Symmetry

The direction reverses

Suppose training establishes that abstract symbol A goes with spoken label B. A symmetry probe presents B as the sample and asks the person to select A without direct B-to-A teaching.

The reverse relation depends on what was taught. If both A-to-B and B-to-A were trained, later B-to-A performance is retention rather than initial symmetry evidence.

Symmetry is not physical mirror symmetry

The term concerns reversal of a learned relation, not whether shapes look balanced or mirrored. A picture and spoken word can participate despite having different sensory forms.

State the sample, comparisons, modality, and response. “The stimuli were symmetrical” is too vague to identify the tested performance.

Compare the other equivalence properties

Reflexivity is untrained identity matching, such as A=A. Transitivity is the emergence of A=C after A=B and B=C training. Symmetry reverses one trained relation.

An equivalence class is commonly evaluated through these properties or combined tests. Passing symmetry on one pair does not prove reflexivity or transitivity.

Document training before probing

List every trained relation, direction, stimulus, trial type, prompt, feedback rule, and mastery criterion. Record prior familiarity with the materials.

The derived-relations literature emphasizes untrained matching emerging from a smaller trained network. Hidden prior teaching weakens that inference.

A fictional symmetry test

Luis learns four picture-to-spoken-name relations to criterion. The reverse spoken-name-to-picture relations never receive direct teaching. Each reverse relation appears three times among four comparison positions.

Luis selects correctly in 10 of 12 unreinforced symmetry probes. Relation-level results are 3/3, 3/3, 2/3, and 2/3. Report those counts rather than only 83.3%.

The result supports symmetry under this arrangement. It does not show why the relations emerged or guarantee performance with new modalities.

Keep probe trials from becoming training

Corrective feedback, differential reinforcement, or repeated exposure can teach the reverse relation. Predefine the initial probe block and use an appropriate nondifferential consequence arrangement.

If teaching follows a failed probe, label later trials as post-teaching. Do not pool them with first-exposure probes.

Control comparison position and instructor cues

Balance correct positions and vary trial order. Match irrelevant properties such as size, wear, and brightness across comparisons.

Use neutral presentation and sample procedural integrity. An instructor's gaze or consistent handling can guide selection without the intended relation.

Establish access and task understanding

Confirm that the person can perceive the stimuli, scan the array, use the response method, and complete the general matching procedure. Provide needed AAC, motor, sensory, and language access.

Practice trials can establish the format using separate stimuli. They should not expose the reverse relations reserved for testing.

Evidence and debate remain active

A historical review called The Search for Symmetry summarizes varied findings and theoretical accounts. Performance depends on species, language history, task, procedure, and other variables.

The BACB Test Content Outline broadly covers emergent relations and generative performance. It does not prescribe a symmetry assessment or resolve theoretical debates.

Connect the probe to a useful question

Symmetry may help study bidirectional vocabulary, symbol-referent relations, or generative learning. A matching result alone does not establish functional communication or academic performance.

Measure use in ordinary contexts, maintenance, generalization, burden, and the person's view separately. Select goals because they matter, not because a relation is technically interesting.

Build the relation map before assessment

Create a square matrix with every stimulus as both a sample row and comparison column. Mark each cell as directly trained, practice-only, reserved symmetry probe, reserved transitivity probe, reserved equivalence probe, or outside scope. Add dates and exposure counts.

This map prevents the reverse direction from being taught accidentally during baseline repair. It also makes relation-level reporting straightforward. If one A-B pair was trained in both directions, remove its B-A cell from the initial-symmetry denominator and explain why.

Interpret chance and mastery cautiously

The number of comparison options changes chance performance. Four correct responses in four two-choice trials and four in four five-choice trials have different chance contexts, while both remain small samples. Predefine the criterion using the task, purpose, and error cost. Report exact counts and comparison-array size so readers can evaluate the pattern.

Repeat with another novel set when the question concerns generalized symmetry. A second set reduces dependence on one stimulus collection, though it still cannot establish every possible relation or setting.

Preserve incomplete probe blocks and explain every exclusion.