Discussion.qmd

# General Discussion

*Experimental Result Summary*

Across three experiments, we investigated the impact of training variability on learning and extrapolation in a visuomotor function learning task. In Experiment 1, participants in the varied training condition, who experienced a wider range of velocity bands during training, showed lower accuracy at the end of training compared to those in the constant training condition. 

Crucially, during the testing phase, the varied group exhibited significantly larger deviations from the target velocity bands, particularly for the extrapolation bands that were not encountered during training. The varied group also showed less discrimination between velocity bands, as evidenced by shallower slopes when predicting response velocity from target velocity band.

Experiment 2 extended these findings by reversing the order of the training and testing bands. Similar to Experiment 1, the varied group demonstrated poorer performance during both training and testing phases. However, unlike Experiment 1, the varied group did not show a significant difference in discrimination between bands compared to the constant group.

In Experiment 3, we provided only ordinal feedback  during training, in contrast to the continuous feedback provided in the previous experiments. Participants were assigned to both an order condition (original or reverse) and a training condition (constant or varied). The varied condition showed larger deviations at the end of training, consistent with the previous experiments. Interestingly, there was a significant interaction between training condition and band order, with the varied condition showing greater accuracy in the reverse order condition. During testing, the varied group once again exhibited larger deviations, particularly for the extrapolation bands. The reverse order conditions showed smaller deviations compared to the original order conditions. Discrimination between velocity bands was poorer for the varied group in the original order condition, but not in the reverse order condition.

All three of our experiments yielded evidence that varied training conditions produced less learning by the end of training, a pattern consistent with much of the previous research on the influence of training variability [@catalanoDistantTransferCoincident1984a; @wrisbergVariabilityPracticeHypothesis1987; @soderstromLearningPerformanceIntegrative2015]. The sole exception to this pattern was the reverse order condition in Experiment 3, where the varied group was not significantly worse than the constant group. Neither the varied condition trained with the same reverse-order items in Experiment 2, nor the original-order varied condition trained with ordinal feedback in Experiment 3 were able to match the performance of their complementary constant groups by the end of training, suggesting that the relative success of the ordinal-reverse ordered varied group cannot be attributed to item or feedback effects alone. 

Our findings also diverge from the two previous studies to cleanly manipulate the variability of training items in a function learning task [@deloshExtrapolationSineQua1997; @vandamMappingShapeVisuomotor2015], although the varied training condition of @vandamMappingShapeVisuomotor2015 also exhibited less learning, neither of these previous studies observed any difference between training conditions in extrapolation to novel items. Like @deloshExtrapolationSineQua1997 , our participants exhibited above chance extrapolation/discrimination of novel items, however they observed no difference between any of their three training conditions. A noteworthy difference difference between our studies is that @deloshExtrapolationSineQua1997 trained participants with either 8, 20, or 50 unique items (all receiving the same total number of training trials). These larger sets of unique items, combined with the fact that participants achieved near ceiling level performance by the end of training - may have made it more difficult to observe any between-group differences of training variation in their study. @vandamMappingShapeVisuomotor2015 's variability manipulation was more similar to our own, as they trained participants with either 2 or 5 unique items. However, although the mapping between their input stimuli and motor responses was technically linear, the input dimension was more complex than our own, as it was defined by the degree of "spikiness" of the input shape. This entirely arbitrary mapping also would have preculded any sense of a "0" point, which may partially explain why neither of their training conditions were able to extrapolate linearly in the manner observed in the current study or in @deloshExtrapolationSineQua1997.


*Modeling Summary*
EXAM is the best model for both groups, but EXAM does relatively good at accounting for the constant group. May have seemed counterintuitive, if one assumed that multiple, varied, examples were necessary to extract a rule. But, EXAM is not a conventional rule model - it doesn't require explictly abstract of a rule, but rather the rule-based response occurs during retrieval. The constant groups formation of a single, accurate, input-output association, in combination with the usefulness of the zero point, may have been sufficient for EXAM, and the constant group,  to perform well. One concern may have been that the assumption of participants making use of the zero point turned the extrapolation problem into an interpolation problem - however this concern is ameliorated by the consistency of the results across both the original and reverse order conditions. 

*Limitations*

While the present study provides valuable insights into the influence of training variability on visuomotor function learning and extrapolation, there are several limitations that should be flagged. 
First, although the constant training group never had experience from a velocity band closer to the extrapolation bands than the varied group, they always had a three times more trials with the nearest velocity band. Such a difference may be an unavoidable consequence of varied vs. constant design which match the total number of training trials between the two groups. However in order to more carefully tease apart the influence of variability from the influence of frequency/repetition effects, future research could explore alternative designs that maintain the variability manipulation while equating the amount of training on the nearest examples across conditions, such as by increasing the total number of trials for the varied group.
Another limitation is that the testing stage did not include any interpolation items, i.e. the participants tested only from the training bands they experienced during training, or from extrapolation bands. The absence of interpolation testing makes it more difficult to distinguish between the effects of training variability on extrapolation specifically, as opposed to generalization more broadly. Of course, the nature of the constant training condition makes interpolation teseting impossible to implement, however future studies might compare a training regimes that each include at least 2 distinct items, but still differ in total amount of variability experienced, which would then allow groups to be compared in terms of both interpolation and extrapolation testing. 
Finally, the task employed in the present study consisted of only a linear, positive function. Previous work in human function learning has repeatedly shown that such functions are among the easiest to learn, but that humans are nonetheless capable of learning negative, non-linear, or discontinuous functions [@deloshExtrapolationSineQua1997; @mcdanielPredictingTransferPerformance2009; @kalishLearningExtrapolatingPeriodic2013; @busemeyerLearningFunctionalRelations1997]. It thus remains an open question as to whether the influence of training variability might interact with various components of the to-be-learned function.