, and the C stimuli were meaningful pictures. In two tests for emergent relations, the LH for Group Short was unchanged, whereas 5 s were added to the LH for the comparisons for Group Long. None of the participants in Group Short responded in accordance with stimulus equivalence in either of the two tests. In Group Long, one participant responded in accordance with stimulus equivalence in the first test, and an additional eight participants formed equivalence classes in the second test.

A descriptive analysis of baseline and equivalence-class performances under many-to-one and one-to-many structures

The purpose of the present experiment was to describe responding as a function of One-to-Many (OTM) and Many-to-One (MTO) training structures and identify baseline performances correlated with the accuracy level in tests for equivalence class formation. Participants were 42 adults assigned to either the MTO or the OTM groups, trained on 24 baseline relations, and assessed on the emergence of three 9-member equivalence classes. Participants in the MTO group presented similar frequencies of responses to each of the comparisons throughout baseline training. Also, the number of trials required to meet the baseline mastery criterion was negatively correlated with test accuracy. Participants in the OTM group presented more variable frequencies of responses to each of the comparisons (participants tended to select some of the comparisons less often than others at the beginning of the training). In addition, the number of reinforced responses to the node presented as a sample during training was positively correlated with the number of correct responses during testing for the OTM group. The experiment contributed to an in-depth stimulus control analysis of baseline and test performances, and its results have implications for understanding potential sources of variability between the training structures.

Enhanced Equivalence Projective Simulation: A Framework for Modeling Formation of Stimulus Equivalence Classes

Formation of stimulus equivalence classes has been recently modeled through equivalence projective simulation (EPS), a modified version of a projective simulation (PS) learning agent. PS is endowed with an episodic memory that resembles the internal representation in the brain and the concept of cognitive maps. PS flexibility and interpretability enable the EPS model and, consequently the model we explore in this letter, to simulate a broad range of behaviors in matching-to-sample experiments. The episodic memory, the basis for agent decision making, is formed during the training phase. Derived relations in the EPS model that are not trained directly but can be established via the network's connections are computed on demand during the test phase trials by likelihood reasoning. In this letter, we investigate the formation of derived relations in the EPS model using network enhancement (NE), an iterative diffusion process, that yields an offline approach to the agent decision making at the testing phase. The NE process is applied after the training phase to denoise the memory network so that derived relations are formed in the memory network and retrieved during the testing phase. During the NE phase, indirect relations are enhanced, and the structure of episodic memory changes. This approach can also be interpreted as the agent's replay after the training phase, which is in line with recent findings in behavioral and neuroscience studies. In comparison with EPS, our model is able to model the formation of derived relations and other features such as the nodal effect in a more intrinsic manner. Decision making in the test phase is not an ad hoc computational method, but rather a retrieval and update process of the cached relations from the memory network based on the test trial. In order to study the role of parameters on agent performance, the proposed model is simulated and the results discussed through various experimental settings.

Using Stimulus-Equivalence Technology to Teach Skills About Nutritional Content

Twenty-two adult participants, assigned to three conditions, were trained nutrition knowledge (i.e., carbohydrate values) for different food items. In a stimulus sorting test, the participants were asked to sort stimuli (names of food items) into one of three different ranges of carbohydrate values ("less than 20", "20–40", "more than 40" gram per 100 gram). Conditional-discrimination training and testing followed the sorting test, and finally, a postclass formation sorting test of the stimuli used in the conditional-discrimination training. The conditional-discrimination training used tailored stimuli, that is, the food items that each of the participants categorized incorrectly in the sorting test. Participants exposed to Conditions 1 and 2 were trained on six conditional discriminations and tested for the formation of three 3-member classes. Conditions 2 and 3 had a “don’t know” option together with the three different ranges of carbohydrate values in the sorting for tailoring the stimuli. Participants exposed to Condition 3 trained were trained on 12 conditional discriminations and tested for the formation of three 5-member classes. The main findings showed that all but one of the participants responded correctly on at least one test for equivalence class formation and sorted the stimuli correctly in the postclass formation sorting test.