The Emergence of Stimulus Relations: Human and Computer Learning.

Traditionally, investigations in the area of stimulus equivalence have employed humans as experimental participants. Recently, however, artificial neural network models (often referred to as connectionist models [CMs]) have been developed to simulate performances seen among human participants when training various types of stimulus relations. Two types of neural network models have shown particular promise in recent years. RELNET has demonstrated its capacity to approximate human acquisition of stimulus relations using simulated matching-to-sample (MTS) procedures (e.g., Lyddy & Barnes-Holmes Journal of Speech and Language Pathology and Applied Behavior Analysis, 2, 14-24, 2007). Other newly developed connectionist algorithms train stimulus relations by way of compound stimuli (e.g., Tovar & Chavez The Psychological Record, 62, 747-762, 2012; Vernucio & Debert The Psychological Record, 66, 439-449, 2016). What makes all of these CMs interesting to many behavioral researchers is their apparent ability to simulate the acquisition of diversified stimulus relations as an analogue to human learning; that is, neural networks learn over a series of training epochs such that these models become capable of deriving novel or untrained stimulus relations. With the goal of explaining these quickly evolving approaches to practical and experimental endeavors in behavior analysis, we offer an overview of existing CMs as they apply to behavior-analytic theory and practice. We provide a brief overview of derived stimulus relations as applied to human academic remediation, and we argue that human and simulated human investigations have symbiotic experimental potential. Additionally, we provide a working example of a neural network referred to as emergent virtual analytics (EVA). This model demonstrates a process by which artificial neural networks can be employed by behavior-analytic researchers to understand, simulate, and predict derived stimulus relations made by human participants.

Transformations of mathematical and stimulus functions.

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formula tests. Seven of the 8 participants showed substantial improvement in identifying formula-to-graph relations; however, in the test of novel graph-to-formula relations, participants tended to select equations in their factored form. Next, we manipulated contextual cues in the form of rules regarding mathematical preferences. First, we informed participants that standard forms of equations were preferred over factored forms. In a subsequent test of 10 additional novel graph-to-formula relations, participants shifted their selections to favor equations in their standard form. This preference reversed during 10 more tests when financial reward was made contingent on correct identification of formulas in factored form. Formula preferences and transformation of novel mathematical and stimulus functions are discussed.

A functional analytic approach to computer-interactive mathematics.

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed.

Learning Skinner's Verbal Operants: Comparing an Online Stimulus Equivalence Procedure to an Assigned Reading.

The purpose of the present study was to compare the effects of an online stimulus equivalence procedure to that of an assigned reading when learning Skinner's taxonomy of verbal behavior. Twenty-six graduate students participated via an online learning management system. One group was exposed to an online stimulus equivalence procedure (equivalence group) that was designed to teach relations among the names, antecedents, consequences, and examples of each elementary verbal operant. A comparison group (reading group) read a chapter from a popular textbook. Tests for the emergence of selection-based and topography-based intraverbal responses were then conducted, as were tests for generalization and maintenance. Overall, results suggest that the online equivalence procedure was not significantly more effective in promoting topography-based responses than the assigned reading. However, performance on selection-based tests was enhanced by the online equivalence procedure as was performance on topography-based tests when participants were required to provide operant names in response to consequences or examples. On average, the equivalence group performed at a level that was 10 percentage points (i.e., a full letter grade) above that of the reading group. The viability of the equivalence-based procedure is discussed in relation to the assigned reading.

Using the stimulus equivalence paradigm to teach course material in an undergraduate rehabilitation course.

In 2 experiments, we examined whether the stimulus equivalence instructional paradigm could be used to teach relations among names, definitions, causes, and common treatments for disabilities using a selection-based intraverbal training format. Participants were pre- and posttested on vocal intraverbal relations and were trained using multiple-choice worksheets in which selection-based intraverbal relations were taught and feedback was delivered until mastery. Most participants in Experiment 1 showed the emergence of vocal intraverbal relations, but responding did not generalize to final written intraverbal tests. Participants in Experiment 2 showed the emergence of not only vocal intraverbal relations but also written intraverbal relations on final tests. Results suggest that the stimulus equivalence paradigm can be effectively implemented using a selection-based intraverbal training format, the protocol may be an effective means of emphasizing important concepts in a college course, and emergent skills may generalize to novel response topographies.

Constructing and deriving reciprocal trigonometric relations: a functional analytic approach.

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula-to-graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula-to-graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.