SE&AI: Stimulus Equivalence and Artificial Intelligence

The study of derived stimulus relations from a behavior analytic account has enriched the understanding of human language and cognition (Barnes-Holmes et al., 2017). The roots of the experimental and conceptual analysis of derived stimulus relations can be traced back to the work of Murray Sidman on stimulus equivalence (Sidman, 1982). During stimulus equivalence (SE) instruction, a series of conditional discriminations are trained, followed by tests of untrained or derived stimulus–stimulus relations (Albright et al., 2016, p. 291). Equivalence relation training is typically conducted through matching-to-sample (MTS) procedures that expose participants to a series of conditional discriminations among stimuli (Ninness et al., 2017 ).

To meet the definition of an equivalence class formation, one must demonstrate reflexivity, symmetry, and transitivity (Cooper et al., 2020).

  • Reflexivity or generalized identity matching is when a stimulus is matched to itself without training or reinforcement (represented by the mathematical statement A=A). In the example below, this is represented by the relation picture of dog=picture of dog.

  • Symmetry is achieved when the reversibility of a sample stimulus with a comparable stimulus is demonstrated (represented by the mathematical statement if A=B, then B=A). In the example below we have 2 symmetrical relations, the picture of dog=the spoken word “Ike"; the spoken word "Ike" =the written word dog.

  • Transitivity, sometimes referred to as a combined test for equivalence, is achieved (represented by the mathematical statement if A=B, and B=C, then A=C)” (Cooper et al., 2020, p.455). In the example below, this is represented by the relation picture of dog=spoken word “Ike”.

Visual depiction of equivalence relations with the

solid lines indicating trained relations

and dotted lines indicating derived relations.

When transitivity is achieved, the learner is thought to have derived accurate relations “for free” (Stewart et al., 2013). In other words, the learner makes untrained accurate connections between stimuli. An equivalence class is formed if all stimuli in that set are reflexive, symmetrical, and transitive with each other. In the example above, the picture of the dog, the spoken word dog, and the written word dog are now considered a three-member response class. “As a correct response is conditional upon a particular sample in a trial, the term conditional discrimination learning is used to describe the type of learning involved in the MTS” (Johansson, 2020, p. 2).

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Relational frame theory contends that relational responding, such as that seen during tests for stimulus equivalence, is a key process in the verbal behavior of humans as evidenced by learned relational networks, typically involved in complex problem solving (Barnes-Holmes et al., 2017). Why is this exciting? Research findings suggest that SE instruction is an efficient instructional strategy that could produce a number of novel skills with minimal training and is also the basis for behavioral analysis of symbolic behavior (Stromer et al., 1996).

Although generalized identity matching (reflexivity) has been demonstrated with nonhumans, including pigeons, monkeys, dolphins sea lions, and rats (Johannson, 2020), stimulus equivalence has not yet been shown in nonhuman animals. Class formation research participants remain most commonly human, but recently, researchers have started to study the effects of conditional discrimination and the emergence of relational responding with artificial intelligence (AI) (Lyddy & Barnes-Holmes, 2007).

Connectionism is a computational approach to modeling cognition that produces complex behavior by manipulating the interconnection of simple units. Connectionist networks have demonstrated usefulness as models of stimulus equivalence and relational responding (Lyddy & Barnes-Holmes, 2007). RELNET is a computational model that simulates train/ test trials using the MTS procedure, often used in equivalence research. In simulated experiments, after teaching a few strategic conditional discriminations, the RELNET model generated response patterns consistent with relational responses exhibited by human participants (Bansai et al., 2017). In a study by Lyddy & Barnes-Holmes, A=B and B=C relations were trained, and researchers tested whether the relation C=A would emerge (2007). Training and testing phases in computational simulations were analogous to training/ testing in experiments with humans with new emergent relations established during the testing phase. Although the training procedures were not identical, the emergence of derived stimulus relations of equivalence has promising implications for programming advanced simulated language and cognition in AI. In another AI study by Cullinan et al., a computational model was used to track exposure to equivalence relations. After pre-training, their computational network successfully demonstrated equivalence without further training on the critical stimuli (1994). Why is this exciting? Derived relational responding as a generalized operant explains how humans expand verbal capabilities without explicit training for each relation (Stewart et al. 2017). Harnessing SE to train this generalized operant can lead to exponential growth in verbal behavior for AI similar to how verbal learning takes place with humans.

As machine learning scientists continue to build AI that simulates “human” features, a significant focus should continue programming for complex naturalistic language. Preliminary research on stimulus equivalence conditional discrimination training suggests an efficient and effective way to program AI to generate complex language. Perhaps machine learning can also offer behavior scientists a better understanding of symbolic human language and cognition development!


Bansal, T., Neelakantan, A., & McCallum, A. (2017, November 16). RelNet: End-to-End Modeling of Entities & Relations.

Barnes-Holmes, D., Finn, M., McEnteggart, C., & Barnes-Holmes, Y. (2017). Derived Stimulus Relations and Their Role in a Behavior-Analytic Account of Human Language and Cognition. Perspectives on Behavior Science, 41(1), 155–173.

Cooper, J. O., Heron, T. E., & Heward, W. L. (2020). Applied behavior analysis. Hoboken, NJ: Pearson Education Limited.

Cullinan, V., Barnes, D., Hampson, P. J. & Lyddy, F. (1994). A transfer of explicitly and non-explicitly trained sequence responses through equivalence relations: An experimental demonstration and connectionist model. The Psychological Record, 44, 559-586.

Hayes, S. C. (1989). NONHUMANS HAVE NOT YET SHOWN STIMULUS EQUIVALENCE. Journal of the Experimental Analysis of Behavior, 51(3), 385–392.

Johansson, R. (2020, June 14). Scientific progress in AGI from the perspective of contemporary behavioral psychology. DIVA.

Lyddy, F., & Barnes-Holmes, D. (2007). Stimulus equivalence as a function of training protocol in a connectionist network. Journal of Speech and Language Pathology and Applied Behavior Analysis, 1.4–2.1, 14–24.

Ninness, C., Ninness, S. K., Rumph, M., & Lawson, D. (2017). The Emergence of Stimulus Relations: Human and Computer Learning. Perspectives on Behavior Science,

YouTube. (2020, August 22). Scientific progress in AGI - Robert Johansson. YouTube.

Vernucio, R. R., & Debert, P. (2016). Computational Simulation of Equivalence Class Formation Using the go/no-go Procedure with Compound Stimuli. The Psychological Record, 66(3), 439–449.

Sidman, M., & Tailby, W. (1982). Conditional discrimination vs. matching to sample: an expansion of the testing paradigm. Journal of the experimental analysis of behavior, 37(1), 5–22.

Stewart, I., McElwee, J., & Ming, S. (2013). Language Generativity, Response Generalization, and Derived Relational Responding. The Analysis of Verbal Behavior, 29(1), 137–155.

Stromer R, Mackay H.A, Remington B. Naming, the formation of stimulus classes, and applied behavior analysis. Journal of Applied Behavior Analysis. 1996;29:409–431.

Trudy Georgio is a Board Certified Behavior Analyst and Licensed Behavior Analyst in the state of Texas. She is the founder of Tru Behavior Development, LLC who is motivated by effecting socially significant behavior change and disseminating the science of behavior to the next generation of behavior analysts!

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