Figure 1. Total implicit learning is shaped by competition with explicit strategy.

(A). Schematic of visuomotor rotation. Participants move from start to target. Hand path is composed of explicit (aim) and implicit corrections. Cursor path is perturbed by rotation. We explored two hypotheses: prediction error (H1, aim vs. cursor) vs. target error (H2, target vs. cursor) drives implicit learning. (B) Prediction error hypothesis predicts that enhancing aiming (dashed magenta) will not change implicit learning (black vs. dashed cyan) according to the independence equation. Target error hypothesis predicts that enhancing aiming (dashed magenta) will decrease implicit adaptation (black vs. dashed cyan). (C) Data reported by Neville and Cressman, 2018. Participants were exposed to either a 20°, 40°, or 60° rotation. Learning curves are shown. The “no aiming” inset shows implicit learning measured via exclusion trials at the end of adaptation. Explicit strategy was calculated as the voluntary reduction in reach angle during the no aiming period. (D) Implicit learning measured during no aiming period in Neville and Cressman yielded a ‘saturation’ phenotype. (E) Explicit strategies calculated in Neville & Cressman dataset by subtracting exclusion trial reach angles from the total adapted reach angle. (F) The implicit learning driving force in the competition theory: difference between rotation and explicit learning in Neville and Cressman. (G) Implicit learning predicted by the competition and independence models in Neville and Cressman. Models were fit assuming that the implicit learning gain was identical across rotation sizes. (H) Experiment 1. Subjects in the stepwise group (n = 37) experienced a 60° rotation gradually in four steps: 15°, 30°, 45°, and 60°. Implicit learning was measured via exclusion trials (points) twice in each rotation period (gray ‘no aiming’). (I) Total implicit learning calculated during each rotation period in the stepwise group yielded a ‘scaling’ phenotype. (J) Explicit strategies were calculated in the stepwise group by subtracting exclusion trial reach angles from the total adapted reach angle. (K) The implicit learning driving force in the competition theory: difference between rotation and explicit learning in the stepwise group. (L) Implicit learning predicted by the competition and independence models in the stepwise group. Models were fit assuming that implicit learning gain was constant across rotation size. (M) Data reported by Tsay et al., 2021a. Participants were exposed to either a 15°, 30°, 60°, or 90° rotation. Learning curves are shown. The “no aiming” inset shows implicit learning measured via exclusion trials at the end of adaptation. (N) Implicit learning measured during no aiming period in Tsay et al. yielded a ‘non-monotonic’ phenotype. (O) Explicit strategies calculated in Tsay et al. dataset by subtracting exclusion trial reach angles from the total adapted reach angle. (P) Implicit learning driving force in the competition theory: difference between rotation and explicit learning in Tsay et al. (Q) Total implicit learning predicted by the competition and independence models in Tsay et al. Models were fit assuming that the implicit learning gain was identical across rotation sizes. Error bars show mean ± SEM, except in the independence predictions in G, L, and Q; independence predictions show mean and standard deviation across 10,000 bootstrapped samples. Points in H, J, M, and O show individual participants.

Figure 1—figure supplement 1. Implicit learning can exhibit various phenotypes in the competition theory.

Here we consider how implicit learning can respond to changes in rotation size in the competition theory. (A) Total implicit learning in the competition theory is altered by explicit strategy. We show three cases: (1) strategy increases at the same rate as rotation size (‘same’, gain = 1), (2) strategy increases more slowly than rotation size (‘slower’, gain <1), (3) strategy increases faster than rotation size (‘faster’, gain >1). Gain here is equal to each line’s slope (it is not dependent on the intercept, which is non-zero). (B) In the competition theory, the driving input to the implicit system is the error (i.e. difference) between the rotation and steady-state explicit strategy. Thus, when explicit strategy and rotation size grow by the same amount (‘same’), the implicit driving force remains constant. When explicit strategy grows more than the rotation (“faster”), the implicit driving force decreases as the rotation gets larger. When explicit strategy grows less than the rotation (“slower”), the implicit driving force increases as the rotation gets larger. (C) In the competition theory (equation at top), implicit learning is proportional to the implicit driving forces depicted in B. The proportionality constant, p_i, depends on implicit error sensitivity and retention (see Equation 4). Thus, in the ‘same’ scenario in A and B, implicit learning will remain the same across rotation sizes. In the ‘slower’ scenario in A and B, implicit learning will increase with the rotation. In the ‘faster’ scenario in A and B, implicit learning with decrease as the rotation increases.

Figure 1—figure supplement 2. Variations between total learning and implicit learning are consistent with the competition model.

In Figure 1, we evaluate how well the competition equations matches data across three distinct implicit learning phenotypes: saturation, scaling, and non-monotonic responses. These three implicit learning phenotypes are shown again here (data, black bars; each group from left to right shows a different phenotype). The competition model is intuitively stated as a relationship between implicit learning and explicit strategy. This equation is denoted in blue: ‘competition model 1’. Blue bars show how much implicit learning was predicted in each experiment, using explicit strategy and ‘competition model 1’ (‘model-1’ under each set of bars). The competition model can be stated another way. Noting that total adaptation is equal to the sum of implicit and explicit learning, we can replace explicit learning in ‘competition model 1’, with total adaptation minus implicit learning. Algebraic simplification yields ‘competition model 2’, shown in gray. This is an equivalent competition model, only this time, it is stated as a relationship between implicit learning and total adaptation (which were measured on separate trials). The gray bars (‘model-2’) show how much implicit learning was predicted by ‘competition model 2’, using measured total adaptation. Competition models 1 (implicit predicted using explicit) and 2 (implicit predicted using total adaptation) yielded nearly identical predictions. More detail on these comparisons is provided in Appendix 3.

Figure 1—figure supplement 3. Scaling, saturation, and non-monotonic phenotypes across the implicit learning timecourse.

(A) A ‘base’ simulation where implicit and explicit systems adapt to target error. A response to a 30° rotation is shown. This response matches the gray bars in B and C. Note the vertical lines. These indicate moments in time where the implicit and explicit responses were calculated in B and C: from left to right, 5, 10, 20, 40, and 150 rotation cycles. Also note the red dashed ‘approximated implicit’ line. This shows the implicit approximation detailed in Appendix 1.1, where x_e is replaced with the average explicit strategy up until that cycle number. In B and C we show implicit and explicit responses measured at each vertical bar in A. Left to right shows the early-to-late evolution of each adaptive process. (B) shows implicit learning. (C) shows explicit learning. Green, blue, and purple bars correspond to a 45° rotation response. In addition to changing the rotation magnitude, explicit error sensitivity was also modulated to create the scaling, saturation, and nonmonotonic implicit learning modes. In green, b_e remained at 0.15 (the same as the gray ‘base’ simulation). In blue, b_e was increased to 0.435. In purple, b_e was increased dramatically to 0.93. The scale, saturate, and nonmonotonic phenotypes can be seen at all timepoints in B.

Figure 1—figure supplement 4. Changes in implicit learning across blocks.

(A) Implicit learning measured during each block in the stepwise group in Exp. 1. (B) Implicit learning measured during each block in the abrupt group in Exp. 1. (C) Implicit learning measured in a stepwise condition in Salomonczyk et al., 2011. (D) Implicit learning measured in a 30° group over three learning blocks in Salomonczyk et al., 2011. (E) Implicit learning measured in a 20° group over three learning blocks in Neville and Cressman, 2018. (F) Same as E, but for a 40° group.