We present the beginnings of a model of the human capacity to learn abstract invariants, such as square. The model is founded on four primary assumptions, which we believe to be neurally plausible and generic: Metric space, Topology, Comparison operations (subtraction, greater-than/less-than), and Extraction of vertices. The model successfully learns to discriminate simple planar quadrilaterals, and generalizes that learning across variations in viewpoint and modest variations in shape.

Adaptive generation of spacing intervals in learning usingresponse times improves learning relative to both adaptivesystems that do not use response times and fixed spacingschemes (Mettler, Massey & Kellman, 2016). Studies haveoften used limited presentations (e.g., 4) of each learningitem. Does adaptive practice benefit learning if items arepresented until attainment of objective mastery criteria? Doesit matter if mastered items drop out of the active learning set? We compared adaptive and non-adaptive spacing underconditions of mastery and dropout. Experiment 1 comparedrandom presentation order with no dropout to adaptivespacing and mastery using the ARTS (AdaptiveResponse-time-based Sequencing) system. Adaptive spacingproduced better retention than random presentation.Experiment 2 showed clear learning advantages for adaptivespacing compared to random schedules that also includeddropout. Adaptive spacing performs better than randomschedules of practice, including when learning proceeds tomastery and items drop out when mastered.

Recent work suggests that optimal spacing in learningrequires adaptive procedures (Mettler, Massey & Kellman,2016). Here, we studied how adaptive techniques might befurther enhanced by combining active and passive learningmodes. Participants learned geography facts that werescheduled using the ARTS (Adaptive Reaction-Time-basedScheduling) system under four conditions involving passiveand/or active trials. Conditions included: a) Passive Onlypresentations of learning items, b) Passive Initial Blocksfollowed by active adaptive scheduling, c) Passive InitialItems followed by active adaptive scheduling for each itemintroduced, or d) Active Only learning with no passivepresentations. We found an advantage for combinations ofactive and passive presentation (by blocks or items) overPassive Only or Active Only presentation. Passive trialspresented in blocks at the beginning of learning showed bestperformance. We discuss possible explanations for thesedifferences and suggest principles underlying optimalcombinations of active and passive modes in adaptivelearning.

Adaptive learning systems that generate spacing intervalsbased on learner performance enhance learning efficiency andretention (Mettler, Massey & Kellman, 2016). Recentresearch in factual learning suggests that initial blocks ofpassive trials, where learners observe correct answers withoutovertly responding, produce greater learning than passive oractive trials alone (Mettler, Massey, Burke, Garrigan &Kellman, 2018). Here we tested whether this passive + activeadvantage generalizes beyond factual learning to perceptuallearning. Participants studied and classified images ofbutterfly genera using either: 1) Passive Only presentations,2) Passive Initial Blocks followed by active, adaptivescheduling, 3) Passive Initial Category Exemplar followed byactive, adaptive scheduling, or 4) Active Only learning. Wefound an advantage for combinations of active and passivepresentations over Passive Only or Active Only presentations.Passive trials presented in initial blocks showed the bestperformance, paralleling earlier findings in factual learning.Combining active and passive learning produces greaterlearning gains than either alone, and these effects occur fordiverse forms of learning, including perceptual learning.